Independence of irrelevant alternativesIndependence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A {\displaystyle A} and B {\displaystyle B} (which are both related) should not depend on the quality of a third, unrelated outcome C {\textstyle C} . There are several different variations of this axiom, which are generally equivalent under mild conditions.Lottery (decision theory)In expected utility theory, a lottery is a discrete distribution of probability on a set of states of nature. The elements of a lottery correspond to the probabilities that each of the states of nature will occur, (e.g. Rain: 0.70, No Rain: 0.30). Much of the theoretical analysis of choice under uncertainty involves characterizing the available choices in terms of lotteries.
Condorcet winnerA Condorcet winner (French:, English: ) is a candidate who would receive more support than their opponent in a one-on-one race against any one of their opponents. Voting systems where a Condorcet winner will always win the election are said to satisfy the Condorcet winner criterion. The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates.
Allan GibbardAllan Fletcher Gibbard (born 1942) is an American philosopher who is the Richard B. Brandt Distinguished University Professor of Philosophy Emeritus at the University of Michigan, Ann Arbor. Gibbard has made major contributions to contemporary ethical theory, in particular metaethics, where he has developed a contemporary version of non-cognitivism.Fractional social choiceFractional social choice (also called stochastic, probabilistic or weighted social choice) is a branch of social choice theory in which the collective decision is not a single alternative, but rather a weighted sum of two or more alternatives. For example, if society has to choose between three candidates (A, B, or C), then in standard social choice exactly one of these candidates is chosen.Dictatorship mechanismIn social choice theory, a dictatorship mechanism is a degenerate voting mechanism where the outcome is controlled by a single predetermined person, called the dictator. Dictatorship mechanisms are not considered desirable for practical applications; their main use is theoretic: in many cases, the only mechanisms that satisfy a certain set of axioms are dictatorship mechanisms. Such cases are proved by dictatorship theorems.Pareto efficiencyIn welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse off than they were before.Social welfare functionIn welfare economics and social choice theory, a social welfare function—also called a socialordering, ranking, utility, or choicefunction—is a function that ranks a set of social states by their desirability. Each person's preferences are combined in some way to determine which outcome is considered better by society as a whole. It can be viewed as mathematically formalizing Rousseau's idea of a general will.Independence of clones criterionIn social choice theory, the independence of (irrelevant) clones criterion says that adding a clone, i.e. a new candidate very similar to an already-existing candidate, should not spoil the results. It can be considered a weak form of the independence of irrelevant alternatives (IIA) criterion that nevertheless is failed by a number of voting rules. A method that passes the criterion is said to be clone independent.
Ranked votingRanked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked vote system depends only on voters' order of preference of the candidates. Ranked voting systems vary dramatically in how preferences are tabulated and counted. This gives them different properties with respect to satisfying various voting groups and adherence to mathematical rules.Electoral systemAn electoral system is a set of rules and mechanisms used to determine the results of an election. Electoral systems are used in politics to elect governments and also in non-political settings such as business, nonprofit organizations and informal organisations.Smith setThe Smithset, sometimes called the top-cycle generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner. Voting systems that always elect a candidate from the Smith set pass the Smith criterion. The Smith set and Smith criterion are both named for mathematician John H. Smith.
Condorcet winnerA Condorcet winner (French:, English: ) is a candidate who would receive more support than their opponent in a one-on-one race against any one of their opponents. Voting systems where a Condorcet winner will always win the election are said to satisfy the Condorcet winner criterion. The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates.Allan GibbardAllan Fletcher Gibbard (born 1942) is an American philosopher who is the Richard B. Brandt Distinguished University Professor of Philosophy Emeritus at the University of Michigan, Ann Arbor. Gibbard has made major contributions to contemporary ethical theory, in particular metaethics, where he has developed a contemporary version of non-cognitivism.Fractional social choiceFractional social choice (also called stochastic, probabilistic or weighted social choice) is a branch of social choice theory in which the collective decision is not a single alternative, but rather a weighted sum of two or more alternatives. For example, if society has to choose between three candidates (A, B, or C), then in standard social choice exactly one of these candidates is chosen.Dictatorship mechanismIn social choice theory, a dictatorship mechanism is a degenerate voting mechanism where the outcome is controlled by a single predetermined person, called the dictator. Dictatorship mechanisms are not considered desirable for practical applications; their main use is theoretic: in many cases, the only mechanisms that satisfy a certain set of axioms are dictatorship mechanisms. Such cases are proved by dictatorship theorems.Pareto efficiencyIn welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse off than they were before.Social welfare functionIn welfare economics and social choice theory, a social welfare function—also called a socialordering, ranking, utility, or choicefunction—is a function that ranks a set of social states by their desirability. Each person's preferences are combined in some way to determine which outcome is considered better by society as a whole. It can be viewed as mathematically formalizing Rousseau's idea of a general will.Independence of clones criterionIn social choice theory, the independence of (irrelevant) clones criterion says that adding a clone, i.e. a new candidate very similar to an already-existing candidate, should not spoil the results. It can be considered a weak form of the independence of irrelevant alternatives (IIA) criterion that nevertheless is failed by a number of voting rules. A method that passes the criterion is said to be clone independent.Ranked votingRanked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked vote system depends only on voters' order of preference of the candidates. Ranked voting systems vary dramatically in how preferences are tabulated and counted. This gives them different properties with respect to satisfying various voting groups and adherence to mathematical rules.Electoral systemAn electoral system is a set of rules and mechanisms used to determine the results of an election. Electoral systems are used in politics to elect governments and also in non-political settings such as business, nonprofit organizations and informal organisations.Smith setThe Smithset, sometimes called the top-cycle generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner. Voting systems that always elect a candidate from the Smith set pass the Smith criterion. The Smith set and Smith criterion are both named for mathematician John H. Smith.*As an Amazon Associate I earn from qualifying purchases.