Smith setIn voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in a particular election such that each member defeats every candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion and are said to be 'Smith-efficient' or to satisfy the Smith criterion.
Marquis de CondorcetMarie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (maʁi ʒɑ̃ ɑ̃twan nikɔla də kaʁita maʁki də kɔ̃dɔʁsɛ; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal public instruction, constitutional government, and equal rights for women and people of all races, have been said to embody the ideals of the Age of Enlightenment, of which he has been called the "last witness", and Enlightenment rationalism.
Tideman alternative methodTideman's Alternative Methods, including Alternative Smith and Alternative Schwartz, are two electoral systems developed by Nicolaus Tideman which select a single winner using votes that express preferences. These methods can also create a sorted list of winners. These methods are Smith- and Schwartz-efficient, respectively, and thus are Condorcet methods. They operate by using instant-runoff voting for cycle resolution. Tideman's Alternative procedure is as follows: Identify the Smith or Schwartz set.
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.
Smith criterionThe Smith criterion (sometimes generalized Condorcet criterion, but this can have other meanings) is a voting systems criterion defined such that it's satisfied when a voting system always elects a candidate that is in the Smith set, which is the smallest non-empty subset of the candidates such that every candidate in the subset is majority-preferred over every candidate not in the subset. (A candidate X is said to be majority-preferred over another candidate Y if, in a one-on-one competition between X & Y, the number of voters who prefer X over Y exceeds the number of voters who prefer Y over X.
Comparison of electoral systemsComparison of electoral systems is the result of comparative politics for electoral systems. Electoral systems are the rules for conducting elections, a main component of which is the algorithm for determining the winner (or several winners) from the ballots cast. This article discusses methods and results of comparing different electoral systems, both those that elect a unique candidate in a 'single-winner' election and those that elect a group of representatives in a multiwinner election.
Social Choice and Individual ValuesKenneth Arrow's monograph Social Choice and Individual Values (1951, 2nd ed., 1963, 3rd ed., 2012) and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. Somewhat formally, the "social choice" in the title refers to Arrow's representation of how social values from the set of individual orderings would be implemented under the constitution.
