Ranked pairs, the Glossary

Table of Contents

1. 23 relations: Absolute value, Condorcet loser criterion, Condorcet method, Condorcet paradox, Condorcet winner criterion, Constitutional Political Economy, First-past-the-post voting, Independence of clones criterion, Independence of irrelevant alternatives, Independence of Smith-dominated alternatives, Instant-runoff voting, Majority favorite criterion, Monotonicity criterion, Nicolaus Tideman, Participation criterion, Ranked voting, Reinforcement criterion, Round-robin tournament, Round-robin voting, Smith criterion, Smith set, Strikethrough, Voting criteria.

2. Monotonic Condorcet methods
3. Single-winner electoral systems

Absolute value

In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign.

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Condorcet loser criterion

In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems.

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Condorcet method

A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. Ranked pairs and Condorcet method are single-winner electoral systems.

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Condorcet paradox

In social choice theory, a Condorcet paradox (or voting paradox) is a situation where majority rule behaves in a way that is self-contradictory.

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Condorcet winner criterion

In an election, a candidate is called a majority winner or majority-preferred candidate if more than half of all voters would support them in a one-on-one race against any one of their opponents.

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Constitutional Political Economy

Constitutional Political Economy is a quarterly peer-reviewed academic journal on constitutional economics published by Springer Science+Business Media.

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First-past-the-post voting

First-preference plurality (FPP)—often shortened simply to plurality—is a single-winner system of positional voting where voters mark one candidate as their favorite, and the candidate with the largest number of points (a '''''plurality''''' of points) is elected. Ranked pairs and First-past-the-post voting are electoral systems and single-winner electoral systems.

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Independence of clones criterion

In social choice theory, the independence of clones criterion says that adding a clone, i.e. a new candidate very similar to an already-existing candidate, should not spoil the results.

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Independence of irrelevant alternatives

Independence of irrelevant alternatives (IIA), also known as binary independence, the independence axiom, is an axiom of decision theory and economics describing a necessary condition for rational behavior.

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Independence of Smith-dominated alternatives

Independence of Smith-dominated alternatives (ISDA, also known as Smith-IIA) is a voting system criterion which says that the winner of an election should not be affected by candidates who are not in the Smith set.

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Instant-runoff voting

Instant-runoff voting (IRV), also known as ranked-choice voting or the alternative vote (AV), combines ranked voting (in which voters rank candidates rather than choosing only a single preferred candidate) together with a system for choosing winners from these rankings by repeatedly eliminating the candidate with the fewest first-place votes and reassigning their votes until only one candidate is left. Ranked pairs and Instant-runoff voting are single-winner electoral systems.

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Majority favorite criterion

The majority favorite criterion is a voting system criterion that says that, if a candidate would win more than half the vote in a first-preference plurality election, that candidate should win.

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Monotonicity criterion

The positive response, '''monotonicity''', or nonperversity criterion is a principle of social choice theory that says that increasing a candidate's ranking or rating should not cause them to lose.

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Nicolaus Tideman

Thorwald Nicolaus Tideman (not; born August 11, 1943, in Chicago, Illinois) is a Georgist economist and professor at Virginia Tech.

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Participation criterion

The participation criterion, also called vote or '''population monotonicity''', is a voting system criterion that says that a candidate should never lose an election as a result of receiving too many votes in support.

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Ranked voting

Ranked voting is any voting system that uses voters' orderings (rankings) of candidates to choose a single winner. Ranked pairs and Ranked voting are electoral systems.

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Reinforcement criterion

A voting system satisfies join-consistency (also called the reinforcement criterion) if combining two sets of votes, both electing A over B, always results in a combined electorate that ranks A over B. It is a stronger form of the participation criterion.

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Round-robin tournament

A round-robin tournament or all-play-all tournament is a competition format in which each contestant meets every other participant, usually in turn.

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Round-robin voting

Round-robin voting (also called paired/pairwise comparison or tournament voting) refers to a set of ranked voting systems that elect winners by comparing all candidates in a round-robin tournament. Ranked pairs and round-robin voting are single-winner electoral systems.

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Smith criterion

The Smith criterion (sometimes the generalized Condorcet criterion) is a voting system criterion that formalizes the concept of a majority rule.

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Smith set

The Smith or Schwartz set, sometimes called the top cycle, is a concept from the theory of electoral systems that generalizes the Condorcet winner to cases where no such winner exists.

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Strikethrough

Strikethrough is a typographical presentation of words with a horizontal line through their center, resulting in text like this.

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Voting criteria

There are a number of different criteria which can be used for voting systems in an election.

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See also

Monotonic Condorcet methods

• Black's method
• Copeland's method
• Kemeny–Young method
• Minimax Condorcet method
• Ranked pairs
• Schulze method

Single-winner electoral systems

• Approval voting
• Black's method
• Borda count
• Bucklin voting
• Condorcet method
• Condorcet methods
• Contingent vote
• Coombs' method
• Exhaustive ballot
• First-past-the-post voting
• First-preference votes
• Graduated majority judgment
• Instant-runoff voting
• Majority judgment
• Oklahoma primary electoral system
• Ranked pairs
• Round-robin voting
• Runoff voting
• STAR voting
• Schulze method
• Score voting
• Tideman alternative method
• Two-round system

References

[1] https://en.wikipedia.org/wiki/Ranked_pairs

Also known as Maximize Affirmed Majorities, Maximum Majority Voting, Ranked pairs method, Ranked-pairs method, Tideman method.