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Choice voting explanation and glossary

This page includes: Choice voting walk-through, Choice voting, and a glossary

Choice Voting Walk-Through

Consider each candidate for a multi-seat board as being a bin which collects voters’ ballots in an election. Under non-PR systems we simply distribute all the ballots, and the bins with the most ballots win. It makes no difference if the 1st-place bin has three times the number of ballots as the 2nd-place bin. Both win a seat and have the same voice. The "extra" ballots in the 1st-place seat bin are effectively wasted. Also, all the ballots in the losing bins are wasted - they have no effect on the outcome of the election.

In choice voting we account for these "wasted" ballots by transferring votes. Every voter provides his or her preferences among the candidates, not just a first choice. For the extra ballots in the 1st place bin we see who these voters named as their second choice. We redistribute the extra ballots to other bins according to these secondary preferences. This gives the 1st place ballots a larger voice, exactly in proportion to their numbers.

To do this we determine how many ballots each candidate, or bin, needs to win one seat. For an 11-seat board, this "victory threshold" is one more vote than 1/12th of the vote, or 8.3% plus one vote. (Note that if there is only one winner, this quota becomes one more than 1/2, or the well-known majority!)

So, if 1000 people are voting, we’ll build our bins so they can hold only 84 ballots.

We then take the stack of ballots and distribute them to their choice bin. Once a bin has 84 ballots, we distribute any additional ballots for that bin to the bin for the ballot’s next-preferred candidate.

When we have distributed all the ballots we probably will not have 11 bins with 84 ballots in them. We then take all the ballots from the bin with the fewest ballots (declaring that candidate defeated), and redistribute them to the next choice on each ballot. If this redistribution would put a ballot into a bin that already has 84, we pass it along to the next choice with fewer than 84.

This process continues until there are only 11 bins with ballots in them. Those are the winners. By doing this we end up with 11 winning bins, each containing no more ballots than needed to win. But, more importantly, almost every ballot ends up helping to elect a winner!

Party List

If four parties or slates run in an election, they may receive the following popular votes:

A: 45%
B: 25%
C: 15%
D: 10%

The seats on an 11-member board would then be distributed in proportion to the popular vote:

A: 5 seats
B: 3 seats
C: 2 seats
D: 1 seat

Note that a party winning only 10% of the popular vote still gains a seat and its voice will be heard.


{Note: Choice voting is also sometimes called "single transferable vote" and "preference voting."}



(a) DEFINITION: "Choice Voting" shall be defined as a voting system which achieves proportional representation by allowing voters to rank candidates for city council in the order of their choice, according to the method described in Article XVIII, Section 1, subdivision B, Third; and by tabulating votes according to the rules described in Article XVIII, Section 1, subdivision B, Fifth.

(b) PRINCIPLE: Choice Voting tabulates votes based on the principle that any vote cast which would not otherwise help elect a voter's most preferred candidate(s), shall be used to help elect that voter's next-most preferred candidate(s). Thus, if a voter's first choice among the candidates receives more than enough votes to win, the surplus proportion of that vote will be transferred to that voter's second or succeeding (next-highest ranking) choice. Alternatively, if a voter's first choice candidate is eliminated, that vote instead will be cast for the voter's second or succeeding (next-highest ranking) choice.


Ballots shall be simple and easy to understand. Sample ballots illustrating voting procedures shall be posted in or near the voting booth, and included in the instruction packet of absentee ballots. Directions provided to voters shall conform substantially to the following specifications


CITY COUNCIL: Vote for up to 9 council candidates in your order of choice. Indicate your first choice by marking an "x" in column 1 next to that candidate's name, your second choice by marking an "x" in column 2, and so on. Do not assign any two candidates the same choice. If you wish, choose only one candidate Note that ranking additional candidates cannot affect a higher-choice candidate's chance to win.

{NOTE: Limiting choices is optional. In addition, tie votes can be allowed, but add new complications to the ballot-count.}

Third. TABULATION OF VOTES: In accordance with the principle expressed in Article XVIII, Section 1, Subdivision B, First, Principle, ballots shall be counted by election authorities according to the following rules:

(a) DETERMINATION OF VICTORY THRESHOLD: For any given election, the number of votes necessary for a candidate to guarantee an elected position shall be termed the "threshold." The threshold is used to determine transferable surpluses as defined in (b)(1) below.

The threshold shall be the fewest number of votes that can be obtained only by the winning number of candidates. This threshold is determined as follows:

[ valid votes cast ] +1
[ (number of seats + 1) ]

{NOTE: An alternative victory threshold -- not used in any public elections as of January 1998 -- is determined simply by dividing the number of valid ballots by the number of positions to be filled.}

(b) RULES REGARDING TRANSFER OF VOTES: The following rules regarding vote transfer shall apply to all stages of the tabulation:

(1) Votes acquired by a candidate in excess of the threshold for that election shall be termed his or her "surplus". A candidate's surplus votes shall be transferred according to the following rule: transfer a portion of each vote determined by dividing the surplus of the candidate by the total number of votes for that candidate. For example, if a candidate receives 15,000 votes in an election whose threshold is 10,000, that candidate has a surplus of 5000 votes and one-third (5000/15,000 = .3333) of a vote from each of those 15,000 ballots is transferred to those voters' next choices.

Votes cast for candidates who are eliminated (as described in (c)(3) below) shall be transferred at their full current value to those voters' next choice(s).

(2) Votes may not be transferred to candidates who have already met the threshold, nor may votes be transferred to candidates who have been eliminated. When a voter's next choice is not eligible for receipt of transferred votes, that vote (or portion of a vote) shall be transferred to the voter's next indicated choice until all choices on that ballot have been exhausted.

(3) If a voter omits or mistakenly designates any choice on his or her ballot, the vote shall be transferred to that voter's next clearly indicated choice.

(4) Any votes cast for eligible write-in candidates shall be tabulated in the same manner as those for candidates whose names are printed on the ballots; provided that the voter assigns any such candidate a choice in relation to other candidates appearing on the ballot for that office.


(1) Vote counting shall start with a tabulation of first-choice votes and with the transfer of a proportion of all surplus votes according to the rules specified in (b) above. Transfer of surpluses shall commence with the candidate having the largest surplus and proceed successively to the candidates with the next largest surplus.

(2) If the transfer of surplus votes to voters' next-choice candidates creates a new surplus, then a proportion of these votes shall be transferred to those voters' succeeding choices, until all surpluses have been transferred or all declared choices on a ballot have been exhausted.

(3) When all surplus votes have been distributed in this manner, a tally shall be taken. All candidates with less than 0.5% of votes shall be eliminated simultaneously. Votes for these candidates shall be transferred at their current value to the next-choice candidates named on these ballots. If a next-choice candidate already has been elected or defeated, then the ballot goes to the succeeding choice.

Any surpluses created by this transfer shall once again be transferred, and a new tally taken, until all surpluses have been transferred. Then the remaining candidate with the least number of votes shall be eliminated.

This process of transferring surpluses followed by eliminating candidates with the least numbers of votes shall continue until the number of candidates remaining matches the number of positions to be filled. Votes of the candidate last eliminated shall be transferred, and the election shall be at an end.

(d) DETERMINATIONS IN THE CASE OF A TIE: For ties between candidates occurring at any stage in the tabulation, determinations shall be made based on whomever was credited with the most votes at the previous stage of tabulation. In the case of any tie to which a previous stage does not apply, the tie shall be resolved in accordance with the general election laws of Washington.

(e) FILLING A CITY COUNCIL VACANCY: Any vacancy of an elected City Council member shall be filled by recounting the ballots from the general election which elected that member, in the manner specified herein for general elections, except that the vacating member's name shall be deleted from all ballots. The candidate accruing the most votes in the recount that was not elected to office in the original count shall fill the vacancy. For the purpose of filling City Council vacancies, all general election ballots shall be retained by election authorities for at least four years.

Fourth. PROVISION FOR CHANGE OF VOTING METHOD: The Council or election authorities may provide for the use of mechanical, electronic or other devices for marking, sorting and counting the ballots and tabulating the results, and may modify the form of the ballots, the directions to voters, and the details with respect to the method of marking, sorting, counting, invalidating, and retaining of ballots, and the tabulating and transferring of votes, provided that no change shall be made which will alter the intent or principles embodied in this Subsection.

Fifth. SEVERABILITY CLAUSE: If any part of this Subsection is declared unconstitutional by a court of competent jurisdiction, the remaining parts shall survive in full force and effect. If a conflict arises between this amendment and any other pro vision of law, the policies and purposes of this amendment shall govern.


Glossary Definition:
  • Proportional Representation (PR) - Any system which consciously attempts to reduce the disparity between a party's share of the national vote and its share of the parliamentary seats. For example, if a party wins 40 per cent of the votes, it should win approximately 40 per cent of the seats.
  • Ballot structure - The way in which electoral choices are presented on the ballot paper. Ballots can be eitherordinal or categorical.
  • Candidate-centered Ballot - A form of ballot in which an elector chooses between candidates.
  • Communal Roll - A register of voters in which ascriptive criteria such as race or ethnicity determine which electors can enroll to vote, and which candidates can be elected, within the wider electoral contest.
  • Constituency - A synonym for district, used predominantly in Anglophone countries outside of the US.
  • Cumulative Vote - The capacity of voters within some voting systems to cast more than one vote for a favored candidate.
  • Distribution Requirements - The requirement that to win election a candidate must not merely win a specified proportion of the vote nationally but also a specified degree of support from different regions.
  • Democratic Consolidation - The process by which a nation's political institutions and democratic procedures become legitimized and broadly accepted by both political actors and the wider population.
  • District - Geographic areas into which a country is divided for electoral purposes. Districts may return one member to parliaments or more than one.
  • Droop Quota - Used in highest average list PR and STV electoral systems to determine how seats are awarded. The quota is ascertained by the following formula: total vote divided by the number of seats plus one, then one is added to the product.
  • Electoral Formula - That part of the electoral system dealing specifically with the translation of votes into seats.
  • Electoral Law - The provisions governing all aspects of the electoral process.
  • Electoral System - That part of the electoral rules which determines electoral outcomes; chiefly, the electoral formula, the ballot structure, and district magnitude.
  • First Past the Post (FPTP) - The simplest form of plurality-majority electoral system, -single-member districts, a categorical ballot and candidate-centered voting. The winning candidate is the one who gains more votes than any other candidate, but not necessarily a majority of votes.
  • Gerrymandering - The deliberate manipulation of district boundaries so as to or disadvantage a particular interest.
  • Hagenbach-Bischoff Formula - Another term for the Droop Quota.
  • Imperiali Quota - Sometimes used in largest remainder PR electoral systems to determine how seats are awarded The quota is ascertained by the following formula: total vote divided by the number of seats plus two.
  • Largest Remainder Method - The Hare, Droop and Imperiali calculation methods which translate votes into seats within list PR systems. There are two stages to the count. First, parties are awarded seats in proportion to the number of quotas they fulfill (quotas vary depending on which of the three systems are used). Second, remaining seats are awarded to parties on the basis of the left over votes they possess after the 'quota' stage of the count. Largest remainder seats are allocated in order of vote size.
  • Malapportionment - The uneven distribution of voters between electoral districts.
  • Multi-Member District - A district from which more than one candidate can be elected.
  • Quota - The threshold for winning a seat in proportional representation systems.
  • Sainte-Lagu Formula - One way of working out list PR results by the method. Uses divisors of 1,3,5,7, etc.
  • Wasted Votes - Those votes which did not ultimately count towards the election of a particular candidate or party. (no such in STV)
  • Highest Average Method - A formula used with list PR systems to translate votes into seats. Party vote totals are divided by a series of devisors, under d'Hondt (by 1,2,3, etc.) or Sainte-Laguy 1,3,5, etc.) formula. After each stage the party with the highest average wins the seat. The count continues with party vote totals being divided by sequential numbers until all seats are filled.
  • Preferential Voting - Electoral systems in which voters can rank-order candidates on the ballot paper in order of their choice. The Alternative Vote, the Single Transferable Vote and the system used to elect the Sri Lankan president are all examples of preferential voting.
    • Alternative Vote (AV) - A preferential, plurality-majority system used in single-member districts in which voters use numbers to mark their preferences on the ballot paper. A candidate who receives over 50% of first-preferences is declared elected. If no candidate achieves an absolute majority of first- preferences, votes are re-allocated unfit one candidate has an absolute majority of votes cast
    • Block Vote - A plurality-majority system used in multi-member districts in which electors have as many votes as there are candidates to be elected. Voting can be either candidate-centered or party- centered. Counting is identical to a First Past the Post system, with the candidates with the highest vote totals winning the seats. Also known as or Bloc Vote.
    • Hare Quota - Used in largest remainder PR electoral systems to determine how seats are awarded. The quota is ascertained by the following formula: total vote divided by the number of seats.
    • Ordinal Ballot - A form of ballot in which a voter's choice can be rank-ordered
    • Reserved Seats - Seats in which some ascriptive criteria such as religion, ethnicity, language, gender etc. is a requirement for election.
    • Single Transferable Vote (STV) - A preferential proportional representation system used in multi- member districts. To gain election, candidates must surpass a specified quota of first-preference votes. Voters' preferences are re-allocated to other continuing candidates when an unsuccessful candidate is excluded or if an elected candidate has a surplus.
    • Threshold - The minimum level of support which a party needs to gain representation; usually expressed as a percentage of the total vote.
  • Additional Member System - Another term for a mixed member proportional system.
  • Categorical Ballot - A form of ballot in which only a single choice for a candidate or party can be made.
  • Free List - A form of list proportional representation which provides for cumulative voting.
  • Limited Vote - A plurality-majority system used in multi-member district in which electors have more than one vote but fewer votes than there are candidates to be elected. Counting is identical to a first past the post system, with the candidates with the highest vote totals winning the seats.
  • List Proportional Representation (List PR) - In its most simple form List PR involves each party presenting a list of candidates to the electorate, voters vote for a party, and parties receive seats in proportion to their overall share of the national vote. Winning candidates are taken from the lists.
  • Majority-Plurality (Two-Round System) - In French Two-Round elections any candidate who has received the votes of over 12.5 per cent of the registered electorate in the first round can stand in the second round. Whoever wins the highest numbers of votes in the second round is then declared aimed, regardless of whether they have won an absolute majority or not. We therefore refer to it as majority- plurality variant of the two-round system.
  • Majority-Runoff (Two-Round System) - The most common method for the second round of voting in a Two-Round System is a straight 'run-off' contest between the two highest vote-winners from the first round - this we term a majority-runoff system.
  • Mixed Member Proportional (MMP) - Systems in which a proportion of the parliament (usually halo is elected from plurality-majority districts, while the remaining members are chosen from PR lists. Under MMP the list PR seats compensate for any disproportionality produced by the district seat results.
  • Plurality-Majority Systems - The distinguishing feature of plurality-majority systems is that they almost always use single-member districts. In a first past the post system, the winner is the candidate with a plurality of votes, but not necessarily an absolute majority of the votes. When this system is used in multi-member districts it becomes the block vote. Majority systems, such as the Australian Alternative Vote and the French two-round system, try to ensure that the winning candidate receives an absolute majority of votes cast.
  • Semi-Proportional Systems (Semi-PR) - Those electoral systems which provide, on average, results which fall some way in between the proportionality of PR systems and the disproportionality of plurality-majority systems.
  • Single-Member District - A district from which only one member is elected to parliament.
  • Single Non-Transferable Vote (SNTV) - A semi-proportional system which combines multi-member district with a first past the post method of vote counting, and in which electors have only one vote.
  • Two-Tier Districting - Where seats are awarded to parties from both single member districts and national PR lists, or both regional and national PR lists.

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