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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
