Preferential voting

This article is about voting systems that use ranked ballots. For other uses, see Preferential voting (disambiguation).

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Preferential voting (preference voting or ranked voting) is a method of balloting in which voters rank candidates in order of preference, and the winner [or winners] is arrived at by elimination. The least competitive candidates are removed one by one, and their supporter's ballots are transferred to each voter's next best choice. It's effective at electing the candidate(s) with the broadest range of electoral support on a single ballot; and when choosing from, or encouraging, a large number of potential candidates.

The voter indicates their first choice with a '1', their second with a '2', and so on, and their single vote is attributed only to their favorite (highest ranked) still eligible candidate in each round. The field is whittled down through successive rounds; removing the single least favorite candidate each round until the favorite(s) of the electorate is found.

When voters are required to rank every candidate on the ballot (as in Australian elections to the Upper House) it's generally termed instant-runoff voting; the results simulate a runoff election by arriving at a crude majority with a single ballot.

Preferential ballots can be used for both single-winner and multiple winner elections.

In May 2011, The UK held a referendum on implementing preferential voting under the name "The Alternative Vote"; the proposition was defeated with only 32.1% support (to 67.9% opposition).

(Other names / forms of preferential (ranked) balloting include: the condorcet methed, the Borda count, and Bucklin voting.)

Ballot variations

There are a number of different but equivalent ways to design a ballot that allows voter to specify a set of rank preferences.

Written numbers

The voter writes a '1' beside their first choice, a '2' beside their second choice, and so on. This is the most common ballot design. Written numeric rankings are compact and easy to hand count.

Column marks

The voter writes marks beside their candidates in the columns of their number order. These ballots are easily counted by optical scanners. The choices are limited to the number of columns provided. In the image above, for example, the voter is limited to three preferences. So, the winner may still come up with less than 50% of the vote if there are fewer columns than candidates.

Written names

Similar to 'Written numbers' but in reverse, the numbers are written on the ballot and the voter must come up with the names of candidates beside them.

Touch screen

When voting is done by computer, a touch screen can be used. In the example above, voters arrange their selections in order by selecting candidates from the unranked area to the ranked area and then rearranging them with arrow keys or dragging. Selections can be removed or added again to and from the unranked and ranked categories until the voter is satisfied with their selections and rankings.

Some election rules may require voters to assign a ranking to all candidates or to a minimum number to be a valid vote. And most election rules disallow the use of tied-rankings.

Uniqueness of votes

If there is a large number of candidates, more common in STV elections, then it becomes more likely that many preference voting patterns will be unique to individual voters. For example, in the Irish general election, 2002, the electronic votes were published for the Dublin North constituency. There were 12 candidates and almost 44,000 votes cast. The most common pattern (for the three candidates from one party in a particular order) was chosen by 800 voters, and more than 16,000 patterns were chosen by just one voter each.

The number of possible complete rankings with no ties is the factorial of the number of candidates, N, but with ties it is equal to the corresponding ordered Bell number and is asymptotic to

$\frac{N!}{2(\ln 2)^{N+1}}$.

In the case common to IRV in which no ties are allowed, except for unranked candidates who are tied for last place, the number of possible rankings for N candidates is precisely

$\sum_{n=1}^{N-1} \frac{N!}{n!} = \lfloor (e-1)N! - 1 \rfloor = \mathrm{floor}\left( (e-1)N! - 1 \right)$

which is asymptotic to (e-1)N!   .

Arrow's theorem

Arrow's theorem showed that no preferential voting system can obey certain desirable voting system criteria such as the majority criterion and independence of irrelevant alternatives. The theorem does not directly apply to rated voting systems.

Australia

Main article: Australian electoral system

Australia uses a preferential voting system in single member constituencies and the single transferable vote in multi-member constituencies.

Preferential voting is used in electing candidates to single-member electorates such as the Australian Federal House of Representatives, state legislative assemblies (except in Tasmania) and local government municipalities.

Single transferable vote (STV) systems are used in electing candidates to multi-member electorates such as the Australian Senate, State upper houses, Tasmania's State House of Assembly, the Australian Capital Territory's legislative assembly, and some local government municipalities.

Ballot papers are counted according to a prescribed set of rules which set out the method used in the counting of the ballots and the distribution of preferences. Voters' preferences are now entered into computer systems that process the recorded votes to determine the results of the election. Copies of the transcribed data file used in the counting of the elections are published and made available for public inspection and scrutiny.

Supporters of the parties and individual candidates hand out "how to vote" cards (HTVs) at the entrance to polling stations or distributed with election material sent in the post, advising voters how to fill in their ballots to support that party or candidate. The information published on a how to vote card is a recommendation only and no voter is obliged to vote as published, but up to 80% of voters follow the recommendations of their preferred party or candidate. The proportion of voters that choose not to follow their preferred candidate's recommendations is called the "preference leakage".

The STV systems of some jurisdictions in Australia (e.g. the Senate) allow group voting tickets or "above the line voting" where a voter can, with a single mark, indicate support for a predefined set of preferences. This reduces the burden on voters, especially where there are large numbers of candidates and when a complete preference list is required to make a vote valid, so about 95% of voters use this option. Voters not wishing to use the "above-the-line-voting" option maintain the entitlement to indicate preferences for individual candidates; this is referred to as below-the-line voting. The allocation of predefined and individual voter preferences is important in determining the results of the election.

List of systems using preferential ballots

• Alternative vote top-up
• Borda count
• Bucklin voting
• Condorcet methods
  • Ranked Pairs
  • Schulze method
  • Nanson's method
  • Kemeny-Young method
• Coombs' method
• Single Transferable Vote
  • Instant-runoff voting (IRV) - single winner Single Transferrable Vote (STV)
    • Contingent vote - two round IRV
      • Sri Lankan contingent vote - two round, three rank IRV
      • Supplementary Vote - two round, two rank IRV

See also

• FairVote

External links and further reading

• Toplak, Jurij. "Preferential Voting: Definition and Classification" Paper presented at the annual meeting of the Midwest Political Science Association 67th Annual National Conference, Chicago, IL, April 2009.
• Works of Richard S. Katz, Arend Lijphart, Lauri Karvonen.
• ACE Project: Single Transferable Vote
• ACE Project: Advantages and Disadvantages of STV
• A Handbook of Electoral System Design from International IDEA
• cassandra: open-source preferential voting software
• Electoral Design Reference Materials from the ACE Project
• Ranked Choice Voting in San Francisco
• Descriptions of some ranked-ballot voting methods by approval voting advocate Rob LeGrand