"Those who cast the votes decide nothing. Those who COUNT the votes decide everything." -- Joseph Stalin



ELECTION OF January 2013

by which the Green Party of Virginia (GPVA) chose representation on the Green National Committee (GNC)

On 5 January 2013, the Green Party of Virginia (GPVA) held an election to choose two delegates and two alternates. A decision was made to tabulate the votes by the method of Single Transferable Vote (STV), the general form of ranked-choice or preference voting. Of the people in attendance, 10 cast ballots. An identification letter is has been assigned to each ballot by the editor for reference. The numbers on the ballot indicate ordinal preference for each candidate: 1 for first choice, 2 for second choice, etc.

BALLOT
CANDIDATE
TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJim
A126435
B1324
C1342
D1423
E156234
F215436
J1324
K213456789
G351426
H635241

(A similar election with eight voters was held in 2010.)

STV (like most forms of ranked-choice voting) requires that each winning candidate receive a minimum number of votes, a quota or threshold. Several quotas are in common use.


Let's take a look at some standard quotas for STV.


Majority as quota

Using a majority as threshold requires that a candidate receive the votes of more than half the valid ballots (either as first choice or by transfer):


These tabulations show how a quota of a majority of ballots would be employed to fill

Fill 2 delegate seats by majority quota
Quota = 10/2 = 5TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
transfer from Charlie+1-1
Round 25221000000010
transfer from Mike+1-1
Round 35320000000010
transfer from Audrey+1-2+1
Round 45400100000010
transfer from CF+1-1
Round 56400000000010
Resultwin by defaultwin by defaulteliminateeliminateeliminateeliminateeliminateeliminateeliminateeliminateeliminate

This is the tabulation for four seats, including two delegates and two alternates:

Fill all 4 seats by majority quota.
Quota = 10/2 = 5TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
Resultwin by defaultwin by defaultwin by defaulteliminateeliminatewin by defaulteliminateeliminateeliminateeliminateeliminate


Hare quota

The Hare quota is defined as the number of valid ballots divided by the number of seats to be filled. Although it may produce the right number of winning candidates, it often falls short.

In this case, the Hare quota produces similar results, with one of the winners exceeding quota:

Fill 2 delegate seats by Hare quota
Quota = 10/2 = 5TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
transfer from Charlie+1-1
Round 25221000000010
transfer from Mike+1-1
Round 35320000000010
transfer from Audrey+1-2+1
Round 45400100000010
transfer from CF+1-1
Round 56400000000010
Resultwin with quotawin by defaulteliminateeliminateeliminateeliminateeliminateeliminateeliminateeliminateeliminate

This is the Hare tabulation for four seats, including two delegates and two alternates:

Fill all 4 seats by Hare quota
Quota = 10/4 = 2.5TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-2.5+0.5+1.5+0.5
Round 22.52.521.50.510000010
transfer from CF+0.5-0.5
Round 32.53.021.5010000010
excess from Joe-0.5+0.083+0.417
Round 42.52.52.0831.917010000010
transfer from Charlie+1-1
Round 52.52.52.0832.917000000010
Resultwin with quotawin with quotawin by defaultwin with quotaeliminateeliminateeliminateeliminateeliminateeliminateeliminate
(
This is a case of a Hare quota smaller than the Droop quota, contrary to Wikipedia's claim.)


Droop quota

The Droop quota is a weird system that was probably developed to simplify arithmetic. Unfortunately, it produces erratic numbers. It may be smaller or larger than the Hare quota. (For example, the Droop quota in an election with 24 ballots and 7 seats is 4, compared to a Hare quota of only 3.43.) Because of its unpredictability, we cannot recommend its use when other quotas are available.

Fill 2 delegate seats by Droop quota
Quota = INT(10/(2+1)+1) = 4TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-1+0.2+0.6+0.2
Round 242.220.60.210000010
transfer from CF+0.2-0.2
Round 342.420.6010000010
transfer from Mike+0.4-0.6+0.2
Round 442.82001.20000010
Resultwin with quotawin by defaulteliminateeliminateeliminateeliminateeliminateeliminateeliminate

This is the tabulation for four seats, including two delegates and two alternates:
Fill all 4 seats by Droop quota
Quota = INT(10/(4+1)+1) = 3TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-2+0.4+1.2+0.4
Round 232.421.20.410000010
transfer from CF+0.4-0.4
Round 332.821.2010000010
transfer from Charlie+1-1
Round 332.822.2000000010
Resultwin with quotawin by defaultwin by defaultwin by defaulteliminateeliminateeliminateeliminateeliminateeliminateeliminate
(This is a case of a Droop quota larger than the Hare quota, contrary to Wikipedia's claim.)


Hagenbach-Bischoff threshold (exclusive)

The Hagenbach-Bischoff quota marks the dividing line between producing just enough winners and the possibility of producing one too many. It is sometimes unwisely used as the threshold a candidate must meet to win, the inclusive limit of eligibility, which is where the extra winner can be found. Instead, the Hagenbach-Bischoff quota should be the threshold a candidate must surpass to win, the exclusive limit of eligibility. If the preference ballots are filled out and tabulated properly, it will be impossible to have too many winners.

Here, we use the Hagenbach-Bischoff quota as the threshold that must be crossed, not merely reached.

Fill 2 delegate seats by Hagenbach-Bischoff threshold
Quota = 10/(2+1) = 3.33TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-1.67+0.33+1+0.33
Round 23.332.33210.3310000010
transfer from CF+0.33-0.33
Round 33.332.6721010000010
transfer from Charlie+1-1
Round 43.332.6722000000010
Resultwin with quotawin by defaulteliminate (tie)eliminate (tie)eliminateeliminateeliminateeliminateeliminateeliminateeliminate

This is the tabulation for four seats, including two delegates and two alternates:

Fill all 4 seats by Hagenbach-Bischoff threshold
Quota = 10/(4+1) = 2TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-3+0.6+1.8+0.6
Round 222.621.80.610000010
excess from Joe0-0.6+0.6
Round 32221.81.210000010
transfer from Charlie+1-1
Round 32222.81.200000010
Resultwin with quotawin with quotawin by defaultwin with quotaeliminateeliminateeliminateeliminateeliminateeliminate


Hagenbach-Bischoff quota (inclusive)

Using the Hagenbach-Bischoff quota inclusively provides that any candidate reaching the quota wins. Otherwise, the computation is exactly the same as in the exclusive case above. The single drawback is the possibility that the number of candidates reaching the quota may exceed the number of seats by one. If they are excluded, as above, there cannot be more winners than seats.

Fill 2 delegate seats by Hagenbach-Bischoff threshold
Quota = 10/(2+1) = 3.33TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-1.67+0.33+1+0.33
Round 23.332.33210.3310000010
transfer from CF+0.33-0.33
Round 33.332.6721010000010
transfer from Charlie+1-1
Round 43.332.6722000000010
Resultwin with quotawin by defaulteliminateeliminateeliminateeliminateeliminateeliminateeliminate

This is the tabulation for four seats, including two delegates and two alternates:

Fill all 4 seats by Hagenbach-Bischoff threshold
Quota = 10/(4+1) = 2TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-3+0.6+1.8+0.6
Round 222.621.80.610000010
excess from Joe0-0.6+0.6
Round 32221.81.210000010
transfer from Charlie+1-1
Round 32222.81.200000010
Resultwin with quotawin with quotawin by defaultwin with quotaeliminateeliminateeliminateeliminateeliminateeliminate


Imperiali quota

The Imperial quota, used in Ecuador, often produces too many winners because of its unusually low quota. Fortunately, it produces the correct number in this case:

Fill 2 delegate seats by Imperiali quota
Quota = 10/(2+2) = 2.5TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-2.5+0.5+1.5+0.5
Round 22.52.521.50.510000010
Resultwin with quotawin with quotaeliminateeliminateeliminateeliminateeliminate

In this four-seat election, four candidates pass the quota, with a fifth hitting it exactly:
Fill all 4 seats by Imperiali quota
Quota = 10/(4+2) = 1.67TamarJoeAudreyMikeCFCharlieKiritSheriCSJohnJimRunning total
Round 15220010000010
excess from Tamar-3.33+2+1.33
excess from Joe-0.33+0.33
excess from Audrey-0.33+0.33
Round 21.671.671.672.331.6710000010
Resultwin with quotawin with quotawin with quotawin with quotapossible win with exact quota


Free speech on the Internet

Questions? Comments? Send mail to ridewaver@gmail.com.

TOP / HOME / FRONT PAGE
SINGLE-TRANSFERABLE VOTE (STV) RANKED-CHOICE PREFERENCE ELECTIONS
GREEN PARTY
ORGANIZATION LEVEL CHART
MEETING SCHEDULE
GREEN TROLL'S PLATFORM PLANKS
POLITICS PAGE
LEGISLATIVE DISTRICTS
ADMINISTRATIVE BOUNDARIES FOR NORTH AMERICA
GEOGRAPHY PAGE

ELECTION INFORMATION
PEACE
GREEN TROLL'S ADVICE ON PREVENTING DAMAGE FROM TERRORISM
RIVERS OF THE WORLD
RAILROAD PAGE
LIFEBOAT ETHICS
HOST PAGE
SEARCH

Last revised: 7 December 2020
visitors since 11 January 2013