Voting system

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Voters at the voting booths in the US in 1945

Voting systems are methods (algorithms) for groups of people to select one or more options from many, taking into account the individual preferences of the group members. Voting is best known for its use in elections and is often seen as the defining feature of democracy, where citizen preferences are used to determine the composition of government. In addition, voting can also be used to award prizes, to select between different plans of action, or as a means for computer programs to evaluate which solution is best for a complex problem.

A key property of voting systems is that, because they are algorithms, they must be formally defined. Consensus, for example, which is sometimes put forward as a voting system, is more properly a broad way of working with others, analogous to democracy or anarchy (See consensus decision making for disciplined consensus methods and how they relate to voting).


Aspects of voting systems

The ballot

Different voting systems have different forms for allowing the individual to express their tolerances or preferences. In ranked ballot or "preference" voting systems, like Instant-runoff voting, the Borda count, or a Condorcet method, voters order the list of options from most to least preferred. In range voting, voters rate each option separately. In first-past-the-post (also known as plurality voting), voters select only one option, while in approval voting, they can select as many as they want. In voting systems that allow "plumping", like cumulative voting, voters may vote for the same candidate multiple times.

District (constituency) size

A voting system may select only one option (usually a candidate, but also an option that represents a decision), in which case it is called a "single winner system", or it may select multiple options, for example candidates to fill an assembly or alternative possible decisions on the measure the ballot posed.

Some countries, like Israel, fill their entire parliament using a single multiple-winner district (constituency), while others, like the Republic of Ireland or Belgium, break up their national elections into smaller, multiple-winner districts, and yet others, like the United States or the United Kingdom, hold only single-winner elections. Some systems, like the Additional member system, embed smaller districts within larger ones.

Party-list systems

In party-list proportional representation systems, candidates can be aligned with, or nominated by, parties, and the party's list of candidates plays a functional role within the system. These parties may in turn be aligned with other parties, to form coalitions, which can play roles beyond those played by the party. These systems are designed to ensure proportional representation, the idea that the candidates selected from a given party (or, in non-party-list systems, informal grouping) should be in proportion to the votes cast for that party. Some of these systems, however, have election thresholds--minimum numbers of votes cast for a party to win any seats. The purpose of an election threshold is generally to keep very small parties from participating in a parliament, in order to maintain stability of governments.

None of the above option

In some voting systems, voters may choose to select none of the candidates (or poll options), by voting for a "None of the above" option. If this option wins, the election fails; typically it will be re-run with a new set of candidates or poll options, all previous ones (having lost to "none of the above") being excluded. The philosophy behind having a "None of the above" option is that all possible alternatives should be considered in a decision; this option represents all of the alternatives not considered explicitly.

Write-in candidate - poll option

Some elections allow voters to write in the name of a person (or of the poll option) not on the ballot as their candidate (or as a poll option). Write-in candidates (poll options) rarely win and votes are often cast for ineligible people or fictional characters. This happens because write-in poll options or candidates are not visible to other voters. This is not usually an issue in the case of an e-voting system, where new write-in poll options or candidates can be made visible as the election takes place. Alternatively, some locations require write-in candidates or poll options to be registered before the election.

List of systems

Single-winner systems

Single-winner systems can be classified by ballot type:

  1. Binary voting A valid vote can only give a yes or nothing to a given candidate.
  2. Ranked voting A valid vote can rank candidates 1,2,3... (Tied rankings are permitted in some methods but not others)
  3. Rated voting A valid vote allows independent numerical values to be associated with each candidate. (The set of valid values is limited.)

They can also be classified on how many times votes can be counted. Methods like Plurality, Borda, and Approval with single counting rounds are simpler since voters can be sure to know how their votes will be applied.

Binary voting methods

  • First-past-the-post (also called Plurality or Relative Majority or Winner-Take-All) - vote for at most one candidate. Most votes wins, even if this is less than a majority.
  • Runoff systems
    • Two-round runoff voting - if no majority, hold a new election with only the top two candidates. This system is used for most single-winner elections in France.
    • Elimination runoff - if no majority, hold a new election with the weakest candidate eliminated. Repeat until there is a majority.
    • Exhaustive runoff - no eliminations, repeat balloting until there is a majority. Common in committees. This system is used by the Papal Conclave (if one considers every cardinal as a candidate).
    • Motion and amendment - treating the choice like another substantial motion, subject to amendment and possibly debate.
  • Approval voting (AV) - Voters may vote for as many candidates as they like. Candidate with most votes wins. Sometimes considered a version of range voting (see below) with a point range of [0,1]
  • Random ballot - May also be used for multiwinner elections, or as a tiebreaker for other methods

Ranked voting methods

Rated voting methods

  • Range voting - voters give points in a specified range (for example 0-100) to each candidate. The candidate with the highest total is the winner.
  • Rated ballots may also be used for ranked voting methods, in cases where tied rankings are allowed.

Multiple-winner systems

Criteria in evaluating voting systems

Various criteria are used in evaluating voting systems. These criteria define potentially desirable properties of voting systems mathematically, so that different systems can be compared using the same criteria.

It is impossible for one voting system to pass all criteria in common use. For example, Arrow's impossibility theorem demonstrates that several desirable features of voting systems are mutually contradictory. For this reason, someone implementing a voting system has to decide which criteria are important for the election.

These criteria include:

A more extensive list of criteria is on the voting system criteria page.

Voting systems are also judged with less-mathematical criteria:

  • Simplicity
  • Speed of vote-counting
  • Reduction of potential for fraud or disputed results
  • Resistance to strategic voting
  • Proportionality (proportional representation), for multiple-winner methods
Majority Monotonicity Participation Condorcet Consistency IA independence clone independence
Approval No Yes Yes No Yes Yes Yes
Borda No Yes Yes No Yes No No (teaming)
Copeland Yes Yes No Yes No Local No (crowding)
IRV Yes No No No No No Yes
Plurality Yes Yes Yes No Yes No No (vote-splitting)
Range voting No Yes Yes No Yes Yes Yes
Ranked Pairs Yes Yes No Yes No Local Yes
Schulze Yes Yes No Yes No Local Yes
Compliance of single-winner systems with some established voting system criteria.

Voting systems can be abstracted as mathematical functions that select between choices based on the utility of each option for each voter. This greatly resembles a social welfare function as studied in welfare economics and many of the same considerations can be studied. For aspects such as simplicity, dispute, and fraud, the practical implementation is far more important than the abstract function. However, the choice of abstract function puts some constraints on the implementation. For instance, certain voting systems such as First Past the Post, Schulze, or Borda count can be tallied in one distributed step, others such as Instant-Runoff require centralization, and others such as multi-round runoff require multiple polling rounds.

Related terminology

voting strategy 
Any way of voting, when it's discussed in terms of its possible or intended affect on the outcome.
strategic or tactical voting 
When a voter self-consciously marks a ballot in a manner different from their actual preferences, in the hope of optimizing the outcome. (While the adjectives 'strategic' and 'tactical' usually have nearly opposite meanings when used to describe other things, in this case, they commonly both have the meaning given here.)

Famous theoreticians of voting systems

See also


External links

(alphabetical by title)

fr:Systme de vote fi:Vaalitapa nl:Kiessysteem pt:Sistemas de votao da:valgmetode ja:選挙方法


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