QUOTA IN RANKED-CHOICE ELECTIONS

Ranked-choice or preference voting requires each winning candidate to meet a quota (threshold) of votes, based on the number of seats and the number of ballots. There are numerous possible quotas. These are definitions of a few (where Q = quota; S = number of seats; B = number of ballots):

Follow this link to tabulations using each of these methods for an election within a state Green party in 2010.

Follow this link to tabulations using most of these methods for an election within a state Green party in 2013.

The fallacy of choosing Droop quota for small electorates

The Droop quota is a quota widely used in public elections. Participation of a large number of voters reduces to insignificance its practice of rounding upward to an integer. Yet, in a small electorate, such as a membership organization or committee, rounding can change the results of an election. Wikipedia claims, "The Droop quota is smaller than the Hare quota. . . ." That can only be true if there are more than twice as many ballots as seats. Furthermore, when the number of ballots is smaller than the square of the number of seats, the Droop quota may be larger than the Hare quota.

Here are a few examples (out of thousands) where the Droop quota exceeds the Hare quota:
BallotsSeatsHare quotaDroop quotaExcess of Droop over HarePercent by which Droop exceeds Hare
832.6730.3313%
1042.5030.5020%
1252.4030.6025%
1352.6030.4015%
1853.6040.4011%
1462.3330.6729%
1562.5030.5020%
1662.6730.3313%
2163.5040.5014%
2263.6740.339%
2864.6750.337%

The people who distribute OpenSTV define the Droop threshold (quota) as "the smallest number such that any candidate receiving this number of votes is guaranteed to be elected". It can be no such thing if the Hare threshold (quota) is smaller and guarantees election. In fact, any threshold higher than the Hagenbach-Bischoff quota gurantees election to candidates who reach it.

Because it is the highest number that can produce more winners than needed, we recommend that the Hagenbach-Bischoff quota (Q=B/(S+1)) be employed as the largest number of votes that does not score a win, that it be the threshold a candidate must exceed for election.


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
POLITICS PAGE
LEGISLATIVE DISTRICTS
ADMINISTRATIVE BOUNDARIES FOR NORTH AMERICA
GEOGRAPHY PAGE

ELECTION INFORMATION
PEACE
SEARCH

Last revised: 9 October 2016
visitors since 20 April 2010