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Kenneth Arrow’s “impossibility” theorem is rightly considered to be a landmark result in economic theory. It is a far-reaching result with implications not just for economics but for political science, philosophy, and many other fields. It has inspired an enormous literature, “social choice theory,” which lies on the interface of economics, politics, and philosophy. Arrow first proved the impossibility theorem in his doctoral dissertation—Social Choice and Individual Values—published in 1951. It is a remarkable result, and had Arrow not proved it, it is unlikely that the theorem would be known today. A social choice is simply a choice made by, or on behalf of, a group of people. Arrow’s theorem is concerned more specifically with the following problem. Suppose that we have a given set of options to choose from and that each member of a group of individuals has his or her own preference over these options. By what method should we construct a single ranking of the options for the group as a whole? Any such method may be represented mathematically by a “social welfare function.” This is a function that receives as its input the preference ordering of each individual and then generates as its output a social preference ordering. Arrow defined some properties that would seem to be essential to any reasonable social welfare function. These properties are called “unrestricted domain,” “weak Pareto,” “independence of irrelevant alternatives,” and “non-dictatorship.” Each of these properties, when taken alone, does appear to be very necessary indeed. Yet, Arrow proved that these properties are in fact mutually incompatible. This troubling fact has been central to the study of social choice ever since.

The first question that is often raised in a discussion of the ethics of voting is whether or not there is a duty to vote. The view that there is a duty to vote is supported by two main arguments. The first holds that since the value of democratic governance is high persons should vote to preserve stable democracy. The second is that there is a duty to vote because if nobody voted the effects would be disastrous. The first of these arguments is criticized by Jason Brennan, who holds that since each individual vote will play little to no role in preserving stable democracy nobody has a duty to vote. The second is criticized by Loren Lomasky and Geoffrey Brennan, who argue that it is incomplete unless its supporters can show that democracy needs everyone to vote to continue. The question of whether there is a duty to vote naturally leads to the question of whether it is permissible for persons to vote in their own self-interest. Jason Brennan argues that persons should only (morally) vote for candidates or policies that they are justified in believing would promote the common good. It is unclear, however, what “the common good” consists of. This discussion of the morality of voting in one’s self-interest leads to the question of whether voting for a politician because she has made campaign promises is morally analogous to a voter selling her vote. In discussing this issue it is important to distinguish between the “restricted” defense of markets in votes (that the purchased votes are to be cast in favor of what the buyer is justified in believing is the common good) and the “unrestricted” defense of such a market (that purchased votes can be cast in any way the buyer pleases). Much of this discussion focuses on the morality of unrestricted markets in votes. Christopher Freiman has offered four main arguments in favor of such a market: (1) that it will make both the buyer and the seller better off; (2) that it is required by respect for voter liberty; (3) that it is relevantly similar to other practices that are currently allowed, such as logrolling; and (4) that it would enable electoral outcomes to better express voter preferences. None of these arguments are persuasive. The first is based on illicitly inferring from the claim that persons would voluntarily buy and sell votes if a market were allowed to the claim that they would thereby desire that this market be allowed. The second argument is flawed because if some persons would prefer that a market not be allowed, this could provide a sufficient reason to restrict their liberty by precluding them from selling their votes. The third argument overlooks important disanalogies between votes traded between voters, and votes traded between legislators. The fourth argument is based on the implausible assumption that vote sellers would not misrepresent their political preferences in a market for votes.