# 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:

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

OC in R Examples (R programs and datasets)

## Examples

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

## Example One: The 107th Senate.

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 Source Code (FORTRAN -- PERFL_2006.FOR) -- this can be compiled in gfortran

Control Card File (PERFSTRT_2006.DAT)

107th Senate Roll Call Data (SEN107KH.ORD)

and place them in the same folder on a WINTEL machine. PERFSTRT_2006.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)```
• The first line is the name of the roll call data file,
• the second line is the title, the
• third line, in order, is the number of dimensions (1), the number of roll calls (633), the number of iterations (20 -- leave as is), the number of "characters" to read off the front of each legislator's record (36 for Roll Call Data -- leave as is -- this can be set as high as 99 depending upon how you have organized your data -- contact me kpoole@ucsd.edu if you have questions about how to do this), the record number of a Senator that you believe is on the "Left" (this just sets "liberal" on the left -- lower ranks or negative values on the first dimension if the scaling is in two or more dimensions -- and "conservative" on the right), and the record number of a Senator that you want to be "Up" on the second dimension (this feature is handy if you want, for example, Southern Democrats to be "Up" or positive on the second dimension -- in other countries, this could be another salient division such as religion). In the 107th 10 is Senator Boxer (D-CA) and 18 is Senator Graham (D-FL). The last two numbers on the line are the minimum number of roll calls for a legislator to be included in the scaling -- 10 in this instance -- and the minimum proportion on the minority side of a roll call for the roll call to be included in the scaling -- 0.005 or 0.5% in this instance. In the Senate, this will select all roll call votes of 99-1 (minority proportion of .01) to 50-50 (minority proportion of .50) and in the House all roll calls votes of 432-3 (minority proportion of .007) to 218-217 (minority proportion of .499).

Technically, the third line is seen by the program as:
`0000100633000200003600010000180001000.005`
This spacing must not be changed! If you want to analyze 1221 roll calls in 3 dimensions with everything else the same the line must look like this:
`    3 1221   20   36   10   18   10 0.005`
• The fourth line is the format of the input roll call matrix.
• The fifth and last line is the format for the coordinate output file (leave as is). Note that the 36 appears in both format statements! The program writes out the front portion of each legislator's record in the legislator output coordinate file. If this number is changed -- see example 3 below -- change the number in both format statements.

At the command line type

PERFL_2006

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 meetthe cutoff criteria in PERFSTRT_2006.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, thetotal 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 agreementscore matrix (second column).  These can be used to make a Skree Plot andare 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_2006.DAT and run PERFL_2006 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.

## Example Two: The 95th House.

Control Card File for 95th House (PERFSTRT.H95) (Rename this to PERFSTRT_2006.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     37600HOU95KH.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.

## Example Three: The Brazilian Legislature 1995-98

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_2006.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     38000BRAZIL2A.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     59800BRAZIL2A.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```

## Example Four: California Assembly 1997-98

This example is courtesy of Jeff Lewis.

Control Card File for California Assembly 1997-98 (PERFSTRT.CALIFORNIA) (Rename this to PERFSTRT_2006.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     51200CA1997.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     87400CA1997.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.