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Calculus of voting refers to any mathematical model which predicts voting behaviour by an electorate, including such features as participation rate. A calculus of voting represents a hypothesized decision-making process.
These models are used in political science in an attempt to capture the relative importance of various factors influencing an elector to vote (or not vote) in a particular way.
One such model was proposed by Anthony Downs (1957) and is adapted by William H. Riker and Peter Ordeshook, in “A Theory of the Calculus of Voting” (Riker and Ordeshook 1968)
where
A political science model based on rational choice used to explain why citizens do or do not vote.
The alternative equation is
Where for voting to occur the (P)robability the vote will matter "times" the (B)enefit of one candidate winning over another combined with the feeling of civic (D)uty, must be greater than the (C)ost of voting
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. Approval voting is currently in use for government elections in St. Louis, Missouri, Fargo, North Dakota and in the United Nations to elect the Secretary General.
Rational choice theory refers to a set of guidelines that help understand economic and social behaviour. The theory originated in the eighteenth century and can be traced back to the political economist and philosopher Adam Smith. The theory postulates that an individual will perform a cost–benefit analysis to determine whether an option is right for them. Rational choice theory looks at three concepts: rational actors, self interest and the invisible hand.
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee a winner will have support from a majority of voters: in some situations, a majority of voters will prefer A to B, B to C, and also C to A, even if every voter's individual preferences are rational and avoid self-contradiction. Examples of Condorcet's paradox are called Condorcet cycles or cyclic ties.
In political science, Duverger's law holds that in political systems with single-member districts and the plurality voting system,, two main parties tend to emerge. In this case, votes for minor parties can potentially be regarded splitting votes away from the most similar major party. In contrast, systems with proportional representation usually have more representation of minor parties in government.
William Harrison Riker was an American political scientist known for applying game theory and mathematics to political science. He helped establish University of Rochester as a center of the behavioral revolution in political science.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
Public choice, or public choice theory, is "the use of economic tools to deal with traditional problems of political science." It includes the study of political behavior. In political science, it is the subset of positive political theory that studies self-interested agents and their interactions, which can be represented in a number of ways—using standard constrained utility maximization, game theory, or decision theory. It is the origin and intellectual foundation of contemporary work in political economy.
Rational ignorance is refraining from acquiring knowledge when the supposed cost of educating oneself on an issue exceeds the expected potential benefit that the knowledge would provide.
In political science, voter turnout is the participation rate of a given election. This is typically either the percentage of registered voters, eligible voters, or all voting-age people. According to Stanford University political scientists Adam Bonica and Michael McFaul, there is a consensus among political scientists that "democracies perform better when more people vote."
The median voter theorem in political science and social choice theory, developed by Duncan Black, states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single-peaked preferences, any voting method that is compatible with majority-rule will elect the candidate preferred by the median voter. The median voter theorem thus shows that under a realistic model of voter behavior, Arrow's theorem, which essentially suggests that ranked-choice voting systems cannot eliminate the spoiler effect, does not apply, and therefore that rational social choice is in fact possible if the election system is using a Condorcet method.
Anthony Downs was an American economist specializing in public policy and public administration. His research focuses included political choice theory, rent control, affordable housing, and transportation economics. He wrote a number of books including, An Economic Theory of Democracy (1957) and Inside Bureaucracy (1967), which have been major influences on the public choice school of political economy. In Downs's Law of Peak-Hour Traffic Congestion (1962), he predicted that expanding expressways could not reduce traffic congestion, since demand would increase as well, and that reducing speeds increases capacity.
Positive political theory (PPT), explanatory political theory, or formal theory is the study of politics using formal methods such as social choice theory, game theory, and statistical analysis. In particular, social choice theoretic methods are often used to describe and (axiomatically) analyze the performance of rules or institutions. The outcomes of the rules or institutions described are then analyzed by game theory, where the individuals/parties/nations involved in a given interaction are modeled as rational agents playing a game, guided by self-interest. Based on this assumption, the outcome of the interactions can be predicted as an equilibrium of the game.
William Ernest Johnson, FBA, usually cited as W. E. Johnson, was a British philosopher, logician and economic theorist. He is mainly remembered for his 3 volume Logic which introduced the concept of exchangeability.
Peter Carl Ordeshook is an American political scientist. He is the Mary Stillman Harkness Professor of Political Science at the California Institute of Technology in Pasadena, California.
The Theory of Political Coalitions is an academic book on positive political theory written by the American political scientist William H. Riker and published in 1962. It uses game theory to formalize political theory. In it, Riker deduces the size principle. On its postulates, politicians are proved to form winning, minimal-size coalitions. The work runs contrary to a previous theory by Anthony Downs that they try to maximize their respective votes. Riker supposes that attracting more votes requires resources and that politicians run to win. A rational politician tries to form a coalition that is as large as necessary to win but not larger.
The paradox of voting, also called Downs' paradox, is that for a rational and 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.
The altruism theory of voting is a model of voter behavior which states that if citizens in a democracy have "social" preferences for the welfare of others, the extremely low probability of a single vote determining an election will be outweighed by the large cumulative benefits society will receive from the voter's preferred policy being enacted, such that it is rational for an “altruistic” citizen, who receives utility from helping others, to vote. Altruistic voting has been compared to purchasing a lottery ticket, in which the probability of winning is extremely low but the payoff is large enough that the expected benefit outweighs the cost.
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.
Heresthetic is an approach to understanding how political actors manipulate the decision-making process so they can win. Heresthetic is a positive political theory, including aspects of game theory, public choice theory, rational choice theory, and social choice theory to political science. Political scientist William H. Riker is considered the creator and one of the most prominent supports of theory.
In political science and social choice theory, the spatialmodel of voting, also known as the Hotelling–Downs model, is a mathematical model of voting behavior. It describes voters and candidates as varying along one or more axes, where each axis represents an attribute of the candidate that voters care about. Voters are modeled as having an ideal point in this space and preferring candidates closer to this point over those who are further away; these kinds of preferences are called single-peaked.