Electoral 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.

Most of voting theory can be thought of as deciding whether and how voters should be allowed to express their preference on more than one candidate, who should win when there isn't a clearly best candidate, and deciding whether elements of proportional representation are desirable.

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

Aspects of voting systems

The ballot

See 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.


Ballot: An expression of a voter's preference between the candidates.

Profile: Also known as preference profile, it is a ballot with a specific preference i.e. A>B>C indicates a voter prefers A over B and C, and prefers B over C. Can optionally be combined with a number beforehand, such as "34: A>B>C", which means "34 voters voted A>B>C". Because of the use of fractional surplus transfer, sometimes a decimal number is used to indicate that only a fraction of a given set of ballots remains i.e. an A>B>C voter whose ballot has lost 50% of its weight is sometimes recorded as "0.5: A>B>C".

"Voting method" refers to the algorithm for combining ballot information to determine a winner. "Electoral system" is by country, and can include several voting methods for different offices as well as other related rules. "Voting system" is an ambiguous term — it can mean either of the preceding, or can refer to the physical hardware for casting and/or counting votes.

List of Parliamentary Systems

In general, there are ranked voting methods and rated voting methods. Rated methods generally aim to find an option that maximizes net-happiness by measuring each voter's happiness or degree of support for each option (on a scale). Ranked methods generally aim to generalize majority rule to situations where there are more than two candidates; the majority criterion, mutual majority criterion, and Condorcet criterion are among the more common methods of evaluating ranked methods in terms of this. There is also discussion of how resistant each voting method is to strategic voting. And to top it all off, there are generalizations of both rated and ranked methods to offer proportional representation, which is where minority groups are allowed some representation. Generally, Proportionality for Solid Coalitions is a criterion used to evaluate ranked PR methods, with various philosophies being used to classify the different cardinal/rated PR methods. Strategic voting concerns here generally revolve around free riding, which is when some groups try to get more representation/seats, generally by trying to appear as if they are various different small groups that each merit a seat rather than a larger coalition that many would feel deserves fewer seats.

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

Overlap with other fields

Voting theory intersects with many other fields. For example, computer science is often used to figure out how to compute and demonstrate the results of a voting method, mathematics is useful in evaluating several things such as how many votes various candidates have, etc. Logic features prominently when proving various properties and criteria that voting methods pass, with statistics helping to model how these methods perform in practice. There are articles on this wiki covering the general concept of binary relations theory, which encompasses relations between pairs of objects, or in this context, candidates.


Tie-breaking in voting methods is often done randomly (i.e. for however many candidates there are in the tie, assign them each an equal chance of being picked), though sometimes more nuanced procedures are used, such as lexicographic ordering. In many cases, the reason for this is to preserve compliance with certain criteria i.e. Sequential Monroe voting can be done with a tiebreaker of picking the candidate in the tie with the highest overall summed score when multiple candidates tie for having the most support from their quota of voters, in order to preserve compliance with the Pareto criterion.

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).

Many voting methods are modeled off of real-world processes. For example, IRV can be thought of as simulating American primary elections, where the least viable candidates (according to FPTP) tend to drop out one by one, with their supporters going towards their next viable choice, until only two candidates remain. In this sense, Condorcet methods can be thought of as simulating negotiation (like in Asset voting) such that no party to the deal can get a better deal by forming a new majority coalition for their preferred alternative. See Condorcet method#Demonstrating pairwise counting for an example.

See the ballot article.

See also

External links

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