Voting system

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Voting systems or election methods are methods for groups of people to select one or more options from many, taking into account the individual preferences of the group members, or more generally to find society's preference among all the candidates (1st place, 2nd place, etc.). Voting is often seen as the defining feature of democracy, and is best known for its use in elections — but it 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.

Several of the popular voting methods, categorized by their important properties

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 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.

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, all candidates or poll options are excluded from a subsequent election.

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.

Government formation

The formation of the government happens after the election and can be done in multiple ways. This is independent of the elections themselves. There are many systems of government, each of which has an electoral system and a system of government formation as components. Typical parliamentary systems use a two-step process, first, an election is called where the representatives are elected by citizens through a balloting system, then the government is formed from the representatives through its own process.

Criteria in evaluating voting systems

Various criteria are used in evaluating voting systems. However, it is impossible for one voting system to pass all criteria in common use. For example, Arrow's impossibility theorem demonstrates that the following criteria are mutually contradictory:

  • The voting system should always give a result
  • If a voter improves the ranking of a particular option, that option should not be disadvantaged (monotonicity criterion)
  • Removing a candidate should not change the winner of an election unless that candidate is the winner (independence of irrelevant alternatives)
  • Every possible outcome should be achievable
  • Non-dictatorship (i.e. more than one person's vote matters)

Other criteria which have been used to judge voting systems include:

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 IRV require centralization, and others such as multi-round runoff require multiple polling rounds.

List of Parliamentary Systems

Regional Systems

Single Member systems

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.

Multi-Member Systems

Partisan Systems

Mixed Systems

Famous theoreticians of voting systems


There must be more candidates than seats to be filled for different voting methods to give different results.

Both Condorcet methods and the two main rated methods, Approval voting and Score voting, attempt to elect a candidate who would win within those methods if it was just that candidate and any other candidate in a head-to-head competition. See Self-referential Smith-efficient Condorcet method.

Bucklin (which can be thought of as one of the rated Majority Judgement family of methods) is a way to make rated methods more majoritarian by passing the mutual majority criterion.

Choose-one FPTP voting can be thought of as a constrained rated method, with IRV being a way to make FPTP more majoritarian by passing the mutual majority criterion (and guaranteeing the Condorcet winner will win if they get over 1/3rd of the active votes in any round).

See the ballot article.

See also

External links

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