Preferential voting

:"This article is about voting systems that use ranked ballots. For alternative meanings, see: Preferential voting (disambiguation). "Preferential ballot," "preferential voting," and "ranked choice voting" redirect here; for their use in elections for a single seat, see Instant-runoff voting."

Preferential voting (or preference voting) is a type of ballot structure used in several electoral systems in which voters rank a list or group of candidates in order of preference. For example, the voter may write a '1' beside their first choice, a '2' beside their second preference, and so on. This contrasts with ballots used by methods which do not allow more than two-valued ranking of candidates (Yes or No, often with No assumed unless Yes is marked), such as Plurality voting or Approval voting.

Preferential ballots are used in Instant runoff voting, Condorcet methods, Borda count, Bucklin voting among many others for single-winner elections, as well as single transferable vote for multiple winner elections.

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. Hand-written numeric rankings are compact and easy to hand count.
*Column marks: The voter places marks in columns to indicate his order of preferences. These ballots can be easily counted by optical scanners. However considerations of space may limit the number of preferences a voter can express. For example in the image above the voter is limited to three preferences.
*Written names: The numbers are written on the ballot paper and the voter must write 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 are asked for their first, second and subsequent preferences. The selections so far are displayed as well as remaining unranked candidates, allowing selections to be removed if the voter makes a mistake or changes his mind during voting.

Some ballot designs (such as the optical scanner versions) may have insufficient rankings to allow preferences between all candidates.

Some election rules may require voters rank all candidates to be a valid vote.

Most election rules disallow the use of tied-rankings.

Uniqueness of votes

If there are 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, but with ties it's equal to the corresponding ordered Bell number and is asymptotic to $frac\{n!\}\{2ln(2)^\{(n+1)$. [cite book | last = Wilf | first = Herbert S. | authorlink = Herbert Wilf | title = generatingfunctionology | origyear = 1990 | url = http://www.math.upenn.edu/~wilf/DownldGF.html | accessdate = 2006-08-06 | edition = Second Edition | year = 1994 | month = January | publisher = Academic Press | id = ISBN 0-12-751956-4 | pages = 175–176 | chapter = Chapter 5: Analytic and asymptotic methods ]

Australia

Australia uses preferential ballots in two different ways: instant-runoff voting and the single transferable vote system, although neither of these names is commonly used in Australia.

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

Single Transferable Vote systems are used in electing candidates to multi-member electorates such as the Australian Senate, State upper houses, Tasmania's State legislative assembly, the Australian Capital Territory's legislative assembly, and some local government municipalities.

Ballot papers are counted according to prescribed set of rules which prescribe the method used in the counting of the ballots and the distribution of preferences. Voters' preferences are now data-entered into computer systems, which then process the recorded votes to determine the results of the election. Copies of the transcribed date 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" [ [http://www.abc.net.au/elections/act/2004/guide/preference.htm Preference Leakage. ACT Election Guide 2004. Australian Broadcasting Corporation (ABC) ] ] .

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 are 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 - single winner STV
*** Contingent vote - two round IRV
**** Sri Lankan contingent vote - two round, three rank IRV
**** Supplementary Vote - two round, two rank IRV

Notes

External links and further reading

*FairVote www.fairvote.org has popularly written arguments for the preferential ballot and other electoral reform.
*Works of Richard S. Katz, Arend Lijphart, Lauri Karvonen.
* [http://www.aceproject.org/ace-en/topics/es/esd/esd02/esd02d/default ACE Project: Single Transferable Vote]
* [http://www.aceproject.org/ace-en/topics/es/esd/esd02/esd02d/esd02d01 ACE Project: Advantages and Disadvantages of STV]
* [http://www.idea.int/publications/esd/index.cfm A Handbook of Electoral System Design] from [http://www.idea.int International IDEA]
* [http://um.com.au/cgi-bin/cassandra/ cassandra: open-source preferential voting software]
* [http://www.aceproject.org/ace-en/topics/es Electoral Design Reference Materials] from the [http://www.aceproject.org ACE Project]
*Ranked Choice Voting in San Francisco [http://beyondchron.org/news/index.php?itemid=2935#more]
*Australianpolitics.com [http://www.australianpolitics.com/voting/systems/preferential.shtml]