Preferential voting

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The term preferential voting (also known as the preference voting) has several different meanings:

(1) A ranked ballot system or ordinal voting system (from "ordinal utility") is a type of voting system in which each voter casts their vote by ranking candidates in order of preference.

Voting systems which use a ranked ballot include:

(2) Preferential voting is a synonym for both instant-runoff voting and single transferable vote, especially in Australia, where such ballots are actually in use in elections. See Australian electoral system.

(3) In Europe, preferential voting denotes what is in United States known as the Open List Proportional Representation (Open list PR). It is a voting system giving a voter an option to vote for one of the party lists and then also express a preference for one of the candidates of this list.

(4) Often the term preferential voting is used for any kind of intraparty preference.[clarification needed]

Ballot design or voting machine instructions are particularly important in such systems, as each voter is expected to express a rather complex set of tolerances or preferences in each vote.

Example: if there are 4 candidates, A, B, C and D, then a voter could rank them as A>B>C=D (A is the voter's 1st choice, but they'll take B if they can't get A because B is their 2nd choice, and C and D are equally preferable), B>C (B is better than C), etc. When a voter doesn't rank all candidates, it's usually assumed they have no preference between the candidates they didn't rank, and that they prefer every candidate they ranked over all of their unranked candidates.

Ballot variations

  • Column marks: Optical scanner ballots use the ballot with column voting with ovals.
    • Column rank ballots have limits rankings due primarily to available paper space. For example the image below is limited to three rankings.
  • Write numbers: Hand-written numeric rankings are more compact to vote and easier to hand count.
  • Write names: Hand-written names as a list from first to last preference.
  • Touch screen: A slightly different category of voting is a computer Touch screen could also be used, asking voters their first, second, etc preferences, and showing the selections so far and remaining choices, allowing selections to be removed if the voter makes a mistake or changes her mind during voting. Some people want touch screen voting to print a paper ballot at the end as a hardcopy backup.

Equal rankings

Another variation of ranked ballots is to allow a voter to give multiple candidates the same ranking. This allows voters to cast range voting style ballots. Ways of dealing with such ballots include:

  • Convert the ballot into a fully-ranked one by breaking ties at random.
  • Use fractional votes. If N candidates are tied on a ballot, each candidate receives 1/N of a first-place vote, 1/N of a second-place vote, etc.
  • In most Condorcet methods, the defeat strength of X over Y can be computed from the X>Y and Y>X votes, while simply ignoring X=Y votes.

For Condorcet methods, the first approach (random tie-breaking) results in the same results in the head-to-head matchups between the tied candidates with probability approaching 1 if many voters do it, and there are only 2 tied candidates. For example, if 100 voters use a 50% probability of ranking one over the other and a 50% probability of the vice versa, then there will be 50 voters preferring one and 50 voters preferring the other in their head-to-head matchup, resulting in no change in the margin between the two. Note that this will change the defeat strength as measured by winning votes or possibly other measures, though; for example, if a candidate had a 2 to 1 (66.66% majority) victory over someone else, and 100 votes are added on both sides, this becomes closer to a 50.1% majority victory.

Scope for corruption

A potential problem with preferential votes is that they can be used to undermine a secret ballot, and thus enable corruption by vote buying. If there are enough candidates then the number of possible voting patterns may be much larger than the number of voters, and it then becomes possible to use early preferences to vote for the desired candidates and then to use later preferences to identify the voter to the person who has purchased the vote and looks at the ballot papers.

As an example, in the Irish general election of 2002, the electronic votes were published for the Dublin North constituency. There were 17 candidates, allowing more than 966 million million possible patterns of preferences, but there were fewer than 44,000 votes cast. The most common pattern (for three of the candidates in a particular order) was chosen by 800 voters, and more than 16,000 patterns were chosen by just one voter each.

One way to avoid this possibility for buying a vote and confirming it has been cast as specified is to prevent partisan observers from systematically viewing individual voter's preferences. Another option is to, when publishing the ballots, truncate preferences that are voted by fewer voters than some threshold. For instance, if a hundred voters all voted A>B>C but then each of these voters ranked the remaining candidates in an unique order, only publish 100: A>B>C.

How to Vote Cards and "Above the line" voting

In Australia, which uses preferential voting for both houses, candidates hand out at the entrance to Polling Stations "How to Vote Cards", which advise voters how best to fill in their ballots to support that candidate, and any cross preference deals they may have arranged with other candidates. These HTVC cards are voluntary, and no voter is obliged to do so, but high proportion are happy to do so. In elections for the upper houses, which use proportional representation as well as preferential voting, it may be daunting to have to fill in 70 boxes - preferences are compulsory. To ease this onerous task, "Above the line" voting, allows the voter to choose one party or group, and all the remaining squares are deemed to be filled in according to a registered party ticket. About 95% of voters choose to use this method.

Parliamentary procedure

Recent editions of Robert's Rules of Order mention preferential voting. The book notes, "While it is more complicated than other methods of voting in common use and is not a substitute for the normal procedure of repeated balloting until a majority is obtained, preferential voting is especially fair and useful in an election by mail if it is impractical to take more than one ballot" (RONR [10th ed.], p. 411, l. 23). Rather than discuss Condorcet, the Borda count, and other lesser-known variations, the book simply states, "Preferential voting has many variations. One method is described here by way of illustration," and proceeds with a description of instant-runoff voting.


Approval voting can be thought of as a special case of a ranked method where voters are constrained to ranking all candidates either 1st or last (this requires allowing equal-rankings). Score voting can be understood in the ranked context by first turning the Score ballots into Approval ballots using the KP transform. It can be of interest to observe what a ranked voting method looks like in its "approval case" (when all voters rank in a way that can be converted into an Approval ballot i.e. rank 1st or last). For example, all Smith-efficient Condorcet methods become Approval voting in their approval case. It has not been investigated very far as to what the approval case of several ranked PR methods looks like: for something like Schulze STV, it is very likely that it reduces to some other Approval PR method, or that its approval case is an interesting new Approval PR method.

Interesting hybrids of rated methods and ranked methods can be thought of when allowing the voter to establish how strong their preference is between each ranking. Rankings generally assume a voter has a maximally strong preference between every pair of candidates they indicate any preference between, while ratings assume a voter's preference in one head-to-head matchup directly influences their preference in another i.e. a voter who votes, with the max score of 5 and the min score of 0, A:5 B:0, is assumed to have no preference between B and C. This can be bridged between by allowing the voter to indicate independently how strong their preference is in each head-to-head matchup; see Order theory#Strength of preference.

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