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 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 (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, 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), in which case it is called a "single winner system", or it may select multiple options, for example candidates to fill an assembly.

Some countries, like Israel, fill their entire parliament using a single multiple-winner district (constituencies), 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.

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

In some voting systems, voters may choose to select none of the candidates, by voting for a "None of the above" option.

Write-in candidate

Some elections allow voters to write in the name of a person not on the ballot as their candidate. Write-in candidates rarely win and votes are often cast for ineligible people or fictional characters. Some locations require write-in candidates to be registered as candidates before the election.

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:

• Proportionality
• Simplicity - speed
• Resistance to strategy
• Reduction of potential for dispute after the fact
• Reduction of potential for fraud

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, Condorcet, 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.

List of systems

Single Winner Systems

Single Winner systems can be classified by ballot type:

1. Yes/No voting A valid vote can only give a yes or no 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.

Yes/No 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.
• Runoff systems
  • Runoff voting - Two Round System - 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 majoirty.
  • Exhaustive runoff - no eliminations, repeat balloting until there is a majority. Common in committees.
• Approval voting (AV) - Voters may vote yes or no on each candidate. Candidate with most yes votes wins. Sometimes considered a version of Cardinal Rankings (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

• Tied rankings not permitted
  • Instant Runoff Voting (IRV, a.k.a. Alternative Vote or 'preference voting')
    • (Supplementary Vote - Simplified IRV process (2 rankings, 2 rounds)
  • Borda count - single round count, more points for higher-ranked
  • Coombs' method - disapproval runoff
• Tied rankings permitted
  • Condorcet method, actually several families of systems that satisfy Condorcet's criterion:
    • Ranked Pairs (RP) and variants such as Maximize Affirmed Majorities and Maximum Majority Voting
    • Cloneproof Schwartz Sequential Dropping (CSSD), which is also known as "Beatpath Method" or "Schulze Method"
    • Copeland's method
    • Other names for Condorcet Compliant methods:
      • VOTE-123 - Another name for Condorcet methods, stands for Virtual One-on-one Tournament Elections using 1st, 2nd, & 3rd choices
      • Majority voting or Maximum Majority voting- another term often used for Condorcet methods
  • Bucklin voting - approval runoff. Voters vote for more candidates each round until a candidate reaches a majority.

Rated Voting methods

• Cardinal Ratings (CR) (Also called Range voting) - voters give whole number points (example 1-10) to each candidate, totaled in single round
• Majority Choice Approval (MCA) - like Approval but with range [0,2] and multiple counting rounds.
• Rated Ballots may also be used for ranked voting methods, in cases where tied rankings are allowed.

Single Winner Variations

Automatic Equal Ranking Line Option (AERLO) 

A voter may mark a line in his/her ranking, meaning that if no one above that line wins, then that voter wants to promote to 1st place all of his/her above-line candidates and have a recount. (In pairwise-count methods the promotion only takes place if, additionally, there's a circular tie containing above-line and below-line candidates).

Automatic Truncation Line Option (ATLO) 

A voter may mark a line in his/her ranking, meaning that if no one above the line wins, then that voter wants to drop from his/her ranking all of his/her below-line candidates and have a recount. (In pairwise-count methods the dropping only takes place if, additionally, there's a circular tie containing above-line and below-line candidates).

Multiple Winner Systems

• Multiple Winner Systems (not party-list)
  • Plurality/majority
    • Block voting - Also called Plurality-at-large
  • Semiproportional
    • Proportional approval voting
    • Cumulative voting
    • Single non-transferable vote
  • Proportional Representation
    • Single transferable vote (STV)
• Party-list proportional representation. Allocation methods:
  • d'Hondt method
  • largest remainder method
  • Sainte-Laguë method
• Mixed Systems
  • Additional Member System (also called Mixed Member Proportional)
  • Parallel voting (also called Supplementary Member system)

Criteria for evaluating election methods

Favorite Betrayal Criterion (FBC) 

a voter should never have to vote a less favored candidate over their favorite

Some would argue that if a voter is not too narrow-minded and understands overall trends and the dynamics of calculating votes, then this criterion should be ignored. Others might consider this cheating.

Strategy Free Criterion (SFC) 

a voter should be able to achieve optimal results by voting their sincere preferences

Strong Defensive Strategy Criterion (SDSC) 

when one faction attempts to use offensive strategy to distort the results, there should be a strategy available for other factions to use to preserve the majority winner

• Related terms:
  • Generalized Strategy-Free Criterion (GSFC)
  • Weak Defensive Strategy Criterion (WDSC) :

Related terminology

voting strategy 

Any way of voting, when it's discussed in terms of its possible or intended affect on the outcome.

strategic voting 

When a voter self-consciously marks a ballot in a manner different than their actual preferences, in the hope of optimizing the outcome.

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 (devised Condorcet's method)
• 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)

See also

• Consensus
• Democracy
• Disapproval voting (anyone not disapproved, effectively wins - this method is more associated with reality game shows than with public elections)
• Duverger's law
• Electoral reform
• Grassroots democracy
• Politics
• Political scientists
• Representative democracy
• Spoiler effect
• Table of voting systems by nation
• Tactical voting
• Party system
• Vote counting systems

External links

• Administration and Costs of Elections Project documents on electoral systems (http://www.aceproject.org/main/english/es/es.htm)
• The history of voting (http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Voting.html)
• Center for Voting and Democracy (http://www.fairvote.org)
• ODP category on voting systems (http://dmoz.org/Society/Politics/Campaigns_and_Elections/Voting_Systems/)
• Election Methods Education and Research Group (http://electionmethods.org/)
• defensive strategy criteria page (http://www.barnsdle.demon.co.uk/vote/sing.html)
• Condorcet.org definitions (http://condorcet.org/emr/)
• Preferential Voting FAQ (http://www.braindoll.net/vote) (see glossary at the end)
• Emocracy (http://www.emocracia.no.sapo.pt) Emocratic Elections Investigation
• James Green-Armytage's voting methods page (http://fc.antioch.edu/~jarmyta@antioch-college.edu/voting.htm) Includes a helpful in-depth tutorial
• A New Monotonic and Clone-Independent Single-Winner Election Method (http://lists.gnu.org/archive/html/demexp-dev/2003-09/pdflQW7IlpAfC.pdf) (PDF) by Markus Schulze (from GNU archive)
• A New Monotonic and Clone-Independent Single-Winner Election Method (http://www.mcs.vuw.ac.nz/~ncj/comp303/schulze.pdf) (PDF) by Markus Schulze (from New Zealand)