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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 method|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 systemsParliamentary Systems ==
 
===[[Single Member systems]]===▼
 
===[[Regional Systems]]===
Single Winner systems can be classified by ballot type:
#'''Binary voting''' A valid vote can only give a yes or nothing to a given candidate.
#'''Ranked voting''' A valid vote can rank candidates 1,2,3... (Tied rankings are permitted in some methods but not others)▼
#'''Rated voting''' A valid vote allows independent numerical values to be associated with each candidate. (The set of valid values is limited.)▼
 
▲====[[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.▼
 
* [[Plurality Voting]]: A valid vote can choose only one candidate
==== Binary voting methods ====
** [[Single Member Plurality]]
 
** [[Random ballot]]
*[[First-past-the-post election system|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.
▲#'''Ranked* voting'''[[Ordinal Voting]]: A valid vote can rank candidates 1,2,3... (Tied rankings are permitted in some methods but not others)
*Runoff systems
*''Tied rankings not permitted''▼
**[[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.
** [[Instant-runoff voting]] (IRV, also known as alternative vote or "preference voting")
**Elimination runoff - if no majority, hold a new election with the weakest candidate eliminated. Repeat until there is a majoirty.
*** [[Supplementary vote]]: simplified IRV process (two rankings, two rounds)▼
**Exhaustive runoff - no eliminations, repeat balloting until there is a majority. Common in committees.
** [[Borda count]]: single round count, more points for higher-ranked▼
*[[Approval voting]] (AV) - Voters may for vote for as many candidates as they like. Candidate with most votes wins. Sometimes considered a version of Cardinal Rankings (see below) with a point range of [0,1]
** [[Coombs' method]]: disapproval runoff▼
*[[Random ballot]] - May also be used for multiwinner elections, or as a tiebreaker for other methods
*''Tied rankings permitted''▼
 
** [[Condorcet method]], actually several families of systems that satisfy Condorcet's criterion:▼
==== Ranked Voting methods ====
*** [[Ranked Pairs]] (RP) and variants such as [[Maximize Affirmed Majorities]] and [[Maximum Majority Voting]]▼
▲*Tied rankings not permitted
** [[Instant-runoffSchulze votingmethod|Schulze]] (IRV, which is also known as alternative"Beatpath voteMethod" or "preferenceCloneproof Schwartz Sequential votingDropping")
*** [[Copeland's method]]▼
▲***[[Supplementary vote]]: simplified IRV process (two rankings, two rounds)
***Other names for ''Condorcet-compliant methods:''▼
▲**[[Borda count]]: single round count, more points for higher-ranked
**** VOTE-123: another name for Condorcet methods, stands for Virtual One-on-one Tournament Elections using 1st, 2nd, & 3rd choices▼
▲**[[Coombs' method]]: disapproval runoff
**** Majority voting or Maximum Majority voting: another term often used for Condorcet methods▼
▲*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]]
***[[Schulze method|Schulze]], which is also known as "Beatpath Method" or "Cloneproof Schwartz Sequential Dropping"
▲***[[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 with virtual runoff; each voters' ballot is counted for more candidates each round until some candidate reaches a majority
▲#'''Rated* [[Cardinal Voting]]: voting''' A valid vote allows independent numerical values to be associated with each candidate. (The set of valid values is limited.)
** [[Approval Voting]]
** [[Score Voting]]
*** [[CumulativeSTAR voting]]▼
** [[Majority Choice Approval]]
 
▲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.
==== 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) - This term is now used to refer to Bucklin methods which allow equal ratings. As explained above, Bucklin systems are like Approval with a virtual runoff; they attempt to find the candidate with an absolute majority at the highest rank. (Previously, MCA referred to a specific system, with 3 rating levels and the possibility of a runoff election).
*Rated Ballots may also be used for ranked voting methods, in cases where tied rankings are allowed.
 
====[[Multi-Member Systems]]====
===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).
 
* [[Block voting | Bloc Systems]]
; 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).
** 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]]
*MixedSequential Systems▼
** [https://en.wikipedia.org/wiki/Sequential_proportional_approval_voting Sequential Proportional Approval Voting]
*** [[Proportional approval voting]]▼
** [[Reweighted Range Voting]]
** [[Sequential Monroe]]
** [[Allocated Score]]
** [[Sequentially Subtracted Score]]
*** [[Single non-transferable vote]]▼
* Optimal Systems
** [https://rangevoting.org/QualityMulti.html Harmonic Voting]
 
===[[Multi-MemberPartisan 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]]
***[[Single transferable vote]] (STV)
*[[Party-list proportional representation]]. Allocation methods:
**[[Highest averages method]]s
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***[[d'Hondt method]]
**[[Largest remainder method]]s
▲*Mixed Systems
**[[Additional Member System]] (also called Mixed Member Proportional) ▼
**[[Parallel voting]] (also called Supplementary Member system)
 
===Related[[Mixed terminologySystems]]===
▲**[[Additional Member System]] (also called| Mixed Member Proportional) ]]
; voting strategy : Any way of voting, when it's discussed in terms of its possible or intended affect on the outcome.
** parallel mixed system
; strategic or [[tactical voting]] : When a voter self-consciously marks a ballot in a manner different than 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.)
** mixed compensatory system
 
== Famous theoreticians of voting systems ==
Dr. Edmonds
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