This article is about voting systems that use ranked ballots. For alternative meanings, see: Preferential voting (disambiguation).

A preferential voting system (or preference voting system) is an electoral system in which voters rank a list of candidates in order of preference. In other words (on the most common kind of ballot paper used) the voter writes a '1' beside her first choice, a '2' beside her second preference, and so on. This contrasts with most non-preferential systems, in which the voter simply marks an 'x' beside one or more candidates.

The two preferential voting systems most commonly in use for political elections are instant runoff voting and the Single Transferable Vote (STV). Other preferential systems include Condorcet's method, Bucklin voting and the Borda count. While STV is a form of proportional representation most other preferential systems are designed for single winner elections.

Ballot variations

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• Written numbers: The voters 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 colums to indicate her 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 her mind during voting.

Uniqueness of votes

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If there are more than a small number of candidates then it becomes 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 $\backslash frac\{n!\}\{2ln(2)^\{(n+1)\}\}$. ^*

Australia

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Australia uses two forms of preferential voting; these are instant-runoff voting and the Single Transferable Vote, although neither of these names is commonly used in Australia. Federal House of Representative ballots (which might have 5 to 10 candidates) are counted by hand. Federal Senate ballots with 50 to 100 candidates are now data-entered into computer systems, which then process the ballots.

Supporters of the parties and candidates hand out "How to Vote" cards (HTVs) at the entrance to polling stations, advising voters how to fill in their ballots to support that candidate. Taking these cards is voluntary, and no voter is obliged to follow their instructions, but a high proportion are happy to do so.

The voting systems of some jurisdiction in Australia 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. However it then gives the political parties drawing up the lists considerable tactical power.

List of preferential systems

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• Alternative vote top-up
• Borda count
• Bucklin voting
• Condorcet methods
  • Ranked Pairs
  • Schulze method
  • Nanson's method
  • Kemeny-Young method
• Coombs' method
• Instant-runoff voting
• Single Transferable Vote
• Supplementary Vote

See also

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• List of democracy and elections-related topics

Further reading

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• Works of Richard S. Katz, David Farrell, Michael Marsh, Arend Lijphart, Lauri Karvonen.
• Ranked Choice Voting in San Francisco ^*
• RCV in San Francisco ^*
• RCV in San Francisco ^*
• Australianpolitics.com ^*

Voting systems | preferential electoral systems