Weighted Vote 2013

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					                                 CITY OF HUDSON

                             in the State of New York




                               COMMON COUNCIL




                     Weighted Voting Reapportionment




                                    January 2013




L. Papayanopoulos, Reapportionment Consultant, 31 Burnett T., West Orange, New Jersey, 07052


                                      (973) 353-5828




                                             1
                               CITY OF HUDSON

                           in the State of New York



                              COMMON COUNCIL



                   Weighted Voting Reapportionment


 CONTENTS:


 Introduction                                                                             3

 Objectives                                                                               5

 Special Majorities                                                                       7

 The Proposed Weighted Voting Plans                                                       8

 Summary of Tables                                                                        10

 Detailed Tables                                                                          11

 References




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013   2
                                     CITY OF HUDSON

                                 in the State of New York

                                    COMMON COUNCIL



                         Weighted Voting Reapportionment


                                     INT RODUCT ION

The five Hudson City Wards range in population from 725 to 2,485
persons with an average Ward population of 1,280.6. In the Common
Council, each Ward is represented by two Aldermen. The President of
the Common Council, the eleventh member, represents all five Hudson
City Wards. The population used in this analysis is as follows.

                                                                  % of Total
                    2010                  Persons per                                 Relative to
   Ward                                                              per
                  population               Alderman                                    average
                                                                  Alderman
    1.                 770                     385                    6%                    0.60

    2.                1,281                   640.5                  10 %                   1.00

    3.                1,142                    571                    9%                    0.89

    4.                 725                    362.5                   6%                    0.57

    5.                2,485                  1242.5                  19 %                   1.94

   Total:             6,403

 Average:            1280.6                   640.3

Populations based on the decennial census, adjusted to exclude institutional inmates and to
reconcile overlapping election districts.




      City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013     3
       The population percentages of three Wards (1, 2, and 4), are
virtually unaltered from those of the 2000 Census reapportionment
cycle. On the other hand, the representation per Alderman in Ward 3
decreased from 13 % (2000) to 9 % (2010) and in Ward 5 increased
from 16 % (2000) to 19 % (2010). The change in Ward 3 is due, to a
large measure, to the removal of the institutional inmate population
from the Census figures of the Ward.
       Despite these shifts, the relative size of Hudson City
constituencies is by no means extreme by weighted voting standards.
As the rightmost column in the above table reveals, the largest Ward is
less than twice the average and the smallest is more than half (60 %)
of the average. It is not unusual to find even more disparate ratios in
weighted voting settings elsewhere in New York. Indeed, it is this kind
of variability that makes weighted voting a stabilizing and practical
approach for local and municipal governments.
      In view of this population disparity among districts, weighted
voting is applied to equalize the effective, a priori voting power of
individual constituents.
      As students of weighted voting have long recognized, the voting
power of a voting member is distinct from that member’s voting weight
(the number of votes allotted to that member). 1 While other methods
of reapportionment may modify geographic lines in order to equalize
populations, weighted voting reapportionment endeavors to modify
voting weights in order to equalize voting power relative to population.
       The objective of the analysis described in this report is to obtain
fair voting plans, i.e. voting plans that meet the One Man-One Vote
principle. The courts have deemed adjusted weighted voting to be fair
and equitable when it attains close alignment between the voting
power of legislative members’ and their constituency fraction (as
closely as practicable). 2

1 See Banzhaf, J.F., III, "Weighted Voting Doesn't Work: A Mathematical Analysis,"
   Rutgers L. Rev., Vol. 19, 1965 and Imrie, R.W., "The Impact of the Weighted Vote
   on Representation in Municipal Governing Bodies of New York State," Ann. of the
   N.Y. Acad.of Sci., Vol. 219, 1973, pp. 183-191.
2 Iannucci vs. Board of Supervisors of Washington County and Saratogian, Inc. vs.
   Board of Supervisors of Saratoga County, 20 N.Y. 2d 244, 299 NE 2d 195, 282
   NYS 2d 502, 1967. Also, Dobish vs. Board of Supervisors of Wayne County, 279
   NYS 2d 565, 282 NYS 2d 791, 1967 and Slater vs. Board of Supervisors of
   Cortland County, 330 NYS 2d 947, 346 NYS 2d 185, 42 A.D. 2d 795, 1972-1973.




     City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013   4
       In this report, voting plans are "adjusted" so as to satisfy this
definition of fair representation. They have been selected from among
nearly one million that were generated for this study. Should one of
the adjusted plans be adopted, it will render each member of the
Council 3 able to affect decisions at a rate very nearly proportional to
the size of his/her constituency.
      Computer methods of legislative apportionment have been used
since the Supreme Court's landmark decisions of the nineteen sixties.
4 The weighted voting (re)apportionment methodology employed here

has been tested and reaffirmed in numerous New York cases, since
then, including the previous reapportionments of Hudson City.
      The Court adopted a simple criterion for rating a weighted voting
plan objectively:
      "Ideally, in any weighted voting plan, it should be
mathematically possible for every member of the legislative body to
cast the decisive vote on legislation in the same ratio which the
population of the constituency bears to the total population ... This is
what is meant by the one man-one vote principle as applied to
weighted voting plans for municipal governments ..." 5
      This set the standard by which a weighted voting plan is
appraised. A plan is fair and acceptable if the discrepancies between
population and mathematical voting power are as small as possible.

                                       OBJECT IVES

       Several objectives guide the present analysis. These are to:
       A.          Minimize discrepancies between population and
                   mathematical voting power,
       B.          Minimize the difference between the voting weights of
                   Aldermen from the same Ward, and
       C.          Minimize the total vote (and consequently to magnitude
                   of individual votes) to simplify tallying of votes.

3 In a mathematical sense, of course. The definition of voting power is based on the
   prior assumption that all voting outcomes are equally probable.
4 In particular, Baker vs. Carr 369 U.S. 186, 1962 and Gray vs. Sanders 372 U.S.
   368, 1963.
5 See Iannucci vs. Board, note 1, supra.




     City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013   5
      Meeting any one of these objectives is mathematically
challenging. Meeting two or more of them simultaneously, increases
computational difficulties exponentially.
      Objective (A) is paramount; it is dictated by the cited court
decisions. Objective (A) is met by all plans included in this report.
       A multimember plan’s egality is the degree to which members of
Wards have equal votes. For weighted voting plans of Hudson City,
the degree of egality may range between 0 and 5. Objective (B) is
desirable but impedes objective (A) as stated earlier; minimizing the
difference between the voting weights in the same Ward is related to
maximizing egality.
       Objective (C) leads to voting plans that are easier to use but it
also gets in the way of meeting objectives (A) and (B).
      In searching for a voting schema with minimal discrepancies,
voting weights are adjusted in order to reduce discrepancies. Vote
assignments derived through such a process are called adjusted plans.
An adjusted plan with minimal discrepancies is deemed to be
(constitutionally) fair. Barring considerations that may render it unfair
in other ways, it is said to satisfy one man-one vote and meets objective
(A).
      The present method of allocating population numbers to the
members of the Council and obtaining fair adjusted plans parallels the
procedure used in the 2005 study. Each of the 10 Aldermen is
assigned one half of their respective Ward’s population. In the plans
included below, voting weights are allocated so as to minimize the
discrepancy between the mathematical voting power afforded to each
Alderman and the assigned population. Voting power and population
are compared in percentages.
      In the tables below, the rightmost column shows the percent
discrepancy between every Council member's percent voting power and
percent population measured by means of the formula


               Discrepancy =100            ( Power - Population).
                                                Population

      This formula was proposed by this author, approved by the
Court and used in the Iannucci (1967) and subsequent cases. For a




     City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013   6
given set of voting weights, it is the percent difference between what a
legislator's mathematical voting strength is and what it should be
ideally.
      Discrepancy figures for the President of the Council are not
meaningful and are omitted. The President's voting weight is set to be
approximately one-eleventh of the total Council vote. In the analysis, it
is permitted to vary in order to meet the principal objective, namely, to
minimize the discrepancy between population and voting power of the
ten Aldermen.
       The plans derived to meet objective (B), have discrepancies of the
order of 4-5% which is within the acceptable range. Several alternate
plans with smaller discrepancies are presented. These are obtained
without strict adherence to objective (B). Should any of these be
implemented, the assignment of votes to the two Aldermen of the Ward
may be made on the basis of seniority or by agreement; for example, in
the latter case, the votes assigned to the two Aldermen may be
switched at half-term. Other protocols are also possible.
        Finally, some plans with smaller (individual and total votes) are
shown. These are viable and meet all of the objectives. The Council
may opt to stay with plans with votes in the vicinity of 2,020 to which
it is accustomed or adopt plans with lower votes for easier counting.

Special Majorities

      Under any given allocation of voting weights, the mathematical
voting power of members differs under different majority rules.
      In Slater v. Board of Supervisors of Cortland County the Court
states: "Ordinarily, a weighted voting plan applicable to a simple
majority vote of the County Legislature will not comply with acceptable
standards when matters need a two-thirds or three-fifths votes for
affirmative action. A legislator's voting power will differ when the votes
needed for affirmative action are increased above a simple majority. 6
      Consequently, weighted voting plans designed for a given
majority rule may be used under that majority rule only. If the
Legislature or Board needs to reach decisions under two-thirds, three-


6 See Slater vs. Board, note 2, supra.




      City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013   7
         quarters, or other special majority formulae then distinct weighted
         voting plans must be devised for use under each such majority rule.

         The Proposed Weighted Voting Plans

                Discrepancies associated with proportional weighted voting
         plans are minimized by adjusting the votes. The search for a fair plan
         often leads to optimal plans at various total vote levels, such as
         approximately 500 votes, 1000 votes, 2000, etc. At each level, the
         plans with the smallest discrepancies are selected.
                This process yields agreement between power and population
         comparable to that obtained for Hudson City under the 2000 census
         figures. All of the adjusted plans presented here (under each majority
         rule) are characterized by discrepancies of about 5 % (five percent) or
         less.
               The Council's task is to select one simple majority plan, one two-
         thirds majority plan, and one three-quarters majority plan for
         adoption. The Council may select and adopt a set of three plans such
         as the following. These plans are recommended because they are the
         closest we were able to construct to the Council’s current plans. These
         plans meet objectives (A) and (B).


                                           Primary Recommendation
  Id      Majority   Discr   4-A    4-B    I-A    I-B   3-A    3-B    2-A    2-B    Pres    5-A     5-B   Tot    Win

433642    simple     4.28    95     95     95     95    180    180    185    185    190     364     364   2028   1015

393259      2/3      3.69    105   105    108    108    161    161    187    187    199     352     352   2025   1350

433598      3/4      4.78    98     98    100    100    153    153    157    157    194     405     405   2020   1515


                The remaining plans presented in this report also meet the
         principal objective (A). Additionally, they meet objectives (B) and/or
         (C). The discrepancy levels of these plans are comparable to the ones
         presented in 2005.
                The Council may consider any of the alternatives in place of any
         or all to the above three. Plan 433645, for example, may substitute
         433642. The two are equivalent in every respect but plan 433645 has




              City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013     8
         smaller votes and may be simpler to use on a routine basis. Similarly,
         plans like 437887 (two-thirds) or 423364 (three quarters) may serve in lieu
         of 393259 or 433598.
               For purposes of comparison, the plans mentioned in the
         preceding paragraph may be summarized as follows.

                                    Valid Alternative Recommendation
  Id       Majority   Discr   4-A   4-B    I-A   I-B   3-A    3-B    2-A    2-B    Pres    5-A      5-B       Tot    Win

433645     simple     4.52    19     19    19    19    36     36     37     37      38      73      73        406    204

437887       2/3      3.69    22     22    22    22    34     34     39     39      44      73      73        424    283

423364       3/4      5.16    81     81    82    82    126    126    129    129    161     335      335       1667   1251


                   A tabulation of all proposed plans appears below.




              City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos -- January 2013         9
                      SUMMARY OF PROPOSED PLANS
                         (Detailed Tables Follow)

                               Simple Majority Plans
Plan Id   Majority Class     Total Vote     Majority Quota      Discrepancy      Egality
433645          1/2             406               204                  4.52%           5
366870          1/2             836               419                  1.88%           3
433626          1/2             2024              1013                 1.88%           4
433642          1/2             2028              1015                 4.28%           5
433644          1/2             2030              1016                 4.52%           5

                                  Two Thirds Plans
Plan Id   Majority Class     Total Vote     Majority Quota      Discrepancy      Egality
437887          2/3             424               283                  3.69%           5
437878          2/3             509               340                  2.02%           5
393219          2/3             843               562                  3.79%           5
393250          2/3             845               564                  1.45%           3
393216          2/3             1293              862                  3.79%           5
393259          2/3             2025              1350                 3.69%           5

                               Three Quarters Plans
Plan Id   Majority Class     Total Vote     Majority Quota      Discrepancy      Egality
433590          3/4             803               603                  1.29%           2
423354          3/4             1666              1250                 3.46%           3
423364          3/4             1667              1251                 5.16%           5
433598          3/4             2020              1515                 4.78%           5




  City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013       10
                 DETAILED COMPUTATION TABLES


      Simple, two-thirds, and three-quarters majorities




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   11
                               SIMPLE MAJORITY PLANS


                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting     Popul-     Discre-
         Ward                    Vote
                       ation            Combin-      Power       ation      pancy
                                          ations
           4-A                    19       128
                        725                          11.59%     11.32%         2.40%
           4-B                    19       128
           I-A                    19       128
                        770                          11.59%     12.03%      -3.59%
           I-B                    19       128
           3-A                    36       188
                       1142                          17.03%     17.84%      -4.52%
           3-B                    36       188
           2-A                    37       220
                       1281                          19.93%     20.01%      -0.39%
           2-B                    37       220
       President                  38       260
           5-A                    73       440
                       2485                          39.86%     38.81%         2.69%
           5-B                    73       440


      Ward totals      6403      368      2208         100%       100%
           Total Vote            406
        Needed to pass           204
          Plan: Hudson-2013-1/2-        433645         4.52     Egality    5
          Range of Discrepancies:         -4.52%       and       2.69%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013     12
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting     Popul-     Discre-
         Ward                   Vote
                       ation            Combin-      Power       ation      pancy
                                          ations
           4-A                   40        128
                        725                          11.43%     11.32%         0.93%
           4-B                   40        128
           I-A                   40        128
                        770                          12.14%     12.03%         0.97%
           I-B                   41        144
           3-A                   74        196
                       1142                          17.50%     17.84%      -1.88%
           3-B                   74        196
           2-A                   75        212
                       1281                          20.36%     20.01%         1.75%
           2-B                   76        244
       President                 80        252
           5-A                   148       432
                       2485                          38.57%     38.81%      -0.61%
           5-B                   148       432


      Ward totals      6403      756      2240         100%       100%
           Total Vote            836
        Needed to pass           419
          Plan: Hudson-2013-1/2-        366870         1.88     Egality    3
          Range of Discrepancies:         -1.88%       and       1.75%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013     13
                       HUDSON CITY Weighted Voting Plan

                     Popul-             Decisive     Voting      Popul-     Discre-
         Ward                   Vote
                      ation             Combin-      Power       ation      pancy
                                         ations
          4-A                    94       120
                        725                          11.43%     11.32%      0.93%
          4-B                    95        136
          I-A                    95        136
                        770                          12.14%     12.03%      0.97%
          I-B                    95        136
          3-A                    180       196
                      1142                           17.50%     17.84%      -1.88%
          3-B                    180       196
          2-A                    185       228
                      1281                           20.36%     20.01%      1.75%
          2-B                    185       228
      President                  189       252
          5-A                    363       432
                      2485                           38.57%     38.81%      -0.61%
          5-B                    363       432


     Ward totals      6403      1835      2240        100%       100%
           Total Vote           2024
        Needed to pass          1013
        Plan: Hudson-2013-1/2-           433626        1.88     Egality:    4


        Range of Discrepancies:          -1.88%         to       1.75%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013    14
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting      Popul-    Discre-
         Ward                   Vote
                       ation            Combin-       Power      ation      pancy
                                          ations
          4-A                    95        128
                        725                          11.51%     11.32%      1.66%
          4-B                    95        128
           I-A                   95        128
                        770                          11.51%     12.03%      -4.28%
           I-B                   95        128
          3-A                    180       196
                       1142                          17.63%     17.84%      -1.17%
          3-B                    180       196
          2-A                    185       228
                       1281                          20.50%     20.01%      2.49%
          2-B                    185       228
       President                 190       260
          5-A                    364       432
                       2485                          38.85%     38.81%      0.10%
          5-B                    364       432


     Ward totals       6403     1838       2224       100%       100%
           Total Vote           2028
        Needed to pass          1015
        Plan: Hudson-2013-1/2-           433642        4.28     Egality    5
        Range of Discrepancies:          -4.28%         to       2.49%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   15
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting      Popul-    Discre-
         Ward                   Vote
                       ation            Combin-       Power      ation      pancy
                                          ations
           4-A                   95        128
                        725                          11.59%     11.32%         2.40%
           4-B                   95        128
           I-A                   95        128
                        770                          11.59%     12.03%      -3.59%
           I-B                   95        128
           3-A                   180       188
                       1142                          17.03%     17.84%      -4.52%
           3-B                   180       188
           2-A                   185       220
                       1281                          19.93%     20.01%      -0.39%
           2-B                   185       220
       President                 190       260
           5-A                   365       440
                       2485                          39.86%     38.81%         2.69%
           5-B                   365       440


     Ward totals       6403     1840       2208        100%       100%
           Total Vote           2030
        Needed to pass          1016
          Plan: Hudson-2013-1/2-        433644         4.52     Egality    5
           Range of Discrepancies:        -4.52%        to       2.69%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013     16
                            TWO THIRDS PLANS
                       HUDSON CITY Weighted Voting Plan


                      Popul-            Decisive     Voting     Popul-     Discre-
         Ward                   Vote
                       ation            Combin-      Power       ation      pancy
                                          ations
          4-A                    22         82
                        725                          11.58%     11.32%      2.29%
          4-B                    22         82
           I-A                   22         82
                        770                          11.58%     12.03%      -3.69%
           I-B                   22         82
          3-A                    34        126
                       1142                          17.80%     17.84%      -0.22%
          3-B                    34        126
          2-A                    39        146
                       1281                          20.62%     20.01%      3.08%
          2-B                    39        146
       President                 44        162
          5-A                    73        272
                       2485                          38.42%     38.81%      -1.01%
          5-B                    73        272


      Ward totals      6403      380      1416        100%       100%
           Total Vote            424
        Needed to pass           283
        Plan: Hudson-2013-2/3-           437887        3.69     Egality    5
        Range of Discrepancies:          -3.69%         to       3.08%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   17
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting     Popul-     Discre-
         Ward                   Vote
                       ation            Combin-      Power       ation      pancy
                                          ations
          4-A                    26         80
                        725                          11.36%     11.32%      0.36%
          4-B                    26         80
           I-A                   27         86
                        770                          12.22%     12.03%      1.58%
           I-B                   27         86
          3-A                    40        126
                       1142                          17.90%     17.84%      0.35%
          3-B                    40        126
          2-A                    46        138
                       1281                          19.60%     20.01%      -2.02%
          2-B                    46        138
       President                 51        154
          5-A                    90        274
                       2485                          38.92%     38.81%      0.28%
          5-B                    90        274


      Ward totals      6403      458      1408        100%       100%
           Total Vote            509
        Needed to pass           340
        Plan: Hudson-2013-2/3-           437878        2.02     Egality    5
        Range of Discrepancies:          -2.02%         to       1.58%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   18
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting     Popul-     Discre-
         Ward                   Vote
                       ation            Combin-      Power       ation      pancy
                                          ations
          4-A                    44         78
                        725                          10.89%     11.32%      -3.79%
          4-B                    44         78
           I-A                   45         84
                        770                          11.73%     12.03%      -2.44%
           I-B                   45         84
          3-A                    67        128
                       1142                          17.88%     17.84%      0.23%
          3-B                    67        128
          2-A                    78        148
                       1281                          20.67%     20.01%      3.32%
          2-B                    78        148
       President                 81        156
          5-A                    147       278
                       2485                          38.83%     38.81%      0.04%
          5-B                    147       278


      Ward totals      6403      762      1432        100%       100%
           Total Vote            843
        Needed to pass           562
        Plan: Hudson-2013-2/3-           393219        3.79     Egality    5
        Range of Discrepancies:          -3.79%         to       3.32%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   19
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting     Popul-     Discre-
         Ward                   Vote
                       ation            Combin-      Power       ation      pancy
                                          ations
          4-A                    44         79
                        725                          11.21%     11.32%      -1.03%
          4-B                    44         79
           I-A                   45         85
                        770                          12.20%     12.03%      1.44%
           I-B                   46         87
          3-A                    68        127
                       1142                          17.87%     17.84%      0.21%
          3-B                    67        125
          2-A                    78        139
                       1281                          19.72%     20.01%      -1.45%
          2-B                    78        139
       President                 81        153
          5-A                    147       275
                       2485                          39.01%     38.81%      0.51%
          5-B                    147       275


      Ward totals      6403      764      1410        100%       100%
           Total Vote            845
        Needed to pass           564
        Plan: Hudson-2013-2/3-           393250        1.45     Egality    3
        Range of Discrepancies:          -1.45%         to       1.44%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   20
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting      Popul-    Discre-
         Ward                   Vote
                       ation            Combin-       Power      ation      pancy
                                          ations
          4-A                    68         78
                        725                          10.89%     11.32%      -3.79%
          4-B                    68         78
           I-A                   69         84
                        770                          11.73%     12.03%      -2.44%
           I-B                   69         84
          3-A                    103       128
                       1142                          17.88%     17.84%      0.23%
          3-B                    103       128
          2-A                    120       148
                       1281                          20.67%     20.01%      3.32%
          2-B                    120       148
       President                 123       156
          5-A                    225       278
                       2485                          38.83%     38.81%      0.04%
          5-B                    225       278


     Ward totals       6403     1170       1432       100%       100%
           Total Vote           1293
        Needed to pass           862
        Plan: Hudson-2013-2/3-           393216        3.79     Egality    5
        Range of Discrepancies:          -3.79%         to       3.32%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   21
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting      Popul-    Discre-
         Ward                   Vote
                       ation            Combin-       Power      ation      pancy
                                          ations
          4-A                    105        82
                        725                          11.58%     11.32%      2.29%
          4-B                    105        82
           I-A                   108        82
                        770                          11.58%     12.03%      -3.69%
           I-B                   108        82
          3-A                    161       126
                       1142                          17.80%     17.84%      -0.22%
          3-B                    161       126
          2-A                    187       146
                       1281                          20.62%     20.01%      3.08%
          2-B                    187       146
       President                 199       162
          5-A                    352       272
                       2485                          38.42%     38.81%      -1.01%
          5-B                    352       272


     Ward totals       6403     1826       1416       100%       100%
           Total Vote           2025
        Needed to pass          1350
        Plan: Hudson-2013-2/3-           393259        3.69     Egality    5
        Range of Discrepancies:          -3.69%         to       3.08%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   22
                          THREE QUARTERS PLANS
                       HUDSON CITY Weighted Voting Plan


                      Popul-            Decisive     Voting     Popul-     Discre-
         Ward                   Vote
                       ation            Combin-      Power       ation      pancy
                                          ations
          4-A                    39         45
                        725                          11.45%     11.32%      1.13%
          4-B                    39         45
           I-A                   40         49
                        770                          11.96%     12.03%      -0.55%
           I-B                   39         45
          3-A                    61         71
                       1142                          18.07%     17.84%      1.29%
          3-B                    61         71
          2-A                    62         77
                       1281                          20.10%     20.01%      0.48%
          2-B                    63         81
       President                 77         81
          5-A                    160       147
                       2485                          38.42%     38.81%      -1.00%
          5-B                    162       155


      Ward totals      6403      726       786        100%       100%
           Total Vote            803       867
        Needed to pass:          603
        Plan: Hudson-2013-3/4-           433590        1.29     Egality    2
        Range of Discrepancies:          -1.00%         to       1.29%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   23
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting      Popul-    Discre-
         Ward                   Vote
                       ation            Combin-       Power      ation      pancy
                                          ations
          4-A                    81         45
                        725                          11.22%     11.32%      -0.89%
          4-B                    81         45
           I-A                   82         49
                        770                          12.22%     12.03%      1.61%
           I-B                   82         49
          3-A                    127        73
                       1142                          17.71%     17.84%      -0.73%
          3-B                    126        69
          2-A                    129        83
                       1281                          20.70%     20.01%      3.46%
          2-B                    129        83
       President                 161        85
          5-A                    335       155
                       2485                          38.15%     38.81%      -1.69%
          5-B                    333       151


     Ward totals       6403     1505       802        100%       100%
           Total Vote           1666
        Needed to pass:         1250
        Plan: Hudson-2013-3/4-           423354        3.46     Egality    3
        Range of Discrepancies:          -1.69%         to       3.46%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   24
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting      Popul-    Discre-
         Ward                   Vote
                       ation            Combin-       Power      ation      pancy
                                          ations
          4-A                    81         46
                        725                          11.44%     11.32%      1.06%
          4-B                    81         46
           I-A                   82         50
                        770                          12.44%     12.03%      3.43%
           I-B                   82         50
          3-A                    126        68
                       1142                          16.92%     17.84%      -5.16%
          3-B                    126        68
          2-A                    129        82
                       1281                          20.40%     20.01%      1.96%
          2-B                    129        82
       President                 161        82
          5-A                    335       156
                       2485                          38.81%     38.81%      -0.01%
          5-B                    335       156


     Ward totals       6403     1506       804        100%       100%
           Total Vote           1667
        Needed to pass:         1251
        Plan: Hudson-2013-3/4-           423364        5.16     Egality    5
        Range of Discrepancies:          -5.16%         to       3.43%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   25
                       HUDSON CITY Weighted Voting Plan

                      Popul-            Decisive     Voting      Popul-    Discre-
         Ward                   Vote
                       ation            Combin-       Power      ation      pancy
                                          ations
           4-A                   98         49
                        725                          11.86%     11.32%         4.78%
           4-B                   98         49
           I-A                   100        51
                        770                          12.35%     12.03%         2.69%
           I-B                   100        51
           3-A                   153        73
                       1142                          17.68%     17.84%      -0.90%
           3-B                   153        73
           2-A                   157        85
                       1281                          20.58%     20.01%         2.87%
           2-B                   157        85
       President                 194        85
           5-A                   405       155
                       2485                          37.53%     38.81%      -3.30%
           5-B                   405       155


     Ward totals       6403     1826       826         100%       100%
           Total Vote           2020
        Needed to pass:         1515
          Plan: Hudson-2013-3/4-        433598         4.78     Egality    5
           Range of Discrepancies:        -3.30%        to       4.78%




City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013     26
                                   REFERENCES
                                (cited in footnotes)




1. Banzhaf, J.F., III, "Weighted Voting Doesn't Work: A
   Mathematical Analysis," Rutgers Law Review, Vol. 19, 1965.


2. Baker vs. Carr 369 U.S. 186, 1962.
   Gray vs. Sanders 372 U.S. 368, 1963.


3. Dobish vs. Board of Supervisors of Wayne County, 279 NYS 2d
   565, 282 NYS 2d 791, 1967.


4. Iannucci vs. Board of Supervisors of Washington County and,
    Saratogian, Inc., vs. Board of Supervisors of Saratoga County,
    20 N.Y. 2d 244, 299 NE 2d 195, 282 NYS 2d 502, 1967.


5. Imrie, R.W., "The Impact of the Weighted Vote on
    Representation in Municipal Governing Bodies of New York
    State," Annals of the New York Academy of Sciences, Vol. 219,
    1973, pp. 183-191.


6. Papayanopoulos, L., "Quantitative Principles Underlying
   Apportionment Methods," Annals of the New York Academy of
   Sciences, Vol. 219, 1973, pp. 183-191.


7. Slater vs. Board of Supervisors of Cortland County, 330 NYS 2d
   947, 346 NYS 2d 185, 42 A.D. 2d 795, 1972-1973.




 City of Hudson, NY -- Weighted Voting Analysis by L. Papayanopoulos – January 2013   27

				
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