Electoral system


 * parent: Category:Electoral systems

An electoral system (also referred to as an election method or voting system) is a system 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 public elections &mdash; 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.

See Category:Electoral systems for the category associated with this article. This category on electowiki corresponds to "electoral systems" category on English Wikipedia (found here: "wikipedia:Category:Electoral systems").

Summary

 * main category: Category:Electoral systems



An electoral system (also referred to as an election method, voting system, voting rule, voting scheme, etc.) is a system 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 public elections &mdash; 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 electoral systems is that, because they are algorithms, they must be formally defined. For example, consensus is sometimes put forward as a voting system. But consensus is a broad way of working with others, analogous to democracy or anarchy.

Most of voting theory can be thought of as deciding the Number of supportable candidates in the voting method, who should win when there isn't a clearly best candidate, and deciding whether elements of proportional representation are desirable.

Also see the voting theory glossary. Vote counting explains how the ballots submitted by the voters can be physically turned into the information needed to compute the result of a voting method.

Voting methods can generally be categorized into rated and ranked methods. Rated methods look for a candidate who is most "satisfying" to voters (based on their ratings of the candidates), i.e. Score voting. Most ranked methods try to extend majority rule to situations where there are more than two candidates. IRV/RCV and Condorcet methods are the most notable of these.

Criteria in evaluating electoral 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 many desirable criteria are mutually inconsistent.

Determinism and delegation
In addition, there are some distinctions between deterministic and non-deterministic voting methods (deterministic means the voting method always gives the same results when the same ballots are inputted; non-deterministic usually means there's some kind of randomness to the voting method. Most likely you're looking for deterministic methods), and delegated and non-delegated methods (delegated methods allow/force voters to give up their voting power to someone else who decides who wins. You're probably looking for non-delegated methods).

Ballot types
It's also worth looking at what type of ballot the voting method uses i.e. if it uses an Approval ballot (voters can either support or oppose each candidate, like rating them thumbs up or down), a ranked ballot (voter ranks candidates 1st, 2nd, 3rd, etc.), etc.

For a categorized list of electoral systems, see Category:Voting methods

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.

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.

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), which is sometimes called a national district system, 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.

Government formation

 * main article: 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 for an ranked voting system:


 * 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:


 * Proportionality
 * Simplicity - speed
 * Resistance to Tactical voting
 * Resistance to Vote splitting
 * Reduction of potential for dispute after the fact
 * Reduction of potential for fraud
 * Monotonicity criterion (MC)
 * Consistency Criterion (ConC)
 * Broadness Criterion (BC)
 * Condorcet Criterion (CC)
 * Generalized Condorcet criterion (GCC)
 * Strategy-Free criterion (SFC)
 * Generalized Strategy-Free criterion (GSFC)
 * Strong Defensive Strategy criterion (SDSC)
 * Weak Defensive Strategy criterion (WDSC)
 * Favorite Betrayal criterion (FBC)
 * Participation criterion (PC)
 * Summability criterion (SC)

Utility
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.

Social utility efficiency (also known as Voter Satisfaction Index or Voter Satisfaction Efficiency) and its inverse, Bayesian regret, are used to measure how much utility a voting method tends to give to voters. Smith efficiency and Condorcet efficiency are used to measure how Smith-efficient a voting method is.

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

Profile: Also known as preference profile, it is the set of all ballot s for a given election. It is usually combined with a number beforehand, such as "34: A>B>C", which means "34 voters voted A>B>C" i.e. 34 voters prefer A over B and C, and prefer B over 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.

Proportional Representation
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.

Single Member systems

 * Plurality Voting: A valid vote can choose only one candidate
 * Single Member Plurality
 * Random ballot
 * Ranked Voting: A valid vote can rank candidates 1,2,3... (Tied rankings are permitted in some methods but not others)
 * Tied rankings usually not permitted
 * Instant-runoff voting (IRV, also known as alternative vote or "preference voting")
 * Supplementary vote: simplified IRV process (two rankings, two rounds)
 * Borda count: single round count, more points for higher-ranked
 * Coombs' method: disapproval runoff
 * Tied rankings usually permitted
 * Condorcet method, actually several families of systems that satisfy Condorcet's criterion (VOTE-123, Majority/Maximum Majority voting being alternative names):
 * Ranked Pairs (RP) and variants such as Maximize Affirmed Majorities and Maximum Majority Voting
 * Schulze, which is also known as "Beatpath Method" or "Cloneproof Schwartz Sequential Dropping"
 * Copeland's method
 * Bucklin voting: approval with virtual runoff; each voters' ballot is counted for more candidates each round until some candidate reaches a majority
 * Cardinal Voting: voting A valid vote allows independent numerical values to be associated with each candidate. (The set of valid values is limited. So it's usually voting on a scale of, say, 0 to 5)
 * Approval Voting
 * Score Voting
 * STAR voting
 * Majority Choice Approval
 * Median Ratings

Vote-counting
They can also be classified on how many times votes can be counted (Vote counting). 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

 * Bloc Systems
 * Bloc Approval Voting: Each voter chooses (no ranking) as many candidates as desired. Only one vote is allowed per candidate. Voters may not vote more than once for any one candidate. Add all the votes. Elect the candidates with the most votes until all positions are filled.
 * Bloc Plurality Voting: Each voter chooses as many candidates as there are seats to be elected. Add all the votes. Elect the candidates with the most votes until all positions are filled.
 * Bloc Score Voting: Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable. Add all the votes. Elect the candidates with the highest scores until all positions are filled.
 * Cumulative voting
 * Sequential Systems
 * Sequential proportional approval voting
 * Single distributed vote
 * Reweighted Range Voting
 * Sequential Monroe
 * Allocated Score
 * Sequentially Spent Score
 * Single transferable vote
 * Single non-transferable vote
 * Sequential Phragmen
 * Optimal Systems
 * Harmonic Voting
 * Proportional approval voting
 * Phragmén's Method
 * Monroe's method
 * Ebert's Method
 * Max Phragmen
 * PAMSAC

Partisan Systems

 * Party-list proportional representation. Allocation methods:
 * Highest averages methods
 * Sainte-Laguë method
 * d'Hondt method
 * Largest remainder methods
 * Hamilton method

Mixed Systems

 * Mixed Member Proportional
 * parallel mixed system
 * mixed compensatory system

Famous theoreticians of voting systems

 * Andrew Inglis Clark (promoted the use of STV in Tasmania)
 * Jean-Charles de Borda (devised the Borda count)
 * Marquis de Condorcet (proposed the Condorcet criterion)
 * Maurice Duverger (observed effects of proportional vs. majoritarian systems)
 * Thomas Hare (devised STV a.k.a. the Hare Method)
 * Victor d'Hondt (devised a method of seat allocation under proportional representation)
 * Kenneth Arrow (mathematically demonstrated the limitations 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.

Ties
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.

Head-to-head winner
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.

Voting methods that are based on real-world processes
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 for an example.

See the ballot article.