Party-list systemA party-list system is a type of electoral system that formally involves political parties in the electoral process, usually to facilitate multi-winner elections. In party-list systems, parties put forward a list of candidates, the party-list who stand for election on one ticket. Voters can usually vote directly for the party-list, but in other systems voters may vote for directly individuals candidates within or across party lists (such systems are referred to as open list and panachage), besides or instead of voting directly for parties (mixed electoral systems).
Mutual majority criterionThe mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidates, such that more than half of the voters strictly prefer every member of S to every candidate outside of S, this majority voting sincerely, the winner must come from S. This is similar to but stricter than the majority criterion, where the requirement applies only to the case that S contains a single candidate.
Nanson's methodThe Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method (also called Total Vote Runoff or TVR). Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings. The Nanson method is based on the original work of the mathematician Edward J. Nanson in 1882.
Majority loser criterionThe majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win. Either of the Condorcet loser criterion or the mutual majority criterion implies the majority loser criterion. However, the Condorcet criterion does not imply the majority loser criterion, since the minimax method satisfies the Condorcet but not the majority loser criterion.
Copeland's methodCopeland's method is a ranked voting method based on a scoring system of pairwise "wins", "losses", and "ties". The method has a long history: Ramon Llull described the system in 1299, so it is sometimes referred to as "Llull's method" The Marquis de Condorcet described a similar system in the 1780s, so the method could be referred to as "Condorcet's method", but instead other systems were subsequently devised that choose the Condorcet winner. Arthur Herbert Copeland described the system in the 1950s, so it has been frequently been called "Copeland's method".
Minimax Condorcet methodIn voting systems, the Minimax Condorcet method (often referred to as "the Minimax method") is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election. It is sometimes referred to as the Simpson–Kramer method, and the successive reversal method. Minimax selects as the winner the candidate whose greatest pairwise defeat is smaller than the greatest pairwise defeat of any other candidate: or, put another way, "the only candidate whose support never drops below [N] percent" in any pairwise contest, with N as high as possible.
Positional votingPositional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will (Eurovision Song Contest) or it may form a mathematical sequence such as an arithmetic progression (Borda count), a geometric one (positional number system) or a harmonic one (Nauru/Dowdall method).
Ranked votingThe term ranked voting, also known as preferential voting or ranked choice voting, pertains to any voting system where voters use a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally.
Sequential proportional approval votingSequential proportional approval voting (SPAV) or reweighted approval voting (RAV) is an electoral system that extends the concept of approval voting to a multiple winner election. It is a simplified version of proportional approval voting. Proposed by Danish statistician Thorvald N. Thiele in the early 1900s, it was used (with adaptations for party lists) in Sweden for a short period from 1909-1921, and was replaced by a cruder "party-list" style system as it was easier to calculate.
Later-no-help criterionThe later-no-help criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner.
Bucklin votingBucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system. Bucklin rules varied, but here is a typical example: Voters are allowed rank preference ballots (first, second, third, etc.
Multiwinner votingMultiwinner voting, also called multiple-winner elections or committee voting or committee elections, is an electoral system in which multiple candidates are elected. The number of elected candidates is usually fixed in advance. For example, it can be the number of seats in a country's parliament, or the required number of members in a committee. There are many scenarios in which multiwinner voting is useful. They can be broadly classified into three classes, based on the main objective in electing the committee: Excellence.
Median voter theoremThe median voter theorem is a proposition relating to ranked preference voting put forward by Duncan Black in 1948. It states that if voters and policies are distributed along a one-dimensional spectrum, with voters ranking alternatives in order of proximity, then any voting method which satisfies the Condorcet criterion will elect the candidate closest to the median voter. In particular, a majority vote between two options will do so. The theorem is associated with public choice economics and statistical political science.
Dual-member proportional representationDual-member proportional representation (DMP), also known as dual-member mixed proportional, is an electoral system designed to produce proportional election results across a region by electing two representatives in each of the region’s districts. The first seat in every district is awarded to the candidate who receives the most votes, similar to first-past-the-post voting (FPTP). The second seat is awarded to one of the remaining district candidates so that proportionality is achieved across the region, using a calculation that aims to award parties their seats in the districts where they had their strongest performances.
Majority judgmentMajority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It uses a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating. Unlike other voting methods, MJ guarantees that the winner between three or more candidates will be the candidate who had received an absolute majority of the highest grades given by all the voters.
Majority criterionThe majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win". Some methods that comply with this criterion include any Condorcet method, instant-runoff voting, Bucklin voting, and plurality voting.
Proportional approval votingProportional approval voting (PAV) is a proportional electoral system for selecting committees. It is an extension of the D'Hondt method of apportionment that additionally allows for personal votes (voters vote for candidates, not for a party list). The voters vote via approval ballots where each voter marks those candidates that the voter finds acceptable. The system was first proposed by Thorvald N. Thiele. It was used in combination with ranked voting in the early 20th century in Sweden, for example between 1909 and 1921 for distributing seats within parties, and in local elections.
Schulze methodThe Schulze method (ˈʃʊltsə) is an electoral system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The method can also be used to create a sorted list of winners. The Schulze method is also known as Schwartz Sequential dropping (SSD), cloneproof Schwartz sequential dropping (CSSD), the beatpath method, beatpath winner, path voting, and path winner.
Electoral reformElectoral reform is a change in electoral systems which alters how public desires are expressed in election results. Reforms can include changes to: Voting systems, such as proportional representation, a two-round system (runoff voting), instant-runoff voting (alternative voting, ranked-choice voting, or preferential voting), Instant Round Robin Voting called Condorcet Voting, range voting, approval voting, citizen initiatives and referendums and recall elections.
Monotonicity criterionThe monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot). That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking.
