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. Typically the voter writes a '1' beside their first choice, a '2' beside their second preference, and so on. This contrasts with most non-preferential ballots, in which the voter simply marks an 'x' beside one or more candidates. An example of a plurality ballot. ... An example of runoff voting. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... A Condorcet method is a single winner election method in which voters rank candidates in order of preference. ... Copelands method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories. ... The Kemeny-Young method is a voting system that uses preferential ballots, a tally table, and sequence scores to identify the most popular choice, and also identify the second-most popular choice, the third-most popular choice, and so on down to the least-popular choice. ... Minimax is often considered to be the simplest of the Condorcet methods. ... The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ... The Coombs method, created by Clyde Coombs, is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... Example Instant-runoff voting ballot Instant-runoff voting (IRV) is a voting system most commonly used for single member elections in which voters have one vote, but can rank candidates in order of preference. ... On an approval ballot, the voter can vote for any number of candidates. ... Range voting (also called ratings summation, average voting, cardinal ratings, 0–99 voting, or the score system or point system) is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins. ... Proportional representation (sometimes referred to as full representation, or PR), is a category of electoral formula aiming at a close match between the percentage of votes that groups of candidates (grouped by a certain measure) obtain in elections and the percentage of seats they receive (usually in legislative assemblies). ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is a voting system used to elect representatives to numerous legislatures around the world. ... Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ... The DHondt method (equivalent to Jeffersons method, and Budder-Ofer method) is a highest averages method for allocating seats in party-list proportional representation. ... The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The Sainte-Laguë method of the highest average (equivalent to Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... This article or section does not adequately cite its references or sources. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... Parallel voting describes a mixed voting system where voters in effect participate in two separate elections using different systems, and where the results in one election have little or no impact on the results of the other. ... The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ... Bloc voting (or block voting) refers to a class of voting systems which can be used to elect several representatives from a single multimember constituency. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Sortition is the method of random selection, particularly in relation to the selection of decision makers also known as allotment. ... For the town in France, see Ballots, Mayenne. ...

In single-winner elections a preferential ballot paper can be redistributed according to the voter's expressed preference. Votes allocated to a candidate that is to be excluded from the election counting process are redistributed and allocated to the subsequent continuing candidate in order of the voter's indicated preference. This is the voting system known as instant runoff voting (IRV). IRV is an alternative to the Two-round system as only a single round is needed to elect a candidate who is required to secure 50% of the votes +1 extra vote to secure the majority win. When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ... An example of runoff voting. ...

In multiple-winner elections the preferential ballot is used in the voting system known as the Single Transferable Vote (STV), a form of proportional representation. This STV ballot for the Australian Senate illustrates group voting tickets. ... Proportional representation (sometimes referred to as full representation, or PR), is a category of electoral formula aiming at a close match between the percentage of votes that groups of candidates (grouped by a certain measure) obtain in elections and the percentage of seats they receive (usually in legislative assemblies). ...

In single-winner elections preferential voting can apply to individual candidates, groups or parties depending on the design of the election ballot. With a preferential ballot supporters of minor candidates or parties are not totally disenfranchised as their votes are redistributed to a candidate or party of their choice. However, unlike proportional voting systems, no single-winner election lets these voters' first choices count.

In single-winner elections the use of a preferential ballot limits the extent in which candidates stand for election as spoilers in an attempt to remove votes that would otherwise be allocated to a particular candidate or party. A preferential ballot also allows people to vote for minor candidates while not spoiling their preferred major candidate. Spoiler could refer to Plot spoiling: a document, review, or comment which discloses plot details of a book, play, or film. ...

Preferential ballots are also used in Condorcet's method and the Borda count in single-winner elections, and in Bucklin voting. Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ...

The Kemeny-Young method uses preferential ballots to fully rank all the candidates from most popular to least popular. The Kemeny-Young method is a voting system that uses preferential ballots, a tally table, and sequence scores to identify the most popular choice, and also identify the second-most popular choice, the third-most popular choice, and so on down to the least-popular choice. ...

Ballot variations

• 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.

Rank ballot example with numbers File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Rank ballot with oval markings - example File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Rank ballot with hand-written names File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Rank ballot example by touch screen File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Nintendo DS Touch screen A touch screen is an input/output device that allows the user to interact with the computer by touching the display screen. ...

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 Irish general election of 2002 was held on Friday 17 May 2002, just over three weeks after the dissolution of the 28th Dáil on Thursday 25 April by President Mary McAleese, at the request of the Taoiseach, Bertie Ahern. ... Dublin North is a parliamentary constituency in the Republic of Ireland, located in the northern area of County Dublin. ...

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 .^[1] In mathematics, a total order, linear order or simple order on a set X is any binary relation on X that is antisymmetric, transitive, and total. ... For factorial rings in mathematics, see unique factorisation domain. ... The 13 possible strict weak orderings on a set of three elements {a, b, c}. Two orderings are shown as connected by an edge if they differ by the presence or absence of a single pair in the relations defining the orderings. ... In mathematics and applications, particularly the analysis of algorithms, asymptotic analysis is a method of classifying limiting behaviour, by concentrating on some trend. ...

Australia

Main article: Australian electoral system

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. This article deals with elections to the Australian Parliament. ... Example Instant-runoff voting ballot Instant-runoff voting (IRV) is a voting system most commonly used for single member elections in which voters have one vote, but can rank candidates in order of preference. ... This STV ballot for the Australian Senate illustrates group voting tickets. ...

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"^[2].

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. Group voting tickets are a way to simplify the voting in a single transferable vote 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

The Alternative Vote Plus (AV+) or Alternative Vote Top-up is a voting system intended for use in elections to an assembly or legislature. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ... A Condorcet method is a single winner election method in which voters rank candidates in order of preference. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. ... The Kemeny-Young method is a voting system that uses preferential ballots, a tally table, and sequence scores to identify the most popular choice, and also identify the second-most popular choice, the third-most popular choice, and so on down to the least-popular choice. ... The Coombs method, created by Clyde Coombs, is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... Example Instant-runoff voting ballot Instant-runoff voting (IRV) is a voting system most commonly used for single member elections in which voters have one vote, but can rank candidates in order of preference. ... The contingent vote is an electoral system used to elect a single winner, in which the voter ranks the candidates in order of preference. ... In Sri Lanka a variant of the contingent vote electoral system is used to elect the President. ... Sample ballot paper The Supplementary Vote (SV) is an electoral system used fore the election of a single candidate. ...

References

1. ^ Wilf, Herbert S. [1990] (January 1994). "Chapter 5: Analytic and asymptotic methods", generatingfunctionology, Second Edition, Academic Press, 175–176. ISBN 0-12-751956-4. Retrieved on 2006-08-06. 
2. ^ http://www.abc.net.au/elections/act/2004/guide/preference.htm

Herbert Wilf (born 1931) is a mathematician, specializing in combinatorics. ... Academic Press (London, New York and San Diego) was an academic book publisher that is now part of Elsevier. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 218th day of the year (219th in leap years) in the Gregorian calendar. ...

External Links and Further reading

• Works of Richard S. Katz, David Farrell, Michael Marsh, 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
• Electoral Design Reference Materials from the ACE Project
• Ranked Choice Voting in San Francisco [1]
• RCV in San Francisco [2]
• RCV in San Francisco [3]
• Australianpolitics.com [4]