Optimal Classification Program


Optimal Classification (OC) is a scaling procedure that performs non-parametric unfolding of binary choice data. Given a matrix of binary choices by individuals (for example, Yes or No) over a series of Parliamentary votes, OC produces a configuration of legislators and cutting lines/planes that maximize the correct classification of the choices. It is discussed in detail in:

The geometry of the roll call voting problem upon which Optimal Classification (OC) is based is covered in the first three chapters of my forthcoming book Spatial Models of Parliamentary Voting.


Examples

107th Senate (Detailed Discussion of Input and Output Files)
95th House
Brazilian Legislature 1995-98
California Assembly 1997-98



  1. Example One: The 107th Senate.
  2. To see how Optimal Classification (OC) works, download the program, the "control card" file, and the 107th Senate Roll Call data files below:

    Optimal Classification (OC) Scaling Program Executable (Compiled For WINTEL Machines -- PERFL.EXE)

    Optimal Classification (OC) Scaling Program Source Code (FORTRAN -- PERFL.FOR)

    Control Card File (PERFSTRT.DAT)

    107th Senate Roll Call Data (SEN107KH.ORD)

    and place them in the same folder on a WINTEL machine. PERFSTRT.DAT looks like this:
    
    SEN107KH.ORD
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF 107TH SENATE
        1  633   20   36   10   18   10 0.005
    (36A1,3900I1)
    (I5,1X,36A1,2I5,50F8.3)
    At the command line type

    PERFL

    The program should only take a few seconds to run and it produces three output files -- PERF21.DAT, PERF23.DAT, and PERF25.DAT. PERF21.DAT should look something like this:
    
     07 MAY       2003  14.44.35.31.This line is simply a Time Stamp
     RANDOM NUMBER SEED     90200   Random number generator seed -- it is used to generate
    SEN107KH.ORD                    random vectors to determine size of legislator polytope
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF 107TH SENATE       
        1  633   20   36   10   18   10 0.005
    (36A1,3900I1)         The lines in Blue are PERF21.DAT -- This is just a safety precaution
    (I5,1X,36A1,2I5,50F8.3)                                         
     ******************************************************************************
      1 ROLL CALLS   1    4098   48758  0.08405  0.91595  0.73766
      2 LEGISLATORS  1    4042   48758  0.08290  0.91710  0.74125  0.99765
      3 ROLL CALLS   1    3994   48758  0.08191  0.91809  0.74432
      4 LEGISLATORS  1    3983   48758  0.08169  0.91831  0.74502  0.99934
      5 ROLL CALLS   1    3966   48758  0.08134  0.91866  0.74611
      6 LEGISLATORS  1    3962   48758  0.08126  0.91874  0.74637  0.99666
      7 ROLL CALLS   1    3949   48758  0.08099  0.91901  0.74720
      8 LEGISLATORS  1    3949   48758  0.08099  0.91901  0.74720  0.99983
      9 ROLL CALLS   1    3938   48758  0.08077  0.91923  0.74790
     10 LEGISLATORS  1    3936   48758  0.08073  0.91927  0.74803  0.99986
     11 ROLL CALLS   1    3930   48758  0.08060  0.91940  0.74842
     12 LEGISLATORS  1    3927   48758  0.08054  0.91946  0.74861  0.99988
     13 ROLL CALLS   1    3924   48758  0.08048  0.91952  0.74880
     14 LEGISLATORS  1    3924   48758  0.08048  0.91952  0.74880  0.99999
     15 ROLL CALLS   1    3922   48758  0.08044  0.91956  0.74893
     16 LEGISLATORS  1    3922   48758  0.08044  0.91956  0.74893  1.00000
                          10.58.05.23.
     ELAPSED TIME OF JOB  10.58.07.62.
    The first column after "ROLL CALLS" or "LEGISLATORS" is the number of dimensions, the second column is the number of classification errors, the third is the total number of choices, the fifth is the error proportion, the sixth column reports the correct classification, the seventh is the Aggregate Proportional Reduction in Error (APRE), and the last column is the Spearman correlation between the current legislator estimates and the previous iteration estimates. For the 107th Senate the algorithm quickly converges to 0.91956 (92.0%) in correct classification. APRE is defined as:
    
     APRE = (Total Number of Choices Cast on Minority Side of all Roll Calls -
              Total Classification Error)/(Total Number of Choices Cast on Minority Side of all Roll Calls)
    In One Dimension the file PERF25.DAT contains the output coordinates for the Senators and the roll calls. In one dimension, this is reported as a rank ordering. The first part of the file shows the Senators in rank order, the second part shows them in the order that they appear in the roll call file with their ranking, the third part shows the rank position of the roll call cutpoint in the order that they appear in the roll call file, and the fourth part shows the roll call cutpoints in rank order:
    
     07 MAY       2003  14.44.35.31.
        1 1074910133 0MINNESO 10011WELLSTONE      5  484   0.990   1.000
        2 1074930925 0WISCONS 10001FEINGOLD      86  498   0.827   2.000
        3 1074010412 0NEW JER 10001CORZINE       31  495   0.937   3.000
        4 1071501171 0CALIFOR 10001BOXER         24  481   0.950   4.000
        5 1071423031 0IOWA    10001HARKIN        30  488   0.939   5.000
        6 1074010133 0MINNESO 10001DAYTON        20  486   0.959   6.000
        7 1071502121 0ILLINOI 10001DURBIN        25  496   0.950   7.000
        8 10714213 1 0CONNECT 10001DODD          27  483   0.944   8.000
        9 10710808 3 0MASSACH 10001KENNEDY, ED   23  480   0.952   9.000
       10 1071303952 0MARYLAN 10001SARBANES      11  498   0.978  10.000
       11 10729142 5 0RHODE I 10001REED          20  497   0.960  11.000
                     etc.
                  The column in red is the number of classification errors
                  The column in purple is the total number of choices
                  The column in green is the proportion correctly classified
                  The column in blue is the rank position (tied ranks are allowed)
                     etc.
                     etc.
      100 1071490853 0OKLAHOM 20001NICKLES, DO   25  495   0.949 100.000
      101 1071462849 0TEXAS   20001GRAMM, PHIL   26  480   0.946 101.000
      102 1071410547 0NORTH C 20001HELMS         16  358   0.955 102.000
      103 1071542961 0ARIZONA 20001KYL           21  495   0.958 103.000
     ******************************************************************************
        1 1079991099 0USA     200  BUSH           2   63   0.968  85.000
        2 1074970041 0ALABAMA 20001SESSIONS      52  481   0.892  67.000
        3 1079465941 0ALABAMA 20001SHELBY        54  488   0.889  66.000
        4 1071490781 0ALASKA  20001MURKOWSKI     24  459   0.948  71.000
        5 1071210981 0ALASKA  20001STEVENS       28  452   0.938  63.000
        6 1071542961 0ARIZONA 20001KYL           21  495   0.958 103.000
        7 1071503961 0ARIZONA 20001MCCAIN       125  478   0.738  58.000
        8 1072930642 0ARKANSA 20001HUTCHINSON,   45  484   0.907  68.000
        9 1072930542 0ARKANSA 10001LINCOLN       33  495   0.933  47.000
       10 1071501171 0CALIFOR 10001BOXER         24  481   0.950   4.000
                   etc.
                   etc.
      100 1074930925 0WISCONS 10001FEINGOLD      86  498   0.827   2.000
      101 1071570325 0WISCONS 10001KOHL          35  484   0.928  39.000
      102 1074970668 0WYOMING 20001ENZI          36  483   0.925  95.000
      103 1071563368 0WYOMING 20001THOMAS        23  486   0.953  96.000
     ******************************************************************************
        1    6  76  24  13  0.458 6 1    27.750
        2    8  59  42   5  0.881 6 1    48.500
        3   15  56  44   3  0.932 6 1    46.500
        4   16  34  65  10  0.706 1 6    35.500
        5   17  58  41   7  0.829 6 1    50.500
        6   18  50  49   5  0.898 6 1    52.500
        7   19  55  41   6  0.854 6 1    48.500
        8   20  55  42   9  0.786 6 1    52.500
        9   21  61  37  15  0.595 6 1    36.500
       10   22  53  47   4  0.915 1 6    51.500
                  etc.
                  etc.
     The column in black is a counter from 1 to the number of scaled roll calls
     The column in indigo is the position of the roll call in the input roll call matrix
     The column in red is the number of Yeas
     The column in blue is the number of Nays
     The column in coral is the number of classification errors
     The column in turquoise is the Proportional Reduction in Error:
               [PRE = (number voting in minority - classification errors)/number voting in minority]
     The column in firebrick is the Predicted Choice Below the Midpoint (1 = Yea, 6 = Nay)
     The column in limegreen is the Predicted Choice Above the Midpoint
     The column in navy is the rank position of the roll call midpoint
                  etc.
                  etc.
      490  625  47  52   2  0.957 1 6    49.500
      491  626  69  30   5  0.833 6 1    33.500
      492  627  73  26   7  0.731 6 1    33.500
      493  628  83  16   7  0.562 6 1    14.500
      494  629  91   9   8  0.111 6 1     2.500
      495  630  56  44   5  0.886 6 1    50.500
      496  631  85  12   8  0.333 1 6    94.500
      497  632  87  11   8  0.273 1 6    99.500
      498  633  92   2   2  0.000 1 6   103.000
     ******************************************************************************
      276  344   1  94   1  0.000 1 6     1.000
      109  128  11  88  11  0.000 1 6     1.000
      328  406  17  80  17  0.000 1 6     1.000
      195  223   3  94   3  0.000 1 6     1.000
       71   88  96   3   2  0.333 6 1     1.500
      269  336   1 100   0  1.000 1 6     1.500
      300  371  88  10   8  0.200 6 1     2.500
      494  629  91   9   8  0.111 6 1     2.500
      439  557  94   3   1  0.667 6 1     2.500
      244  300  90   7   4  0.429 6 1     3.500
      488  622  58  36  34  0.056 6 1     3.500
       65   80  94   6   5  0.167 6 1     3.500
      291  360  33  65  30  0.091 1 6     3.500
      174  198  93   6   4  0.333 6 1     4.500
                   etc.
                   etc.
      182  207  42  58   6  0.857 6 1    54.500
      424  532  50  46   0  1.000 1 6    54.500
      394  498  58  35  11  0.686 1 6    54.500
      187  215  55  43   5  0.884 1 6    54.500
      445  567  48  51   5  0.896 6 1    54.500
      170  194  52  45   2  0.956 1 6    54.500
      312  383  39  45   0  1.000 6 1    54.500
       63   78  54  46  11  0.761 6 1    55.500
      183  210  46  52   3  0.935 6 1    55.500
      436  548  55  43   2  0.953 1 6    55.500
      204  232  52  48   3  0.938 1 6    55.500
      450  577  57  42   6  0.857 1 6    55.500
      125  146  55  43   9  0.791 1 6    55.500
      193  221  42  54  12  0.714 1 6    55.500
      181  206  55  45   2  0.956 1 6    55.500
      241  293  56  44   3  0.932 1 6    55.500
      184  211  54  44   1  0.977 1 6    55.500
      256  316  46  54   0  1.000 6 1    56.500
      166  189  51  49  11  0.776 6 1    56.500
      390  494  58  38   8  0.789 1 6    56.500
      191  219  37  59   9  0.757 6 1    56.500
      173  197  43  57   3  0.930 6 1    56.500
      168  191  52  47   3  0.936 1 6    56.500
       19   32  56  43   3  0.930 1 6    57.500
      306  377  54  44   2  0.955 1 6    57.500
      156  179  42  58  10  0.762 6 1    57.500
                   etc.
                   etc.
      147  169  96   1   1  0.000 1 6   103.000
      146  168  97   1   1  0.000 1 6   103.000
      143  164  98   2   2  0.000 1 6   103.000
       79   97  98   1   1  0.000 1 6   103.000
       77   95  95   3   3  0.000 1 6   103.000
       59   74  99   1   1  0.000 1 6   103.000
      498  633  92   2   2  0.000 1 6   103.000
    The file PERF23.DAT has some miscellaneous diagnostics for the program some of which are only needed for de-bugging purposes. Below are portions of the file that may be of interest:
    
    The two lines below show how many roll calls and legislators meet
    the cutoff criteria in PERFSTRT.DAT
     ROLL-CALLS READ=     633  NUMBER REJECTED=     135  NUMBER ACCEPTED=     498  CUTOFF= 0.005
     LEGISLATORS READ= 103  NUMBER REJECTED=   0  NUMBER ACCEPTED= 103  CUTOFF=  10
    This shows the distribution of roll calls by margin
      DISTRIBUTION OF SCALABLE ROLL CALLS
       1 50 - 55     128  0.257
       2 56 - 60      98  0.197
       3 61 - 65      51  0.102
       4 66 - 70      44  0.088
       5 71 - 75      30  0.060
       6 76 - 80      27  0.054
       7 81 - 85      18  0.036
       8 86 - 90      21  0.042
       9 91 - 95      26  0.052
      10 96 - 99.5    55  0.110
    This shows the number of choices on the majority side, the
    total number of choices, and the proportion on the majority side
     AVERAGE MAJORITY MARGIN=    33137   48758  0.67962
                etc.
                etc.
    Below are the eigenvalues of the double-centered agreement
    score matrix (second column).  These can be used to make a Skree Plot and
    are a good check on the dimensionality of the data (see below).
    PERFORMANCE INDEX EIGENVALUE/VECTOR ROUTINE=    1  103    0     0
       1    9.1248   66.8391   66.8391   11.4701   56.3429   56.3429
       2    0.4053    2.9686   69.8078    0.7339    3.6050   59.9479
       3    0.2800    2.0508   71.8585    0.5025    2.4685   62.4164
       4    0.2454    1.7974   73.6559    0.3837    1.8846   64.3011
       5    0.1658    1.2141   74.8700    0.3777    1.8553   66.1564
       6    0.1502    1.1005   75.9705    0.3205    1.5742   67.7306
       7    0.1420    1.0404   77.0109    0.2752    1.3520   69.0825
       8    0.1278    0.9361   77.9471    0.2560    1.2577   70.3402
       9    0.1057    0.7743   78.7214    0.2217    1.0891   71.4293
      10    0.0916    0.6709   79.3923    0.1962    0.9635   72.3928
      11    0.0762    0.5582   79.9505    0.1914    0.9404   73.3332
      12    0.0719    0.5263   80.4768    0.1802    0.8853   74.2186
      13    0.0669    0.4898   80.9666    0.1642    0.8066   75.0251
      14    0.0654    0.4790   81.4456    0.1538    0.7557   75.7808
      15    0.0583    0.4269   81.8725    0.1511    0.7424   76.5233
      16    0.0548    0.4011   82.2736    0.1429    0.7021   77.2254
      17    0.0499    0.3657   82.6393    0.1409    0.6919   77.9173
      18    0.0468    0.3428   82.9821    0.1364    0.6701   78.5874
      19    0.0438    0.3211   83.3032    0.1333    0.6548   79.2422
      20    0.0400    0.2930   83.5962    0.1217    0.5980   79.8402
                  etc.
                  etc.
    The second column with a first entry of 9.1248 are the eigenvalues. These can be used to make a Skree Plot like the one below.



    If you change the number of dimensions from 1 to 2 in PERFSTRT.DAT and run PERFL again (be sure to save the output files from the one-dimensional run first!!!! -- they will be overwritten by the new ones!). PERF21.DAT should look something like this:
    
     07 MAY       2003  14.05.12.23.
     RANDOM NUMBER SEED     23100
    SEN107KH.ORD                          
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF 107TH SENATE       
        2  633   20   36   10   18   10 0.005
    (36A1,3900I1)                                                   
    (I5,1X,36A1,2I5,50F8.3)                                         
     ******************************************************************************
      1 ROLL CALLS   2    3831   48758  0.07857  0.92143  0.75475           0.00000
        LEGISLATORS  2    3752   48758  0.07695  0.92305  0.75981  0.00000
      2 ROLL CALLS   2    3688   48758  0.07564  0.92436  0.76391           0.99015
        LEGISLATORS  2    3662   48758  0.07511  0.92489  0.76557  0.97539
      3 ROLL CALLS   2    3628   48758  0.07441  0.92559  0.76775           0.99454
        LEGISLATORS  2    3623   48758  0.07431  0.92569  0.76807  0.99878
      4 ROLL CALLS   2    3623   48758  0.07431  0.92569  0.76807           0.99849
        LEGISLATORS  2    3619   48758  0.07422  0.92578  0.76832  0.99951
      5 ROLL CALLS   2    3612   48758  0.07408  0.92592  0.76877           0.99940
        LEGISLATORS  2    3612   48758  0.07408  0.92592  0.76877  0.99996
      6 ROLL CALLS   2    3610   48758  0.07404  0.92596  0.76890           0.99982
        LEGISLATORS  2    3610   48758  0.07404  0.92596  0.76890  0.99997
      7 ROLL CALLS   2    3609   48758  0.07402  0.92598  0.76896           0.99989
        LEGISLATORS  2    3607   48758  0.07398  0.92602  0.76909  0.99976
      8 ROLL CALLS   2    3605   48758  0.07394  0.92606  0.76922           0.99851
        LEGISLATORS  2    3604   48758  0.07392  0.92608  0.76928  0.99999
      9 ROLL CALLS   2    3601   48758  0.07385  0.92615  0.76948           0.99925
        LEGISLATORS  2    3601   48758  0.07385  0.92615  0.76948  0.99999
     10 ROLL CALLS   2    3601   48758  0.07385  0.92615  0.76948           0.99975
        LEGISLATORS  2    3600   48758  0.07383  0.92617  0.76954  0.99986
     11 ROLL CALLS   2    3600   48758  0.07383  0.92617  0.76954           0.99893
        LEGISLATORS  2    3599   48758  0.07381  0.92619  0.76961  0.99997
     12 ROLL CALLS   2    3598   48758  0.07379  0.92621  0.76967           0.99965
        LEGISLATORS  2    3598   48758  0.07379  0.92621  0.76967  0.99999
     13 ROLL CALLS   2    3598   48758  0.07379  0.92621  0.76967           0.99993
        LEGISLATORS  2    3597   48758  0.07377  0.92623  0.76973  0.99968
     14 ROLL CALLS   2    3597   48758  0.07377  0.92623  0.76973           0.99995
        LEGISLATORS  2    3596   48758  0.07375  0.92625  0.76980  0.99999
     15 ROLL CALLS   2    3596   48758  0.07375  0.92625  0.76980           0.99965
        LEGISLATORS  2    3596   48758  0.07375  0.92625  0.76980  1.00000
     16 ROLL CALLS   2    3596   48758  0.07375  0.92625  0.76980           0.99845
        LEGISLATORS  2    3596   48758  0.07375  0.92625  0.76980  1.00000
     17 ROLL CALLS   2    3596   48758  0.07375  0.92625  0.76980           0.99792
        LEGISLATORS  2    3596   48758  0.07375  0.92625  0.76980  1.00000
     18 ROLL CALLS   2    3596   48758  0.07375  0.92625  0.76980           0.99990
        LEGISLATORS  2    3596   48758  0.07375  0.92625  0.76980  1.00000
     19 ROLL CALLS   2    3596   48758  0.07375  0.92625  0.76980           0.99954
        LEGISLATORS  2    3596   48758  0.07375  0.92625  0.76980  1.00000
     20 ROLL CALLS   2    3544   48758  0.07269  0.92731  0.77313           0.99770
        LEGISLATORS  2    3542   48758  0.07264  0.92736  0.77325  0.99954
     MEAN VOLUME LEG.   0.0079   0.0490
     MACHINE PREC.   2    3542   48758  0.07264  0.92736  0.77325
     MACHINE PREC.   2    3542   48758  0.07264  0.92736  0.77325
                          14.05.12.28.
     ELAPSED TIME OF JOB  14.07.10.32.
    The correct classification is now 92.736% (0.92736). The last column shows the mean cosine between the current estimated normal vectors and the normal vectors from the previous iteration. The Line:
     MEAN VOLUME LEG.   0.0079   0.0490
    reports some statistics about the average legislator polytope size. The first number is the average maximum distance to a polytope boundary, 0.0079, and the second number is the standard deviation of the maximum distance to a polytope boundary 0.0490. When there are more than 100 roll calls the space is so finely "chopped up" that these two numbers will typically be very small. The last two lines
     MACHINE PREC.   2    3542   48758  0.07264  0.92736  0.77325
     MACHINE PREC.   2    3542   48758  0.07264  0.92736  0.77325
    are simply redundancy checks at convergence. These two lines should always be the same.

    In Two Dimensions PERF25.DAT first lists the legislator coordinates and then the roll call normal vectors and cutting points. The file should look very similar to this:
     07 MAY       2003  14.05.12.23.
        1 1079991099 0USA     200  BUSH           1     63      0.984   0.036   0.164   0.063
        2 1074970041 0ALABAMA 20001SESSIONS      26    481      0.946   0.002   0.157  -0.168
        3 1079465941 0ALABAMA 20001SHELBY        44    488      0.910   0.002   0.128  -0.100
        4 1071490781 0ALASKA  20001MURKOWSKI     25    459      0.946   0.002   0.161   0.038
        5 1071210981 0ALASKA  20001STEVENS       32    452      0.929   0.002   0.128  -0.006
        6 1071542961 0ARIZONA 20001KYL           29    495      0.941   0.002   0.213  -0.044
        7 1071503961 0ARIZONA 20001MCCAIN       110    478      0.770   0.002   0.097  -0.074
        8 1072930642 0ARKANSA 20001HUTCHINSON,   46    484      0.905   0.002   0.147   0.021
        9 1072930542 0ARKANSA 10001LINCOLN       40    495      0.919   0.002  -0.089   0.080
       10 1071501171 0CALIFOR 10001BOXER         22    481      0.954   0.002  -0.204  -0.081
                     etc.
                  The column in red is the number of classification errors
                  The column in purple is the total number of choices
                  The column in green is the proportion correctly classified
                  The column in black is the maximum size of the polytope containing the legislator
                  The last two columns in blue are the two dimensional coordinates
                     etc.
                     etc.
      100 1074930925 0WISCONS 10001FEINGOLD      40    498      0.920   0.002  -0.184  -0.503
      101 1071570325 0WISCONS 10001KOHL          29    484      0.940   0.003  -0.135   0.058
      102 1074970668 0WYOMING 20001ENZI          33    483      0.932   0.002   0.180  -0.028
      103 1071563368 0WYOMING 20001THOMAS        26    486      0.947   0.002   0.187  -0.001
        1    6  76  24  10  23  80 6 1  0.583 -0.172  0.991 -0.133
        2    8  59  42   3  47  56 6 1  0.929 -0.057  0.937 -0.350
        3   15  56  44   2  45  58 6 1  0.955 -0.081  0.995  0.101
        4   16  34  65   7  30  73 1 6  0.794 -0.163  0.995 -0.096
        5   17  58  41   8  44  59 6 1  0.805 -0.052  0.925  0.380
        6   18  50  49   4  50  53 6 1  0.918 -0.010  0.974  0.228
        7   19  55  41   5  41  62 6 1  0.878 -0.102  0.983  0.181
        8   20  55  42   8  46  57 6 1  0.810 -0.038  0.906  0.423
        9   21  61  37  16  45  58 6 1  0.568 -0.053  0.926  0.376
       10   22  53  47   3  54  49 1 6  0.936  0.060  0.985 -0.170
                  etc.
                  etc.
     The column in black is a counter from 1 to the number of scaled roll calls
     The column in indigo is the position of the roll call in the input roll call matrix
     The column in red is the number of Yeas
     The column in blue is the number of Nays
     The column in coral is the number of classification errors
     The column in teal is the number of Predicted Choices Below the Projected Midpoint
     The column in deeppink is the number of Predicted Choices Above the Projected Midpoint
     The column in firebrick is the Predicted Choice Below the Projected Midpoint (1 = Yea, 6 = Nay)
     The column in limegreen is the Predicted Choice Above the Projected Midpoint
     The column in turquoise is the Proportional Reduction in Error
     The column in magenta is the projected midpoint on the Line defined by the Normal Vector
     The last two columns in darkblue is the Normal Vector for the Cutting Plane
                  etc.
                  etc.
      490  625  47  52   2  48  55 1 6  0.957 -0.029  0.890  0.456
      491  626  69  30   2  30  73 6 1  0.933 -0.133  0.958  0.286
      492  627  73  26   4  30  73 6 1  0.846 -0.134  0.959  0.282
      493  628  83  16   6  21  82 6 1  0.625 -0.079  0.449  0.893
      494  629  91   9   7   2 101 6 1  0.222 -0.249  0.970  0.243
      495  630  56  44   4  49  54 6 1  0.909 -0.046  0.978 -0.207
      496  631  85  12   3  88  15 1 6  0.750  0.149  0.814 -0.581
      497  632  87  11   7  94   9 1 6  0.364  0.179  0.957 -0.290
      498  633  92   2   2   0 103 6 1  0.000 -0.325  0.955  0.296
    Below is a plot of the first five cutting lines. The Red Arrows at the ends of the cutting lines point in the direction of a Yea vote. The Blue Dot is President Bush's position. With Just these five votes the Polytope President Bush is in predicts the voting pattern YYYNY.



    Below is a plot of the Senator coordinates. The R tokens are Republicans, the S tokens are Southern Democrats (11 states of the Confederacy plus Kentucky and Oklahoma), the D tokens are Northern (Non-Southern) Democrats, and the P is President Bush.



  3. Example Two: The 95th House.
  4. Control Card File for 95th House (PERFSTRT.H95) (Rename this to PERFSTRT.DAT)

    95th House Roll Call Data (HOU95KH.ORD)

    PERF21.DAT for the 95th in two dimensions should look something like this:
     07 MAY       2003  15.14.18.17.
     RANDOM NUMBER SEED     37600
    HOU95KH.ORD                           
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF 95TH HOUSE         
        2 1540   20   36    1    5   10 0.005
    (36A1,3900I1)                                                   
    (I5,1X,36A1,2I5,50F8.3)                                         
     ******************************************************************************
      1 ROLL CALLS   2   67910  554899  0.12238  0.87762  0.51180           0.00000
        LEGISLATORS  2   67239  554899  0.12117  0.87883  0.51662  0.00000
      2 ROLL CALLS   2   66802  554899  0.12039  0.87961  0.51976           0.99849
        LEGISLATORS  2   66636  554899  0.12009  0.87991  0.52096  0.99512
      3 ROLL CALLS   2   66487  554899  0.11982  0.88018  0.52203           0.99895
        LEGISLATORS  2   66427  554899  0.11971  0.88029  0.52246  0.99963
      4 ROLL CALLS   2   66367  554899  0.11960  0.88040  0.52289           0.99890
        LEGISLATORS  2   66334  554899  0.11954  0.88046  0.52313  0.99967
      5 ROLL CALLS   2   66308  554899  0.11950  0.88050  0.52331           0.99922
        LEGISLATORS  2   66282  554899  0.11945  0.88055  0.52350  0.99990
      6 ROLL CALLS   2   66263  554899  0.11941  0.88059  0.52364           0.99975
        LEGISLATORS  2   66251  554899  0.11939  0.88061  0.52372  0.99991
      7 ROLL CALLS   2   66236  554899  0.11937  0.88063  0.52383           0.99993
        LEGISLATORS  2   66223  554899  0.11934  0.88066  0.52392  0.99985
      8 ROLL CALLS   2   66215  554899  0.11933  0.88067  0.52398           0.99996
        LEGISLATORS  2   66210  554899  0.11932  0.88068  0.52402  0.99993
      9 ROLL CALLS   2   66208  554899  0.11932  0.88068  0.52403           0.99999
        LEGISLATORS  2   66206  554899  0.11931  0.88069  0.52405  0.99999
     10 ROLL CALLS   2   66201  554899  0.11930  0.88070  0.52408           0.99897
        LEGISLATORS  2   66200  554899  0.11930  0.88070  0.52409  1.00000
     11 ROLL CALLS   2   66199  554899  0.11930  0.88070  0.52410           0.99995
        LEGISLATORS  2   66198  554899  0.11930  0.88070  0.52410  1.00000
     12 ROLL CALLS   2   66196  554899  0.11929  0.88071  0.52412           1.00000
        LEGISLATORS  2   66194  554899  0.11929  0.88071  0.52413  1.00000
     13 ROLL CALLS   2   66192  554899  0.11929  0.88071  0.52415           1.00000
        LEGISLATORS  2   66192  554899  0.11929  0.88071  0.52415  1.00000
     14 ROLL CALLS   2   66191  554899  0.11928  0.88072  0.52415           0.99997
        LEGISLATORS  2   66188  554899  0.11928  0.88072  0.52418  0.99986
     15 ROLL CALLS   2   66184  554899  0.11927  0.88073  0.52421           0.99999
        LEGISLATORS  2   66178  554899  0.11926  0.88074  0.52425  0.99993
     16 ROLL CALLS   2   66173  554899  0.11925  0.88075  0.52428           0.99999
        LEGISLATORS  2   66171  554899  0.11925  0.88075  0.52430  0.99999
     17 ROLL CALLS   2   66170  554899  0.11925  0.88075  0.52431           0.99999
        LEGISLATORS  2   66170  554899  0.11925  0.88075  0.52431  1.00000
     18 ROLL CALLS   2   66170  554899  0.11925  0.88075  0.52431           0.99999
        LEGISLATORS  2   66169  554899  0.11925  0.88075  0.52431  1.00000
     19 ROLL CALLS   2   66169  554899  0.11925  0.88075  0.52431           0.99998
        LEGISLATORS  2   66169  554899  0.11925  0.88075  0.52431  1.00000
     20 ROLL CALLS   2   65322  554899  0.11772  0.88228  0.53040           0.99095
        LEGISLATORS  2   65226  554899  0.11755  0.88245  0.53109  0.99826
     MEAN VOLUME LEG.   0.0034   0.0035
     MACHINE PREC.   2   65223  554899  0.11754  0.88246  0.53111
     MACHINE PREC.   2   65223  554899  0.11754  0.88246  0.53111
                          15.14.18.21.
     ELAPSED TIME OF JOB  15.41.01.21.
    The correct classification is 88.246% (0.88246) with an APRE of 0.53111. The 95th (1977-78) House was part of the 3-Party period from the late 1930s to the mid-1980s when the Democratic Party was split into Northern and Southern blocs (see my book with Howard Rosenthal Congress: A Political-Economic History of Roll Call Voting, our paper D-NOMINATE After 10 Years: A Comparative Update to Congress: A Political-Economic History of Roll Call Voting [a version of this paper was published in Legislative Studies Quarterly, 26:5-29, 2001], and my monograph with Nolan McCarty and Howard Rosenthal Income Redistribution and the Realignment of American Politics, 1997, AEI Press. Congressional voting through this period was two dimensional.

    Below is a Skree Plot of the Eigenvalues of the Double-Centered agreement score matrix. In contrast to the Skree Plot for the 107th Senate, note that the "elbow" is not as sharp indicating the possible presence of a 2nd dimension:



    Below is a plot of the Representative coordinates. The R tokens are Republicans, the S tokens are Southern Democrats (11 states of the Confederacy plus Kentucky and Oklahoma), the D tokens are Northern (Non-Southern) Democrats, and the P is President Carter.



  5. Example Three: The Brazilian Legislature 1995-98
  6. This example is courtesy of Barry Ames via Scott Morgenstern and is discussed in detail in Scott's forthcoming book Patterns of Legislative Politics: Roll Call Voting in Latin America and the United States.

    Control Card File for Brazilian Legislature (PERFSTRT.BRAZIL) (Rename this to PERFSTRT.DAT)

    Brazil Roll Call Data for 1995-98 (BRAZIL2A.TXT)

    The PERF21.DAT should look something like this in one dimension:
     08 MAY       2003  12.02.34.98.
     RANDOM NUMBER SEED     38000
    BRAZIL2A.TXT                                                    
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING                       
        1  420   20   43    2    1   10 0.005
    (43a1,3600I1)                                                   
    (I5,1X,43A1,2I5,50F8.3)                                         
     ******************************************************************************
      1 ROLL CALLS   1   14534  139474  0.10421  0.89579  0.60489
      2 LEGISLATORS  1   13432  139474  0.09630  0.90370  0.63485  0.98111
      3 ROLL CALLS   1   13108  139474  0.09398  0.90602  0.64366
      4 LEGISLATORS  1   12879  139474  0.09234  0.90766  0.64988  0.98837
      5 ROLL CALLS   1   12755  139474  0.09145  0.90855  0.65326
      6 LEGISLATORS  1   12674  139474  0.09087  0.90913  0.65546  0.99684
      7 ROLL CALLS   1   12648  139474  0.09068  0.90932  0.65616
      8 LEGISLATORS  1   12616  139474  0.09045  0.90955  0.65703  0.99703
      9 ROLL CALLS   1   12598  139474  0.09033  0.90967  0.65752
     10 LEGISLATORS  1   12577  139474  0.09017  0.90983  0.65809  0.99849
     11 ROLL CALLS   1   12569  139474  0.09012  0.90988  0.65831
     12 LEGISLATORS  1   12565  139474  0.09009  0.90991  0.65842  0.99977
     13 ROLL CALLS   1   12557  139474  0.09003  0.90997  0.65864
     14 LEGISLATORS  1   12555  139474  0.09002  0.90998  0.65869  0.99943
                          12.31.42.17.
     ELAPSED TIME OF JOB  12.32.32.96.
    The correct classification is 91.0% (0.90998) with an APRE of .659 (0.65869). Although the correct classification is very high, the average majority margin for the roll calls is 73.6% (0.73626), this is printed out in PERF23.DAT) which is why the APRE, although quite high, is only .659. The eigenvalue pattern suggests that there may be two or three dimensions underlying the data.



    Below is the rank ordering from Left to Right. The party codes are in the column next to the classification errors (some are missing). The political parties are:
               PT   = Worker's Party
               PPB  = Brazilian Progressive Party
               PDT  = Democratic Labor Party
               PMDB = Party of the Brazilian Democratic Movement
               PFL  = Party of the Liberal Front
               PSDB = Party of Brazilian Social Democracy   
               PTB  = Brazilian Labor Party
    Parties in Red are generally considered to be on the Left, parties in Magenta are generally considered to be in the Center, and parties in Blue are generally considered to be on the Right.
        1 PAULO BERNARDO                     PR   PT     3  335   0.991   1.000
        2 PAULO PAIM                         RS   PT     5  362   0.986   2.500
        3 LUCIANO ZICA                       SP   PT     7  358   0.980   2.500
        4 JOSE PIMENTEL                      CE   PT     8  372   0.978   4.000
        5 ANA JULIA                          PA   PT     1  204   0.995   5.000
        6 MARCELO DEDA                       SE   PT     4  361   0.989   7.500
        7 ARLINDO CHINAGLIA                  SP   PT     7  360   0.981   7.500
        8 MARIA DA CONCEICAO TAVARES         RJ   PT     5  215   0.977   7.500
        9 CHICO FERRAMENTA                   MG   PT     4  199   0.980   7.500
       10 LUIZ ALBERTO                                   2  133   0.985  10.000
       11 HAROLDO SABOIA                     MA   PT     1  210   0.995  11.000
       12 JOANA DARC                                     0  142   1.000  13.000
       13 JOSE AUGUSTO                                  11  159   0.931  13.000
       14 GERALDO PASTANA                                1  153   0.993  13.000
       15 LUIZ GUSHIKEN                      SP   PT    13  347   0.963  21.000
       16 PADRE ROQUE                        PR   PT     8  316   0.975  21.000
       17 MARIA LAURA                        DF   PT     6  326   0.982  21.000
       18 NILMARIO MIRANDA                   MG   PT     5  297   0.983  21.000
       19 EDUARDO JORGE                      SP   PT     8  386   0.979  21.000
       20 JOSE MACHADO                       MG  PPB     4  366   0.989  21.000
       21 JAIR MENEGUELLI                    SP   PT     3  335   0.991  21.000
       22 CELSO DANIEL                       SP   PT     3  203   0.985  21.000
       23 NEDSON MICHELETI                   PR   PT     5  341   0.985  21.000
       24 ESTHER GROSSI                      RS   PT     5  280   0.982  21.000
       25 JOSE FORTUNATI                     RS   PT     4  185   0.978  21.000
       26 JOAO PAULO                         MG   PT     2  344   0.994  21.000
       27 JOSE FRITSCH                       SC  PPB     4  207   0.981  21.000
       28 MILTON TEMER                       RJ   PT     2  358   0.994  31.500
       29 JAQUES WAGNER                      BA   PT     4  317   0.987  31.500
       30 ALCIDES MODESTO                    BA   PT     6  343   0.983  31.500
       31 MIGUEL ROSSETTO                    RS   PT     4  350   0.989  31.500
       32 DOMINGOS DUTRA                     MA   PT     6  198   0.970  31.500
       33 CARLOS SANTANA                     RJ   PT     3  306   0.990  31.500
       34 JOAO COSER                         ES   PT     3  353   0.992  31.500
       35 ADAO PRETTO                        RS   PT     3  349   0.991  31.500
       36 HELIO BICUDO                       SP   PT     5  324   0.985  42.500
       37 HUMBERTO COSTA                     PE   PT     7  368   0.981  42.500
       38 PAULO ROCHA                        PA   PT     6  359   0.983  42.500
       39 IVAN VALENTE                       SP   PT     2  363   0.994  42.500
       40 JOSE GENOINO                       SP   PT     5  379   0.987  42.500
       41 MILTON MENDES                      SC  PPB     4  382   0.990  42.500
       42 LUIZ MAINARDI                      RS   PT     5  342   0.985  42.500
       43 MARTA SUPLICY                      SP   PT     6  300   0.980  42.500
       44 GILNEY VIANA                       MT   PT     4  340   0.988  42.500
       45 AUGUSTO CARVALHO                   DF         31  387   0.920  42.500
       46 FERNANDO FERRO                     PE   PT     5  360   0.986  42.500
       47 JOAO FASSARELLA                                4  388   0.990  42.500
       48 PEDRO WILSON                       GO   PT     5  362   0.986  42.500
       49 JOSE AUGUSTO RAMOS                 SP   PT     6  216   0.972  42.500
       50 CHICO VIGILANTE                    DF   PT     7  331   0.979  50.000
       51 PAULO DELGADO                      MG   PT     9  332   0.973  51.000
       52 LUIZ EDUARDO GREENHALGH                        2  134   0.985  52.000
       53 RICARDO GOMYDE                     PR         15  290   0.948  53.500
       54 ALDO ARANTES                       GO         17  359   0.953  53.500
       55 FERNANDO LOPES                     RJ  PDT    13  320   0.959  56.500
       56 JANDIRA FEGHALI                    RJ         14  377   0.963  56.500
       57 ALDO REBELO                        SP         16  338   0.953  56.500
       58 HAROLDO LIMA                       BA         16  334   0.952  56.500
       59 AGNELO QUEIROZ                     DF         15  351   0.957  59.000
       60 LINDBERG FARIAS                    RJ         12  292   0.959  60.000
       61 INACIO ARRUDA                      CE         14  348   0.960  61.000
       62 GILVAN FREIRE                      PB         47  351   0.866  62.000
       63 JOSE CARLOS SABOIA                 MA          5   88   0.943  63.000
       64 NILSON GIBSON                      PE         36  358   0.899  64.000
       65 GERVASIO OLIVEIRA                  AP  PDT    13  302   0.957  65.000
       66 FERNANDO GABEIRA                   RJ         62  311   0.801  66.000
       67 DERCIO KNOP                                   14  158   0.911  67.000
       68 RAQUEL CAPIBERIBE                  AP         14  284   0.951  68.000
       69 RICARDO HERACLIO                   PE         27  315   0.914  69.500
       70 ALEXANDRE CARDOSO                  RJ         18  310   0.942  69.500
       71 NEIVA MOREIRA                          PDT     8  139   0.942  71.500
       72 GONZAGA PATRIOTA                   PE  PDT    20  279   0.928  71.500
       73 EDSON EZEQUIEL                     RJ  PDT     8  213   0.962  73.000
       74 CARLOS CARDINAL                    RS  PDT    11  384   0.971  74.000
       75 CIDINHA CAMPOS                     RJ  PDT    14  342   0.959  75.500
       76 FERNANDO ZUPPO                                19  365   0.948  75.500
       77 FERNANDO LYRA                      PE         10  203   0.951  77.000
       78 PEDRO VALADARES                    SE         21  303   0.931  78.500
       79 MATHEUS SCHMIDT                    RS  PDT    16  363   0.956  78.500
       80 AIRTON DIPP                        RS  PDT    19  378   0.950  80.500
       81 RENAN KURTZ                        RS  PDT    10  331   0.970  80.500
       82 MARCIA CIBILIS VIANA               RJ  PDT    13  313   0.958  82.000
       83 ENIO BACCI                         RS  PDT    26  330   0.921  84.000
       84 JOSE MAURICIO                      RJ  PDT    16  327   0.951  84.000
       85 MIRO TEIXEIRA                      RJ  PDT    18  360   0.950  84.000
       86 CORIOLANO SALES                    BA  PDT    32  350   0.909  86.000
       87 GIOVANNI QUEIROZ                   PA  PDT    22  344   0.936  87.000
       88 EURIPEDES MIRANDA                  RO  PDT    24  308   0.922  88.000
       89 FERNANDO RIBAS CARLI                   PPB    44  217   0.797  89.000
       90 LEONEL PAVAN                       SC  PDT    25  218   0.885  90.000
       91 LUIZ DURAO                         ES  PDT    62  264   0.765  91.000
       92 ANTONIO BRASIL                     PA PMDB    52  351   0.852  92.000
       93 MAURICIO REQUIAO                   PR PMDB    55  376   0.854  93.000
       94 JOAO COLACO                        PE         38  193   0.803  94.000
       95 RAIMUNDO BEZERRA                   CE PMDB     9   36   0.750  95.000
       96 JERONIMO REIS                      SE          7   37   0.811  96.000
       97 NOEL DE OLIVEIRA                   RJ PMDB    33  285   0.884  97.000
       98 JOSE PINOTTI                       SP         45  227   0.802  98.000
       99 BOSCO FRANCA                       SE PMDB    33  123   0.732  99.000
      100 IZIDORIO OLIVEIRA                              3   20   0.850 100.000
      101 MARCELO BARBIERI                   SP PMDB    44  249   0.823 101.000
      102 ARNALDO FARIA DE SA                SP  PPB    97  386   0.749 102.000
      103 ALVARO VALLE                       RJ         33  177   0.814 103.000
      104 JARBAS LIMA                        RS  PPB    64  402   0.841 104.000
      105 ADYLSON MOTTA                      RS  PPB    71  388   0.817 105.000
      106 PRISCO VIANA                       BA  PPB    87  325   0.732 106.000
      107 HERMES PARCIANELLO                 PR PMDB    58  292   0.801 107.000
      108 ELCIONE BARBALHO                   PA PMDB    66  311   0.788 108.000
      109 RITA CAMATA                        ES PMDB     8   49   0.837 109.000
      110 JAIR BOLSONARO                     RJ  PPB    79  362   0.782 110.000
      111 JOAO THOME MESTRINHO               AM         62  295   0.790 111.000
      112 JAIR SOARES                        RS  PPB    84  368   0.772 112.000
      113 COLBERT MARTINS                               27  148   0.818 113.000
      114 DOMINGOS LEONELLI                  BA         75  324   0.769 114.000
      115 MOACYR ANDRADE                     AL  PPB    68  271   0.749 115.000
      116 LUIZ BUAIZ                         ES         91  357   0.745 116.000
      117 OSMAR LEITAO                       RJ  PFL    76  201   0.622 117.000
      118 ADELSON SALVADOR                   ES PMDB   106  365   0.710 118.000
      119 FLAVIO ARNS                        PR PSDB    82  359   0.772 119.000
      120 PAES DE ANDRADE                    CE PMDB    40  201   0.801 120.000
      121 EDUARDO COELHO                                48  156   0.692 121.500
      122 CHICAO BRIGIDO                     AC PMDB    96  332   0.711 121.500
      123 ANA CATARINA                                  41  162   0.747 123.000
      124 JOAO TOTA                          AC  PPB    38  119   0.681 124.000
      125 MARCOS VINICIUS DE CAMPOS                     47  168   0.720 125.000
      126 PAULO NASCIMENTO                              28  159   0.824 126.000
      127 ANTONIO JOAQUIM                    MT PSDB    76  250   0.696 127.000
      128 AECIO DE BORBA                     CE  PPB    35  138   0.746 128.000
      129 ELIAS ABRAHAO                      PR PMDB    24  200   0.880 129.000
      130 CARLOS MENDES                      GO PMDB    35  156   0.776 130.000
      131 NELSON BORNIER                     RJ PSDB     1   16   0.938 131.000
      132 EDUARDO BARBOSA                    MG PSDB     9  121   0.926 132.000
      133 CASSIO CUNHA LIMA                  PB PMDB    34  169   0.799 133.000
      134 ODAISA FERNANDES                              28  166   0.831 134.000
      135 FRANCISCO DIOGENES                 AC  PFL     6   43   0.860 135.000
      136 JOSE MELO                          AC  PFL    29  167   0.826 136.500
      137 RAIMUNDO COLOMBO                              28  161   0.826 136.500
      138 MAURICIO CAMPOS                    MG PSDB    53  350   0.849 138.000
      139 PEDRO LUIS ALBUQUERQUE                        26  133   0.805 139.000
      140 MARCOS VINICIUS                               29  169   0.828 140.000
      141 MESSIAS GOIS                       SE  PFL    34  165   0.794 141.000
      142 PEDRO NOVAES                       MA PMDB    45  161   0.720 142.500
      143 HUGO LAGRANHA                      RS  PTB    55  211   0.739 142.500
      144 MAURI SERGIO                       AC PMDB     9  123   0.927 144.000
      145 JORGE ANDERS                       ES PSDB    12  182   0.934 145.000
      146 NILTON GOMES (BAIANO)              ES         28  182   0.846 146.000
      147 EDSON SOARES                       MG PSDB    13   84   0.845 147.000
      148 REGIS DE OLIVEIRA                  SP  PFL    43  226   0.810 148.000
      149 ADOLFO FETTER JUNIOR               RS  PPB    28  109   0.743 149.000
      150 JAIR SIQUEIRA                      MG  PPB    27  208   0.870 150.000
      151 ANDRE PUCCINELLI                   MS PMDB    15  148   0.899 151.000
      152 ILDEMAR KUSSLER                    RO PSDB    16  164   0.902 152.000
      153 LUIS PIAUHYLINO                    PE         37  204   0.819 153.500
      154 FATIMA PELAEZ                      AP PSDB     8  174   0.954 153.500
      155 LUIZ CARLOS SANTOS                 SP PMDB    34  308   0.890 156.000
      156 JOSE ELIAS MURAD                   MG PSDB     8  216   0.963 156.000
      157 BENEDITO SA                        PI PSDB     8  201   0.960 156.000
      158 MELQUIADES NETO                    TO  PFL    29  262   0.889 158.000
      159 MARCIO FORTES                      RJ PSDB    34  304   0.888 160.000
      160 AYRTON XEREZ                       RJ PSDB    37  331   0.888 160.000
      161 JOSE MUCIO MONTEIRO                PE         37  362   0.898 160.000
      162 EDUARDO MASCARENHAS                RJ PSDB    32  284   0.887 162.000
      163 ADELAIDE NERI                      AC PMDB    25  157   0.841 163.000
      164 IVO MAINARDI                       RS PMDB    33  324   0.898 164.000
      165 JOAO MAIA                          AC  PFL    39  320   0.878 166.000
      166 ELISEU PADILHA                     RS PMDB    34  272   0.875 166.000
      167 MARCELO TEIXEIRA                   CE PMDB    31  307   0.899 166.000
      168 MAURICIO NAJAR                         PFL    38  361   0.895 168.000
      169 CANDIDO MENDES                                22  127   0.827 169.000
      170 JOSE COSTA                         AL         26  144   0.819 170.000
      171 EDSON QUEIROZ                      CE         50  295   0.831 171.000
      172 LUIZ DANTAS                                   19  127   0.850 172.000
      173 OLAVO CALHEIROS                    AL PMDB    69  328   0.790 173.000
      174 MARCOS LIMA                        MG PMDB    94  326   0.712 174.000
      175 ARMANDO COSTA                      MG PMDB    64  348   0.816 175.000
      176 ALMINO AFFONSO                     SP         66  331   0.801 176.000
      177 AYRES DA CUNHA                     SP  PFL    41  366   0.888 177.000
      178 LEONIDAS CRISTINO                  CE         54  391   0.862 178.000
      179 CARLOS MOSCONI                     MG PSDB     9  219   0.959 179.000
      180 ALVARO RIBEIRO                     PE         38  152   0.750 180.000
      181 ANTONIO KANDIR                     SP PSDB     8  154   0.948 181.000
      182 OSWALDO SOLER                         PSDB    19  194   0.902 183.000
      183 JOAO NATAL                         GO PMDB    38  302   0.874 183.000
      184 IBERE FERREIRA                                18  140   0.871 183.000
      185 NELSON HARTER                                 44  150   0.707 185.000
      186 LUIS ROBERTO PONTE                 RS         66  263   0.749 186.000
      187 PAULO LUSTOSA                      CE  PPB    48  122   0.607 187.000
      188 CARLOS AIRTON                      AC  PPB    62  261   0.762 188.000
      189 CELIA MENDES                       AC  PPB    69  289   0.761 189.000
      190 PAULO DE VELASCO                               1   15   0.933 190.500
      191 NILTON CERQUEIRA                   RJ          1   20   0.950 190.500
      192 ANTONIO BALHMANN                   CE         50  323   0.845 192.000
      193 JOFRAN FREJAT                      DF         80  363   0.780 193.000
      194 BENEDITO DOMINGOS                  DF         37  330   0.888 195.000
      195 NILTON BAIANO                          PPB    35  157   0.777 195.000
      196 JOSE LINHARES                      CE         64  356   0.820 195.000
      197 ERALDO TRINDADE                    AP  PPB    89  319   0.721 197.000
      198 EDISON ANDRINO                     SC PMDB    72  301   0.761 198.500
      199 HELIO ROSAS                        SP PMDB    27  308   0.912 198.500
      200 ASDRUBAL BENTES                    PA PMDB    18  129   0.860 200.500
      201 PAULO RITZEL                       RS PMDB    37  347   0.893 200.500
      202 EMERSON OLAVO PIRES                RO PSDB    28  202   0.861 202.500
      203 JOSE COIMBRA                       SP  PTB    58  343   0.831 202.500
      204 IVANDRO CUNHA LIMA                 PB PMDB    53  346   0.847 205.500
      205 JOSE ALDEMIR                       PB PMDB    68  352   0.807 205.500
      206 FEU ROSA                           ES  PPB    42  319   0.868 205.500
      207 JOSE LUIZ CLEROT                   PB PMDB    95  347   0.726 205.500
      208 EZIDIO PINHEIRO                    RS PSDB    74  376   0.803 208.000
      209 MARIA ELVIRA                       MG PMDB    23  243   0.905 209.000
      210 FIRMO DE CASTRO                    CE PSDB    44  342   0.871 210.000
      211 MARIO MARTINS                      PA PMDB    10  209   0.952 213.500
      212 LUIZ MAXIMO                           PSDB    17  135   0.874 213.500
      213 OSCAR GOLDONI                      MS PMDB    61  267   0.772 213.500
      214 MARISA SERRANO                     MS PSDB    39  367   0.894 213.500
      215 MARCAL FILHO                          PSDB    23  196   0.883 213.500
      216 REGINA LINO                                   21  139   0.849 213.500
      217 JOAO LEAO                          BA PSDB    25  367   0.932 221.500
      218 CARLOS APOLINARIO                  SP PMDB    25  350   0.929 221.500
      219 PINHEIRO LANDIM                    CE PMDB    18  315   0.943 221.500
      220 JOAO ALMEIDA                       BA PMDB    29  351   0.917 221.500
      221 CARLOS NELSON                      SP PMDB    36  295   0.878 221.500
      222 CONFUCIO MOURA                     RO PMDB    29  321   0.910 221.500
      223 JOAO HENRIQUE                      PI PMDB    19  323   0.941 221.500
      224 FERNANDO DINIZ                     MG PMDB    18  318   0.943 221.500
      225 FREIRE JUNIOR                      TO         39  208   0.812 221.500
      226 ORCINO GONCALVES                   GO PMDB    27  333   0.919 221.500
      227 DJALMA DE ALMEIDA CESAR                        8  167   0.952 229.000
      228 NEUTO DE CONTO                     SC PMDB    18  132   0.864 229.000
      229 FETTER JUNIOR                                 35  153   0.771 229.000
      230 PIMENTEL GOMES                     CE         46  341   0.865 229.000
      231 NICIAS RIBEIRO                     PA PSDB    17  187   0.909 229.000
      232 FERNANDO GOMES                     BA  PTB     7  181   0.961 232.500
      233 LAIRE ROSADO                       RN PMDB    10  183   0.945 232.500
      234 JOSE CHAVES                        PE PMDB    28  281   0.900 234.500
      235 MARIO NEGROMONTE                   BA PSDB    17  355   0.952 234.500
      236 BARBOSA NETO                       GO PMDB    21  242   0.913 237.500
      237 JOSE PRIANTE                       PA PMDB    34  307   0.889 237.500
      238 LIDIA QUINAN                       GO PMDB    24  335   0.928 237.500
      239 GENESIO BERNARDINO                 MG PMDB    28  364   0.923 237.500
      240 DEJANDIR DALPASQUALE               SC PMDB     8  108   0.926 241.000
      241 B. SA                                          6  146   0.959 241.000
      242 ARY KARA                           SP         35  311   0.887 241.000
      243 ANTONIO DO VALLE                   MG PMDB    60  394   0.848 244.000
      244 EDINHO ARAUJO                      SP PMDB    38  387   0.902 244.000
      245 GEDDEL VIEIRA LIMA                 BA PMDB    16  320   0.950 244.000
      246 GERMANO RIGOTTO                    RS PMDB    21  333   0.937 247.500
      247 JORGE TADEU MUDALEN                SP  PPB    31  321   0.903 247.500
      248 JOAO MAGALHAES                        PMDB    25  184   0.864 247.500
      249 HENRIQUE EDUARDO ALVES             RN PMDB    24  303   0.921 247.500
      250 EDINHO BEZ                         SC PMDB    28  358   0.922 250.000
      251 ODACIR KLEIN                       RS PMDB     7  188   0.963 253.000
      252 DARCISIO PERONDI                   RS PMDB    33  349   0.905 253.000
      253 DE VELASCO                                    11  161   0.932 253.000
      254 ARMANDO ABILIO                     PB PMDB    22  380   0.942 253.000
      255 LUIZ PIAUHYLINO                                9  150   0.940 253.000
      256 MOREIRA FRANCO                     RJ PMDB    28  377   0.926 257.000
      257 ALBERICO FILHO                     MA PMDB    27  287   0.906 257.000
      258 GONZAGA MOTA                                  52  311   0.833 257.000
      259 HUMBERTO SOUTO                     MG  PFL     1   59   0.983 259.000
      260 ALOYSIO NUNES FERREIRA             SP PSDB    44  395   0.889 260.500
      261 OSCAR ANDRADE                          PFL     9  179   0.950 260.500
      262 ISRAEL PINHEIRO                    MG  PTB    11  148   0.926 263.000
      263 ARTHUR VIRGILIO                                3  122   0.975 263.000
      264 PAULO HESLANDER                    MG  PTB    43  335   0.872 263.000
      265 EMANUEL FERNANDES                              1   62   0.984 265.000
      266 ELIAS MURAD                                    4  132   0.970 267.500
      267 CUNHA LIMA                         SP  PPB    85  376   0.774 267.500
      268 BONIFACIO DE ANDRADA               MG PSDB    25  367   0.932 267.500
      269 MURILO DOMINGOS                               15  193   0.922 267.500
      270 PEDRO YVES                             PPB    82  250   0.672 270.000
      271 PAULO MOURAO                       TO PSDB    22  282   0.922 271.500
      272 MARCIA MARINHO                     MA PSDB    17  225   0.924 271.500
      273 JOAO FAUSTINO                      RN PSDB     8  136   0.941 273.000
      274 ALBERTO GOLDMAN                    SP PSDB    32  352   0.909 276.000
      275 MARINHA RAUPP                      RO PSDB    24  238   0.899 276.000
      276 JOSE ANIBAL                        SP PSDB     9  303   0.970 276.000
      277 NELSON OTOCH                       CE PSDB    13  299   0.957 276.000
      278 ANTONIO CARLOS PANNUNZIO           SP PSDB    17  371   0.954 276.000
      279 JOSE THOMAZ NONO                   AL PSDB    36  290   0.876 283.500
      280 ARNALDO MADEIRA                               20  391   0.949 283.500
      281 ALZIRA EWERTON                     AM PSDB    24  251   0.904 283.500
      282 CANDINHO MATTOS                       PSDB    26  305   0.915 283.500
      283 MARCONI PERILLO                    GO PSDB    28  340   0.918 283.500
      284 JOVAIR ARANTES                     GO PSDB    29  347   0.916 283.500
      285 LUIZ CARLOS HAULY                  PR PSDB    12  362   0.967 283.500
      286 FRANCO MONTORO                     SP PSDB    14  288   0.951 283.500
      287 KOYU IHA                           SP PSDB    17  349   0.951 283.500
      288 NELSON MARCHEZAN                   RS PSDB    20  381   0.948 283.500
      289 DALILA FIGUEIREDO                             27  143   0.811 290.000
      290 FATIMA PELAES                                  6  140   0.957 290.000
      291 ARNON BEZERRA                      CE PSDB    12  314   0.962 290.000
      292 ADEMIR LUCAS                       MG PSDB    29  215   0.865 294.000
      293 RAIMUNDO GOMES DE MATOS                        7  159   0.956 294.000
      294 PEDRO HENRY                           PSDB     8  247   0.968 294.000
      295 NESTOR DUARTE                      BA PSDB    19  327   0.942 294.000
      296 OCTAVIO ELISIO                     MG PSDB    20  165   0.879 294.000
      297 LUIZ HENRIQUE                      SC PMDB    15  167   0.910 297.000
      298 ALEXANDRE SANTOS                   RJ PSDB    12  331   0.964 298.000
      299 DANILO DE CASTRO                   MG PSDB    11  364   0.970 301.500
      300 AECIO NEVES                        MG PSDB    10  303   0.967 301.500
      301 JOSE DE ABREU                      SP PSDB    21  290   0.928 301.500
      302 ANTONIO FEIJAO                     AP PSDB    21  345   0.939 301.500
      303 ITAMAR SERPA                       RJ PSDB    17  301   0.944 301.500
      304 LUCIANO CASTRO                     RR PSDB    21  338   0.938 301.500
      305 MOISES BENNESBY                                6  117   0.949 305.000
      306 JAYME SANTANA                      MA PSDB    25  298   0.916 306.500
      307 PAULO FEIJO                        RJ PSDB     5  358   0.986 306.500
      308 EDSON SILVA                        CE PSDB    12  253   0.953 311.000
      309 ADELSON RIBEIRO                    SE PSDB    35  377   0.907 311.000
      310 OLAVIO ROCHA                                   2  157   0.987 311.000
      311 CIPRIANO CORREIA                   RN PSDB    14  312   0.955 311.000
      312 CECI CUNHA                         AL PSDB    19  344   0.945 311.000
      313 JOSE TELES                                    25  133   0.812 311.000
      314 ALDIR CABRAL                                  12  161   0.925 311.000
      315 OSMANIO PEREIRA                    MG PSDB    13  319   0.959 315.000
      316 CARLOS ALBERTO                     RN PSDB     5  242   0.979 317.000
      317 ARTHUR VIRGILIO NETO               AM PMDB     4  207   0.981 317.000
      318 LUIZ FERNANDO                      AM  PPB    18  323   0.944 317.000
      319 BENITO GAMA                        BA  PFL    13  362   0.964 322.000
      320 NARCIO RODRIGUES                               9  203   0.956 322.000
      321 ADROALDO STRECK                    RS PSDB    15  383   0.961 322.000
      322 RENATO JOHNSSON                    PR PSDB    23  345   0.933 322.000
      323 DILSO SPERAFICO                                9  155   0.942 322.000
      324 RICARDO RIQUE                      PB PMDB     5  189   0.974 322.000
      325 MOACIR MICHELETTO                     PMDB    51  141   0.638 322.000
      326 LAURA CARNEIRO                     RJ  PFL    38  275   0.862 326.500
      327 FERNANDO TORRES                    AL PSDB    42  299   0.860 326.500
      328 MARCUS VICENTE                                 3  142   0.979 328.000
      329 JOSE EGYDIO                        RJ  PFL    22  208   0.894 329.000
      330 LUIZ MOREIRA                       BA  PFL    19  345   0.945 330.000
      331 ANTONIO AURELIANO                  MG PSDB     6  223   0.973 331.000
      332 MARCIO REINALDO MOREIRA                       17  160   0.894 332.000
      333 MARIO DE OLIVEIRA                  MG         38  307   0.876 334.000
      334 PEDRO CANEDO                       GO         52  294   0.823 334.000
      335 NAIR XAVIER LOBO                   GO PMDB    20  306   0.935 334.000
      336 OLAVO ROCHA                        PA PSDB    11  206   0.947 336.500
      337 DUILIO PISANESCHI                  SP  PTB    33  344   0.904 336.500
      338 LUCIANO PIZZATO                    PR         12  178   0.933 338.000
      339 DOLORES NUNES                          PFL    24  320   0.925 340.000
      340 CELSO RUSSOMANNO                   SP  PPB    20  347   0.942 340.000
      341 PHILEMON RODRIGUES                 MG  PTB    44  336   0.869 340.000
      342 ALBERICO CORDEIRO                  AL  PTB    39  246   0.841 344.000
      343 EXPEDITO JUNIOR                    RO  PFL    33  314   0.895 344.000
      344 AUGUSTO FARIAS                     AL  PFL    72  295   0.756 344.000
      345 NELSON TRAD                        MS  PTB    32  313   0.898 344.000
      346 FERNANDO GONCALVES                 RS  PPB    17  378   0.955 344.000
      347 FLAVIO PALMIER DA VEIGA            RJ PSDB     9  132   0.932 348.000
      348 LUCIANO PIZZATTO                               5  137   0.964 348.000
      349 ETEVALDA GRASSI DE MENEZES                     8  162   0.951 348.000
      350 ANIVALDO VALE                      PA PSDB    21  364   0.942 351.500
      351 JURANDYR PAIXAO                    SP  PPB    18  222   0.919 351.500
      352 DARCI COELHO                       TO  PFL     8  259   0.969 351.500
      353 LEOPOLDO BESSONE                   MG  PTB    68  314   0.783 351.500
      354 OSVALDO REIS                       TO         25  251   0.900 354.000
      355 JOSE LOURENCO                      BA  PFL     5  154   0.968 356.000
      356 LUIS BARBOSA                       RR  PPB    16  341   0.953 356.000
      357 HERCULANO ANGHINETTI               MG PSDB    23  311   0.926 356.000
      358 FRANCISCO HORTA                    MG  PFL    29  355   0.918 358.000
      359 ALCIONE ATHAYDE                    RJ  PPB    26  381   0.932 359.000
      360 JOSE CARLOS COUTINHO               RJ  PFL    12  176   0.932 361.000
      361 LAEL VARELLA                       MG  PFL     5  286   0.983 361.000
      362 PEDRO IRUJO                        BA PMDB    42  336   0.875 361.000
      363 ELTON ROHNELT                      RR  PFL    13  304   0.957 363.000
      364 AUGUSTINO FREITAS                  MT          4   67   0.940 364.500
      365 MOISES LIPNIK                      RR         24  246   0.902 364.500
      366 PAULO TITAN                        PA PMDB    38  212   0.821 368.500
      367 MARILU GUIMARAES                   MS  PFL    26  283   0.908 368.500
      368 JOSE CARLOS VIEIRA                 SC  PFL    14  359   0.961 368.500
      369 MICHEL TEMER                       SP PMDB    13  215   0.940 368.500
      370 HOMERO OGUIDO                      PR PMDB     9  219   0.959 368.500
      371 EULER RIBEIRO                      AM  PFL    19  298   0.936 368.500
      372 CORAUCI SOBRINHO                   SP  PFL    93  394   0.764 372.000
      373 ELISEU MOURA                       MA  PFL    25  247   0.899 373.000
      374 OSMIR LIMA                         AC  PFL    11  181   0.939 374.000
      375 CHICO DA PRINCESA                  PR  PTB    34  359   0.905 376.000
      376 OSVALDO COELHO                     PE  PFL     8  266   0.970 376.000
      377 OSVALDO BIOLCHI                    RS  PTB    29  341   0.915 376.000
      378 CARLOS MELLES                      MG  PFL    10  305   0.967 378.000
      379 ELISEU RESENDE                     MG  PFL    12  362   0.967 379.500
      380 MALULY NETTO                       SP  PFL    22  320   0.931 379.500
      381 REMI TRINTA                        MA         21  201   0.896 381.000
      382 LAMARTINE POSELLA                             10  156   0.936 383.500
      383 ARLINDO VARGAS                                 3  119   0.975 383.500
      384 JOSE REZENDE                                   9  106   0.915 383.500
      385 JOSE SANTANA DE VASCONCELLOS                   3  146   0.979 383.500
      386 INOCENCIO DE OLIVEIRA              PE  PFL     4  239   0.983 387.500
      387 ABELARDO LUPION                    PR  PFL    13  348   0.963 387.500
      388 JOSE TUDE                          BA  PTB     5  226   0.978 387.500
      389 LIMA NETTO                         RJ  PFL    22  349   0.937 387.500
      390 HUGO RODRIGUES DA CUNHA            MG  PPB    14  344   0.959 390.000
      391 MARCOS MEDRADO                     BA          5  142   0.965 391.000
      392 CARLOS MAGNO                       SE  PFL    20  360   0.944 392.500
      393 JULIO CESAR                        PI  PFL    13  306   0.958 392.500
      394 DAVI ALVES SILVA                   MA  PPB    14  203   0.931 394.000
      395 OSORIO ADRIANO                     DF  PFL     8  325   0.975 396.000
      396 JOSE CARLOS LACERDA                RJ PSDB    24  198   0.879 396.000
      397 JOSE JORGE                         PE  PFL    13  289   0.955 396.000
      398 BENEDITO DE LIRA                   AL         31  369   0.916 399.500
      399 JAIRO AZI                          BA  PFL     6  360   0.983 399.500
      400 AUGUSTO VIVEIROS                              44  371   0.881 399.500
      401 EFRAIM MORAIS                      PB  PFL     6  355   0.983 399.500
      402 JOAO IENSEN                        PR  PPB    19  279   0.932 403.000
      403 ANTONIO JOAQUIM ARAUJO             MA         33  232   0.858 403.000
      404 RAUL BELEM                         MG  PFL     6  245   0.976 403.000
      405 MAURO LOPES                        MG PMDB    24  333   0.928 405.500
      406 AFFONSO CAMARGO                    PR  PFL    11  294   0.963 405.500
      407 MAX ROSENMANN                      PR PSDB    42  235   0.821 407.500
      408 ARACELY DE PAULA                   MG  PFL     7  363   0.981 407.500
      409 JOSE BORBA                         PR  PTB    24  328   0.927 409.000
      410 FRANCISCO RODRIGUES                RR  PTB    19  287   0.934 410.000
      411 IBERE FERREIRA DE SOUZA            RN  PFL     0  188   1.000 411.000
      412 NAN SOUZA                          MA  PFL    19  232   0.918 412.000
      413 ALCESTE ALMEIDA                    RR PMDB    45  314   0.857 413.500
      414 CARLOS ALBERTO CAMPISTA            RJ  PFL     4  128   0.969 413.500
      415 MURILO PINHEIRO                    AP  PFL    13  325   0.960 416.000
      416 PAULO CORDEIRO                     PR  PFL    24  331   0.927 416.000
      417 LEUR LOMANTO                       BA  PFL     6  351   0.983 416.000
      418 CESAR BANDEIRA                     MA  PFL    11  321   0.966 421.000
      419 ADAUTO PEREIRA                     PB  PFL     6  320   0.981 421.000
      420 ALVARO GAUDENCIO NETO              PB  PFL    10  360   0.972 421.000
      421 HILARIO COIMBRA                    PA PSDB    23  334   0.931 421.000
      422 RAIMUNDO SANTOS                    PA  PFL    43  284   0.849 421.000
      423 COSTA FERREIRA                     MA  PFL    18  320   0.944 421.000
      424 JONIVAL LUCAS                      BA  PFL     5  346   0.986 421.000
      425 DJALMA CESAR                                   0   15   1.000 425.000
      426 CLAUDIO CHAVES                         PFL    15  170   0.912 428.000
      427 ADEMIR CUNHA                                   8  162   0.951 428.000
      428 ANTONIO GERALDO                               11  288   0.962 428.000
      429 INOCENCIO OLIVEIRA                             2  163   0.988 428.000
      430 JOAO RIBEIRO                       TO  PFL    36  156   0.769 428.000
      431 JOAO CARLOS BACELAR                BA  PFL     1  127   0.992 431.000
      432 ODILIO BALBINOTTI                  PR PSDB    30  295   0.898 436.000
      433 PAULO BAUER                        SC  PFL    72  350   0.794 436.000
      434 EUJACIO SIMOES                     BA          9  331   0.973 436.000
      435 LUIZ BRAGA                         BA  PFL     9  380   0.976 436.000
      436 JOAO MELLAO NETO                   SP  PFL     6  303   0.980 436.000
      437 MAGNO BACELAR                      MA  PFL    38  334   0.886 436.000
      438 MANOEL CASTRO                      BA  PFL    16  381   0.958 436.000
      439 ALEXANDRE CERANTO                  PR  PFL     7  270   0.974 436.000
      440 JAIME FERNANDES                    MA  PFL     4  379   0.989 436.000
      441 ATILA LINS                         AM  PFL     7  276   0.975 441.000
      442 PAULO GOUVEA                       SC  PFL    20  381   0.948 442.500
      443 PAULO LIMA                             PFL    20  254   0.921 442.500
      444 PEDRO NOVAIS                                  11  133   0.917 444.000
      445 ANTONIO DOS SANTOS                 CE  PFL    17  234   0.927 445.000
      446 FELIX MENDONCA                     BA  PTB    10  375   0.973 446.000
      447 PAULO BORNHAUSEN                   SC  PFL    11  321   0.966 449.500
      448 CLAUDIO CAJADO                     BA  PFL     5  376   0.987 449.500
      449 PAES LANDIM                        PI  PFL    11  289   0.962 449.500
      450 MUSSA DEMES                        PI  PFL    13  298   0.956 449.500
      451 JOSE ROCHA                         BA  PFL     6  386   0.984 449.500
      452 JOSE CARLOS ALELUIA                BA  PFL     8  359   0.978 449.500
      453 HERACLITO FORTES                   PI PMDB    18  334   0.946 454.000
      454 MAURO FECURY                       MA  PFL    11  173   0.936 454.000
      455 JAIRO CARNEIRO                     BA  PFL     6  364   0.984 454.000
      456 AROLDO CEDRAZ                      BA  PFL     4  355   0.989 456.000
      457 ALBERTO SILVA                      PI PMDB    11  294   0.963 457.000
      458 MENDONCA FILHO                     PE  PFL    10  353   0.972 458.000
      459 JOSE MENDONCA BEZERRA              PE  PFL     5  311   0.984 459.500
      460 JAIME MARTINS                      MG  PFL    19  296   0.936 459.500
      461 LUIS EDUARDO                       BA  PFL     2  159   0.987 461.000
      462 PEDRINHO ABRAO                     GO  PTB    10  243   0.959 462.000
      463 EUDORO PEDROZA                                 5   61   0.918 463.000
      464 AROLDE DE OLIVEIRA                 RJ  PFL    11  308   0.964 464.500
      465 CIRO NOGUEIRA                      PI  PFL    15  345   0.957 464.500
      466 RICARDO BARROS                     PR  PPB    20  284   0.930 466.000
      467 PEDRO CORREA                       PE  PPB    18  332   0.946 467.500
      468 CARLOS DA CARBRAS                  AM  PPB     7  175   0.960 467.500
      469 JOSE JANENE                        PR         28  325   0.914 470.000
      470 JOAO MENDES                        RJ  PPB    27  329   0.918 470.000
      471 MARQUINHO CHEDID                   SP         13  262   0.950 470.000
      472 ANTONIO JORGE                      TO  PFL    18  354   0.949 472.000
      473 BASILIO VILLANI                    PR PSDB    14  285   0.951 473.500
      474 RICARDO IZAR                       SP  PPB    18  348   0.948 473.500
      475 DELFIM NETTO                       SP  PPB    36  277   0.870 475.500
      476 NELSON MARQUEZELLI                 SP  PTB    19  334   0.943 475.500
      477 BETO MANSUR                        SP  PPB     5  150   0.967 477.000
      478 PAUDERNEY AVELINO                  AM  PFL    10  297   0.966 478.000
      479 HUGO BIEHL                         SC  PPB    34  355   0.904 479.000
      480 FLAVIO DERZI                       MS         23  259   0.911 480.000
      481 ANTONIO UENO                       PR  PFL    10  283   0.965 481.500
      482 MARCIO MOREIRA                     MG         19  227   0.916 481.500
      483 LAPROVITA VIEIRA                   RJ         35  310   0.887 483.000
      484 ANIBAL GOMES                       CE PSDB    29  345   0.916 485.000
      485 NEWTON CARDOSO                     MG         38  191   0.801 485.000
      486 JOSE RESENDE                       MG  PPB     7  238   0.971 485.000
      487 EURICO MIRANDA                     RJ  PPB    21  309   0.932 491.000
      488 CARLOS CAMURCA                     RO         24  147   0.837 491.000
      489 JOSE TELLES                        SE  PPB    40  211   0.810 491.000
      490 ARI MAGALHAES                      PI  PPB    28  241   0.884 491.000
      491 AUGUSTO NARDES                     RS  PPB    58  352   0.835 491.000
      492 ARY VALADAO                            PPB     2   73   0.973 491.000
      493 ODELMO LEAO                        MG         16  388   0.959 491.000
      494 NELSON MEURER                      PR         24  355   0.932 491.000
      495 JULIO REDECKER                     RS  PPB    54  306   0.824 491.000
      496 NEY LOPES                          RN  PFL    12  306   0.961 496.000
      497 BENEDITO GUIMARAES                 PA  PPB    21  304   0.931 498.500
      498 JOAO PIZZOLATTI                    SC  PPB    45  352   0.872 498.500
      499 MARIA VALADAO                      GO  PTB    26  305   0.915 498.500
      500 MARIO CAVALLAZZI                   SC  PPB    38  344   0.890 498.500
      501 FAUSTO MARTELLO                    SP  PPB    30  262   0.885 501.000
      502 DILCEU SPERAFICO                   PR         38  388   0.902 503.000
      503 ENIVALDO RIBEIRO                   PB  PPB    12  317   0.962 503.000
      504 BETINHO ROSADO                     RN  PFL    37  325   0.886 503.000
      505 FRANCISCO DORNELLES                RJ  PPB     8  120   0.933 505.000
      506 GERSON PERES                       PA  PPB    28  340   0.918 506.000
      507 JORGE WILSON                       RJ PMDB    27  354   0.924 507.500
      508 FELIPE MENDES                      PI  PPB    20  370   0.946 507.500
      509 NEIF JABUR                         MG PMDB    14  102   0.863 509.000
      510 IBRAHIM ABI-ACKEL                  MG  PPB    43  333   0.871 510.000
      511 CUNHA BUENO                        SP  PPB    73  232   0.685 511.000
      512 CLEONANCIO FONSECA                 SE PMDB    66  263   0.749 512.000
      513 ADHEMAR DE BARROS FILHO            SP  PPB    47  232   0.797 513.000
      514 FRANCISCO SILVA                               56  308   0.818 514.000
      515 JACKSON PEREIRA                    CE PSDB     0   52   1.000 515.000
      516 EMILIO ASSMAR                                 60  164   0.634 516.000
      517 DILSON SPERAFICO                   MS PSDB    28  212   0.868 517.000
      518 AGNALDO TIMOTEO                    RJ  PDT    17  178   0.904 518.000
    
    In two dimensions the PERF21.DAT should look something like this:
     08 MAY       2003  13.36.09.50.
     RANDOM NUMBER SEED     59800
    BRAZIL2A.TXT                                                    
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING                       
        2  420   20   43    2    1   10 0.005
    (43a1,3600I1)                                                   
    (I5,1X,43A1,2I5,50F8.3)                                         
     ******************************************************************************
      1 ROLL CALLS   2   13483  139474  0.09667  0.90333  0.63346           0.00000
        LEGISLATORS  2   12103  139474  0.08678  0.91322  0.67098  0.00000
      2 ROLL CALLS   2   11869  139474  0.08510  0.91490  0.67734           0.99271
        LEGISLATORS  2   11655  139474  0.08356  0.91644  0.68316  0.95625
      3 ROLL CALLS   2   11581  139474  0.08303  0.91697  0.68517           0.99325
        LEGISLATORS  2   11499  139474  0.08245  0.91755  0.68740  0.98592
      4 ROLL CALLS   2   11459  139474  0.08216  0.91784  0.68849           0.99876
        LEGISLATORS  2   11427  139474  0.08193  0.91807  0.68936  0.99609
      5 ROLL CALLS   2   11411  139474  0.08181  0.91819  0.68979           0.99852
        LEGISLATORS  2   11387  139474  0.08164  0.91836  0.69044  0.99597
      6 ROLL CALLS   2   11380  139474  0.08159  0.91841  0.69063           0.99865
        LEGISLATORS  2   11366  139474  0.08149  0.91851  0.69102  0.98805
      7 ROLL CALLS   2   11354  139474  0.08141  0.91859  0.69134           0.99930
        LEGISLATORS  2   11343  139474  0.08133  0.91867  0.69164  0.99432
      8 ROLL CALLS   2   11337  139474  0.08128  0.91872  0.69180           0.99917
        LEGISLATORS  2   11312  139474  0.08110  0.91890  0.69248  0.99245
      9 ROLL CALLS   2   11309  139474  0.08108  0.91892  0.69256           0.99833
        LEGISLATORS  2   11301  139474  0.08103  0.91897  0.69278  0.99956
     10 ROLL CALLS   2   11298  139474  0.08100  0.91900  0.69286           0.99964
        LEGISLATORS  2   11274  139474  0.08083  0.91917  0.69352  0.99946
     11 ROLL CALLS   2   11271  139474  0.08081  0.91919  0.69360           0.99951
        LEGISLATORS  2   11264  139474  0.08076  0.91924  0.69379  0.99946
     12 ROLL CALLS   2   11259  139474  0.08072  0.91928  0.69392           0.99767
        LEGISLATORS  2   11254  139474  0.08069  0.91931  0.69406  0.99926
     13 ROLL CALLS   2   11252  139474  0.08067  0.91933  0.69411           0.99674
        LEGISLATORS  2   11244  139474  0.08062  0.91938  0.69433  0.99971
     14 ROLL CALLS   2   11242  139474  0.08060  0.91940  0.69439           0.99957
        LEGISLATORS  2   11235  139474  0.08055  0.91945  0.69458  0.99886
     15 ROLL CALLS   2   11235  139474  0.08055  0.91945  0.69458           0.99960
        LEGISLATORS  2   11232  139474  0.08053  0.91947  0.69466  0.99946
     16 ROLL CALLS   2   11231  139474  0.08052  0.91948  0.69469           0.99985
        LEGISLATORS  2   11227  139474  0.08050  0.91950  0.69479  0.99982
     17 ROLL CALLS   2   11222  139474  0.08046  0.91954  0.69493           0.99969
        LEGISLATORS  2   11197  139474  0.08028  0.91972  0.69561  0.98847
     18 ROLL CALLS   2   11194  139474  0.08026  0.91974  0.69569           0.99980
        LEGISLATORS  2   11191  139474  0.08024  0.91976  0.69577  0.99966
     19 ROLL CALLS   2   11191  139474  0.08024  0.91976  0.69577           0.99994
        LEGISLATORS  2   11191  139474  0.08024  0.91976  0.69577  0.99989
     20 ROLL CALLS   2   11096  139474  0.07956  0.92044  0.69836           0.99640
        LEGISLATORS  2   11067  139474  0.07935  0.92065  0.69914  0.99402
     MEAN VOLUME LEG.   0.0337   0.0642
     MACHINE PREC.   2   11058  139474  0.07928  0.92072  0.69939
     MACHINE PREC.   2   11058  139474  0.07928  0.92072  0.69939
                          13.36.09.56.
     ELAPSED TIME OF JOB  13.43.58.48.
    The percent correctly classified is 92.1% (0.92072) and the APRE is .699 (0.69939). In the two-dimensional plot below the party tokens are:
    
          w PT   = Worker's Party
          p PPB  = Brazilian Progressive Party
          d PDT  = Democratic Labor Party
          b PMDB = Party of the Brazilian Democratic Movement
          L PFL  = Party of the Liberal Front
          s PSDB = Party of Brazilian Social Democracy   
          t PTB  = Brazilian Labor Party
          u      = Unknown


  7. Example Four: California Assembly 1997-98
  8. This example is courtesy of Jeff Lewis.

    Control Card File for California Assembly 1997-98 (PERFSTRT.CALIFORNIA) (Rename this to PERFSTRT.DAT)

    California Assembly Roll Call Data for 1997-98 (CA1997.TXT)

    The PERF21.DAT should look something like this in one dimension:
     11 MAY       2003  15.28.08.51.
     RANDOM NUMBER SEED     51200
    CA1997.TXT                                                      
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF 1997 CA LEGISLATURE
        1 1569   20   33    4    1   10 0.005
    (33A1,3900I1)                                                   
    (I5,1X,33A1,2I5,50F8.3)                                         
     ******************************************************************************
      1 ROLL CALLS   1    5015  115044  0.04359  0.95641  0.80876
      2 LEGISLATORS  1    4984  115044  0.04332  0.95668  0.80994  0.99906
      3 ROLL CALLS   1    4945  115044  0.04298  0.95702  0.81143
      4 LEGISLATORS  1    4943  115044  0.04297  0.95703  0.81150  0.99936
      5 ROLL CALLS   1    4920  115044  0.04277  0.95723  0.81238
      6 LEGISLATORS  1    4919  115044  0.04276  0.95724  0.81242  0.99973
      7 ROLL CALLS   1    4916  115044  0.04273  0.95727  0.81253
      8 LEGISLATORS  1    4916  115044  0.04273  0.95727  0.81253  0.99990
                          15.28.08.62.
     ELAPSED TIME OF JOB  15.28.13.07.
    The correct classification is a very high 95.7% (0.95727) with an APRE of .813 (0.81253). This legislature is essentially unidimensional. Further evidence of this is shown by the skree plot of the eigenvalues of the double-centered agreement score matrix. The second eigenvalue is very small and only slightly higher than the 3rd.



    Below is the rank ordering from Left to Right. The the red D's are Democrats and the blue R's are Republicans. There is no overlap of the two political parties.
        1 MIGDEN      CAROLE        D  37 1510   0.975   1.000
        2 ARONER      DION          D  35 1464   0.976   2.000
        3 MARTINEZ    DIANE         D 152 1441   0.895   3.000
        4 KUEHL       SHEILA        D  30 1495   0.980   4.000
        5 VILLARAIGOSAANTONIO R.    D  46 1491   0.969   5.000
        6 BOWEN       DEBRA         D 107 1477   0.928   6.000
        7 ORTIZ       DEBORAH V.    D  30 1501   0.980   7.000
        8 FLOYD       RICHARD       D 142 1031   0.862   8.000
        9 ESCUTIA     MARTHA M.     D  30 1504   0.980   9.000
       10 SHELLEY     KEVIN         D  13 1508   0.991  10.000
       11 KNOX        WALLY         D  25 1471   0.983  11.000
       12 SWEENEY     MICHIEAL      D  44 1508   0.971  12.000
       13 STROM-MARTINVIRGINIA      D  27 1478   0.982  13.000
       14 HONDA       MIKE          D  28 1514   0.982  14.000
       15 FIGUEROA    LIZ           D  15 1450   0.990  15.000
       16 PERATA      DON           D  25 1516   0.984  16.000
       17 MAZZONI     KERRY         D  44 1516   0.971  17.500
       18 MURRAY      KEVIN         D  33 1402   0.976  17.500
       19 NAPOLITANO  GRACE F.      D  21 1510   0.986  19.000
       20 WAYNE       HOWARD        D  36 1452   0.975  20.000
       21 LEMPART     TED           D  24 1485   0.984  21.000
       22 TORLAKSON   TOM           D  15 1536   0.990  22.000
       23 BROWN       VALERIE       D  33 1480   0.978  23.000
       24 DAVIS       SUSAN         D  11 1464   0.992  24.000
       25 KEELEY      FRED          D  20 1530   0.987  25.000
       26 THOMSON     HELEN         D  28 1516   0.982  26.000
       27 ALQUIST     ELAINE WHITE  D  15 1510   0.990  27.000
       28 WILDMAN     SCOTT         D  45 1462   0.969  28.500
       29 CALDERA     LOUIS         D  85  797   0.893  28.500
       30 WASHINGTON  CARL          D  40 1419   0.972  30.500
       31 SCOTT       JACK          D  36 1425   0.975  30.500
       32 GALLEGOS    MARTIN        D  15 1468   0.990  32.000
       33 CARDENAS    TONY          D   9 1466   0.994  33.000
       34 BUSTAMANTE  CRUZ M.       D   4 1504   0.997  34.000
       35 HERTZBERG   ROBERT M.     D  11 1504   0.993  35.000
       36 DUCHENY     DENISE MORENO D  16 1432   0.989  36.000
       37 HAVICE      SALLY         D 125 1491   0.916  37.000
       38 VINCENT     EDWARD        D  14 1491   0.991  38.000
       39 BACA        JOE           D  24 1505   0.984  39.000
       40 WRIGHT      RODERICK      D  58 1450   0.960  40.000
       41 PAPAN       LOU           D  28 1428   0.980  41.000
       42 MACHADO     MICHAEL J.    D  16 1394   0.989  42.000
       43 CARDOZA     DENNIS A.     D  32 1461   0.978  43.000
       44 CUNNEEN     JIM           R  62 1473   0.958  44.000
       45 FRUSETTA    PETER         R  66 1391   0.953  45.000
       46 KUYKENDALL  STEVEN T.     R  35 1411   0.975  46.000
       47 FIRESTONE   BROOKS        R  46 1365   0.966  47.000
       48 MORRISSEY   JIM           R  68 1481   0.954  48.000
       49 PACHECO     ROD           R 115 1410   0.918  49.000
       50 PRENTER     ROBERT M.     R  72 1345   0.946  50.000
       51 AGUIAR      FRED          R  66 1470   0.955  51.000
       52 GOLDSMITH   JAN           R 119 1397   0.915  52.000
       53 RICHTER     BERNIE        R 104 1099   0.905  53.000
       54 TAKASUGI    NAO           R  75 1472   0.949  54.000
       55 GRANLUND    BRETT         R 145 1512   0.904  55.000
       56 LEACH       LYNNE C.      R  85 1397   0.939  56.000
       57 BATTIN      JIM           R  81 1451   0.944  57.000
       58 CAMPBELL    BILL          R 113 1476   0.923  58.000
       59 WOODS       TOM           R 115 1371   0.916  59.000
       60 MARGETT     BOB           R  62 1362   0.954  60.000
       61 ASHBURN     ROY           R  64 1459   0.956  61.000
       62 BORDONARO   TOM J.        R 102 1490   0.932  62.000
       63 MILLER      GARY          R  71 1491   0.952  63.000
       64 BOWLER      LARRY         R 117 1464   0.920  64.000
       65 ALBY        BARBARA       R  67 1286   0.948  65.000
       66 HOUSE       GEORGE        R 148 1454   0.898  66.000
       67 POOCHIGIAN  CHARLES S.    R  35 1453   0.976  67.000
       68 BREWER      MARILYN C.    R 120 1475   0.919  68.000
       69 MARROW      BILL          R 107 1486   0.928  69.000
       70 LEONARD     BILL          R 151 1468   0.897  70.000
       71 RUNNER      GEORGE        R  82 1384   0.941  71.000
       72 OLBERG      KEITH         R  46 1353   0.966  72.000
       73 THOMPSON    BRUCE         R 157 1360   0.885  73.000
       74 KALOOGIAN   HOWARD        R  65 1361   0.952  74.000
       75 OLLER       THOMAS (RICO) R  49 1477   0.967  75.000
       76 ACKERMAN    RICHARD (DICK)R 104 1550   0.933  76.000
       77 BAUGH       SCOTT         R  90 1465   0.939  77.000
       78 PRINGLE     CURT          R  91 1335   0.932  78.000
       79 BALDWIN     STEVE         R  83 1400   0.941  79.000
       80 MCCLINTOCK  TOM J.        R 114 1493   0.924  80.000
    PERF21.DAT for the California Assembly in two dimensions should look something like this:
     11 MAY       2003  15.54.16.54.
     RANDOM NUMBER SEED     87400
    CA1997.TXT                                                      
    NON-PARAMETRIC MULTIDIMENSIONAL UNFOLDING OF 1997 CA LEGISLATURE
        2 1569   20   33    4    1   10 0.005
    (33A1,3900I1)                                                   
    (I5,1X,33A1,2I5,50F8.3)                                         
     ******************************************************************************
      1 ROLL CALLS   2    4498  115044  0.03910  0.96090  0.82847           0.00000
        LEGISLATORS  2    4474  115044  0.03889  0.96111  0.82939  0.00000
      2 ROLL CALLS   2    4409  115044  0.03832  0.96168  0.83187           0.99637
        LEGISLATORS  2    4398  115044  0.03823  0.96177  0.83228  0.99958
      3 ROLL CALLS   2    4369  115044  0.03798  0.96202  0.83339           0.99877
        LEGISLATORS  2    4367  115044  0.03796  0.96204  0.83347  0.99980
      4 ROLL CALLS   2    4354  115044  0.03785  0.96215  0.83396           0.99922
        LEGISLATORS  2    4353  115044  0.03784  0.96216  0.83400  0.99998
      5 ROLL CALLS   2    4347  115044  0.03779  0.96221  0.83423           0.99922
        LEGISLATORS  2    4345  115044  0.03777  0.96223  0.83431  0.99994
      6 ROLL CALLS   2    4342  115044  0.03774  0.96226  0.83442           0.99792
        LEGISLATORS  2    4341  115044  0.03773  0.96227  0.83446  0.99999
      7 ROLL CALLS   2    4332  115044  0.03766  0.96234  0.83480           0.99929
        LEGISLATORS  2    4331  115044  0.03765  0.96235  0.83484  1.00000
      8 ROLL CALLS   2    4328  115044  0.03762  0.96238  0.83495           0.99901
        LEGISLATORS  2    4328  115044  0.03762  0.96238  0.83495  1.00000
      9 ROLL CALLS   2    4328  115044  0.03762  0.96238  0.83495           0.99967
        LEGISLATORS  2    4328  115044  0.03762  0.96238  0.83495  1.00000
     10 ROLL CALLS   2    4325  115044  0.03759  0.96241  0.83507           0.99891
        LEGISLATORS  2    4325  115044  0.03759  0.96241  0.83507  1.00000
     11 ROLL CALLS   2    4325  115044  0.03759  0.96241  0.83507           0.99901
        LEGISLATORS  2    4324  115044  0.03759  0.96241  0.83511  1.00000
     12 ROLL CALLS   2    4323  115044  0.03758  0.96242  0.83514           0.99922
        LEGISLATORS  2    4323  115044  0.03758  0.96242  0.83514  1.00000
     13 ROLL CALLS   2    4323  115044  0.03758  0.96242  0.83514           0.99890
        LEGISLATORS  2    4323  115044  0.03758  0.96242  0.83514  1.00000
     14 ROLL CALLS   2    4321  115044  0.03756  0.96244  0.83522           0.99875
        LEGISLATORS  2    4321  115044  0.03756  0.96244  0.83522  1.00000
     15 ROLL CALLS   2    4321  115044  0.03756  0.96244  0.83522           0.99896
        LEGISLATORS  2    4321  115044  0.03756  0.96244  0.83522  1.00000
     16 ROLL CALLS   2    4321  115044  0.03756  0.96244  0.83522           0.99840
        LEGISLATORS  2    4321  115044  0.03756  0.96244  0.83522  1.00000
     17 ROLL CALLS   2    4320  115044  0.03755  0.96245  0.83526           0.99927
        LEGISLATORS  2    4320  115044  0.03755  0.96245  0.83526  1.00000
     18 ROLL CALLS   2    4319  115044  0.03754  0.96246  0.83530           0.99922
        LEGISLATORS  2    4319  115044  0.03754  0.96246  0.83530  1.00000
     19 ROLL CALLS   2    4319  115044  0.03754  0.96246  0.83530           0.99894
        LEGISLATORS  2    4319  115044  0.03754  0.96246  0.83530  1.00000
     20 ROLL CALLS   2    4178  115044  0.03632  0.96368  0.84067           0.99622
        LEGISLATORS  2    4178  115044  0.03632  0.96368  0.84067  1.00000
     MEAN VOLUME LEG.   0.0024   0.0013
     MACHINE PREC.   2    4178  115044  0.03632  0.96368  0.84067
     MACHINE PREC.   2    4178  115044  0.03632  0.96368  0.84067
                          15.54.16.60.
     ELAPSED TIME OF JOB  15.59.13.70.
    The correct classification is now 96.4% (0.96368) with an APRE of 0.84067. The increase of .641% in correct classification was paid for by increasing the number of parameters from 80+1569 = 1649 in one dimension to (80+1569)*2 = 3298 in two dimensions. In other words increasing the correct classification by 4916-4178 = 738 was paid for by adding 1649 parameters -- more than two parameters for each additional correctly classified choice!

    Below is a two-dimensional plot of the California Assembly Representatives. The R tokens are Republicans and the D tokens are Democrats.





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