Approval voting is a single-winner electoral system in which voters mark all the candidates they support, instead of just choosing one. The candidate with the highest approval rating is elected.
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of behavioral relations. It is now an umbrella term for the science of rational decision making in humans, animals, and computers.
Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. Score voting includes the well-known approval voting, but also lets voters give partial (in-between) approval ratings to candidates.
Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results. For example, in plurality or instant-runoff, a voter may recognize their favorite candidate is unlikely to win and so instead support a candidate they think is more likely to win.
In social choice theory, a Condorcet paradox is a situation where majority rule behaves in a way that is self-contradictory. In such a situation, every possible choice is rejected by the electorate in favor of another, because there is always some other outcome that a majority of voters consider to be better.
Arrow's impossibility theorem is a key result in social choice showing that no rank-order method for collective decision-making can behave rationally or coherently. Specifically, any such rule violates independence of irrelevant alternatives, the principle that a choice between and should not depend on the quality of a third, unrelated option .
The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.
In political science and social choice theory, Black'smedian voter theorem states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single peaked preferences, any voting method satisfying the Condorcet criterion will elect the candidate preferred by the median voter.
Social choice theory is the branch of welfare economics which studies processes of collective decision-making. It contrasts with political science in that it is a normative science studying how societies should make decisions, whereas political science is descriptive. Social choice incorporates insights from economics, mathematics, philosophy, and game theory to find the best ways to combine individual preferences into a coherent whole, called a social welfare function.
Hobart Peyton Young is an American game theorist and economist known for his contributions to evolutionary game theory and its application to the study of institutional and technological change, as well as the theory of learning in games. He is currently centennial professor at the London School of Economics, James Meade Professor of Economics Emeritus at the University of Oxford, professorial fellow at Nuffield College Oxford, and research principal at the Office of Financial Research at the U.S. Department of the Treasury.
The paradox of voting, also called Downs' paradox, is that for a rational, self-interested voter, the costs of voting will normally exceed the expected benefits. Because the chance of exercising the pivotal vote is minuscule compared to any realistic estimate of the private individual benefits of the different possible outcomes, the expected benefits of voting are less than the costs.
Roger Bruce Myerson is an American economist and professor at the University of Chicago. He holds the title of the David L. Pearson Distinguished Service Professor of Global Conflict Studies at The Pearson Institute for the Study and Resolution of Global Conflicts in the Harris School of Public Policy, the Griffin Department of Economics, and the college. Previously, he held the title The Glen A. Lloyd Distinguished Service Professor of Economics. In 2007, he was the winner of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel with Leonid Hurwicz and Eric Maskin for "having laid the foundations of mechanism design theory." He was elected a Member of the American Philosophical Society in 2019.
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets n − 1 points, where n is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.
Instant-runoff voting (IRV), also known as ranked-choice voting or the alternative vote (AV), combines ranked voting 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. It can be seen as a modified form of a runoff election or exhaustive ballot in which, after eliminating some candidates, the choice among the rest is made from already-given voter rankings rather than from a separate election. Many sources conflate this system of choosing winners with ranked-choice voting more generally, for which several other systems of choosing winners have also been used.
Ranked voting is any voting system that uses voters' orderings (rankings) of candidates to choose a single winner. For example, Dowdall's method assigns 1, 1⁄2, 1⁄3... points to the 1st, 2nd, 3rd... candidates on each ballot, then elects the candidate with the most points. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives each one very different properties.
A major branch of social choice theory is devoted to the comparison of electoral systems, otherwise known as social choice functions. Viewed from the perspective of political science, electoral systems are rules for conducting elections and determining winners from the ballots cast. From the perspective of economics, mathematics, and philosophy, a social choice function is a mathematical function that determines how a society should make choices, given a collection of individual preferences.
Impartial culture (IC) or the culture of indifference is a probabilistic model used in social choice theory for analyzing ranked voting method rules.
A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely to be correct than a decision attained by a single expert. It serves as a formal argument for the idea of wisdom of the crowd, for decision of questions of fact by jury trial, and for democracy in general.
Multiwinner, at-large, or committeevoting refers to electoral systems that elect several candidates at once. Such methods can be used to elect parliaments or committees.
Fractional 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, while in fractional social choice, it is possible to choose "2/3 of A and 1/3 of B".
