Part of the Politics series |
Voting |
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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.
Responses to the paradox have included the view that voters vote to express their preference for a candidate rather than affect the outcome of the election, that voters exercise some degree of altruism, or that the paradox ignores the collateral benefits associated with voting besides the resulting electoral outcome.
The issue was noted by Nicolas de Condorcet in 1793 when he stated, "In single-stage elections, where there are a great many voters, each voter's influence is very small. It is therefore possible that the citizens will not be sufficiently interested [to vote]" and "... we know that this interest [which voters have in an election] must decrease with each individual's [i.e. voter's] influence on the election and as the number of voters increases." [1]
In 1821, Hegel made a similar observation in his Elements of the Philosophy of Right : "As for popular suffrage, it may be further remarked that especially in large states it leads inevitably to electoral indifference, since the casting of a single vote is of no significance where there is a multitude of electors." [2] [3]
The mathematician Charles L. Dodgson, better known as Lewis Carroll, published the paper "A Method of Taking Votes on More than Two Issues" in 1876. [4]
This problem in modern public choice theory was analysed by Anthony Downs in 1957. [5]
Alternative responses modify the postulate of egoistic rationality in various ways. For example, Geoffrey Brennan and Loren Lomasky suggest that voters derive "expressive" benefits from supporting particular candidates – analogous to cheering on a sports team – rather than voting in hopes of achieving the political outcomes they prefer. This implies that the rational behavior of voters is restricted to the instrumental as opposed to the intrinsic value they derive from their vote. [6] [7]
Another suggestion, known as the altruism theory of voting, is that voters are rational but not fully egoistic. In this view voters have some degree of altruism, and perceive a benefit if others are benefited. Since an election affects many others, it could still be rational to cast a vote with only a small chance of affecting the outcome. [8]
Some[ who? ] argue that the paradox appears to ignore the collateral benefits associated with voting, besides affecting the outcome of the vote. For instance, magnitudes of electoral wins and losses are very closely watched by politicians, their aides, pundits and voters, because they indicate the strength of support for candidates, and tend to be viewed as an inherently more accurate measure of such than mere opinion polls (which have to rely on imperfect sampling). Another argument that has been raised, is that researching who or what to vote for may increase the voter's political knowledge and community awareness, both of which may contribute to a general sense of civic duty, although in such a case the act of voting itself contributes nothing to this.[ citation needed ]
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.
In social choice theory, a Condorcet cycle or 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.
In social choice theory and politics, the spoiler effect or Arrow's paradox refers to a situation where a losing candidate affects the results of an election. A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives or independence of spoilers.
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. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Public choice, or public choice theory, is "the use of economic tools to deal with traditional problems of political science." Its content 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.
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 .
Independence of irrelevant alternatives (IIA) is a major axiom of decision theory which codifies the intuition that a choice between and should not depend on the quality of a third, unrelated outcome . There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski-Young theorem, and the money pump arguments.
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."
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. Voting systems where a majority winner will always win are said to satisfy the majority-rule principle, because they extend the principle of majority rule to elections with multiple candidates.
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. More formally, it says that adding more voters who prefer Alice to Bob should not cause Alice to lose the election to Bob.
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.
The Myth of the Rational Voter: Why Democracies Choose Bad Policies is a 2007 book by the economist Bryan Caplan, in which the author challenges the idea that voters are reasonable people whom society can trust to make laws. Rather, Caplan contends that voters are irrational in the political sphere and have systematically biased ideas concerning economics.
The Borda method or order of merit is a positional voting rule which gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. Once all votes have been counted, the option or candidate with the most points is the winner.
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.
The concept known as rational irrationality was popularized by economist Bryan Caplan in 2001 to reconcile the widespread existence of irrational behavior with the assumption of rationality made by mainstream economics and game theory. The theory, along with its implications for democracy, was expanded upon by Caplan in his book The Myth of the Rational Voter.
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.
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.
Impartial culture (IC) or the culture of indifference is a probabilistic model used in social choice theory for analyzing ranked voting method rules.