This essay lays out the common reasoning underlying a diversity of arguments for decision making using lotteries. This reasoning appeals to the sanitizing effects of ignorance. Lotteries ensure that bad reasons are unable to affect a decision. (They also ensure that good reasons have no effect as well, which is why care must be applied in deciding to use them.) All arguments for or against the use of a lottery to make a particular decision will thus appeal to the same property that lotteries possess. This fact is compatible with continued vigorous disagreement about whether particular decisions should be made by lot. Such disagreements, however, will focus on the nature of the circumstances surrounding the decision. People can thus agree that a given set of circumstances calls for the use of a lottery even as they disagree over whether those circumstances hold.
Sid Z. Leiman, "The Ethics of Lottery," Kennedy Institute Quarterly Report 4 (1978): 8. On lotteries and justice, see Hank Greely, "The Equality of Allocation by Lot," Harvard Civil Rights-Civil Liberties Law Review 12 (1977): 113-41; George Sher, "What Makes a Lottery Fair?" Noûs 14 (1980): 203-16; Lewis A. Kornhauser and Lawrence G. Sager, "Just Lotteries," Social Science Information 27 (1988): 483-516; John Broome, "Selecting People Randomly," Ethics 95 (1984): 38-55; John Broome, "Fairness," Proceedings of the Aristotelian Society, 91 (1990-1991): 87-102; Conall Boyle, "Organizations Selecting People: How the Process Could Be Made Fairer by the Appropriate Use of Lotteries," Statistician 47, no. 2 (1998): 291-321; Barbara Goodwin, Justice by Lottery, 2nd ed. (Exeter: Imprint Academic, 2005); and Peter Stone, "Why Lotteries Are Just," Journal of Political Philosophy 15, no. 3 (2007): 276-95. On the selection of political officials by lot, see Dennis C. Mueller, Robert D. Tollison, Thomas D. Willett, "Representative Democracy via Random Selection," Public Choice 12 (1972): 57-68; Richard G. Mulgan, "Lot as a Democratic Device of Selection," Review of Politics 46 (1984): 539-60; Fredrik Engelstad, "The Assignment of Political Office by Lot," Social Science Information 28 (1989): 23-50; Howard DeLong, A Refutation of Arrow's Theorem (Lanham, MD: University Press of America, 1991); James S. Fishkin, Democracy and Deliberation: New Directions for Democratic Reform (New Haven, CT: Yale University Press, 1991); Lyn Carson and Brian Martin, Random Selection in Politics (New York: Praeger, 1999); Peter Stone, "The Luck of the Draw: Revisiting the Lot as a Democratic Institution" (PhD diss., University of Rochester, 2000); John Burnheim, Is Democracy Possible? 2nd ed. (Sydney: Sydney University Press, 2006); Kevin O'Leary, Saving Democracy: A Plan for Real Representation in America (Stanford, CA: Stanford University Press, 2006); Anthony Barnett and Peter Carty, The Athenian Option: Radical Reform for the House of Lords, 2nd ed. (Exeter: Imprint Academic, 2008); Ernest Callenbach, Michael Philips, and Keith Sutherland, A Citizen Legislature/A People's Parliament (Exeter: Imprint Academic, 2008); and Oliver Dowlen, The Political Potential of Sortition (Exeter: Imprint Academic, 2008). On other political uses of the lot, see Akhil Reed Amar, "Choosing Representatives by Lottery Voting," Yale Law Journal 93 (1984): 1283-308; Thomas Gangale, "The California Plan: A Twenty-First Century Method for Nominating Presidential Candidates," PS: Political Science and Politics 37, no. 1 (2004): 81-87; and Andrew Rehfeld, The Concept of Constituency: Political Representation, Democratic Legitimacy, and Institutional Design (New York: Cambridge University Press, 2005). On contemporary applications to deliberative democracy, see John Stewart, Elizabeth Kendall, and Anna Coote, Citizen's Juries (London: Institute for Public Policy Research, 1994); Ned Crosby, "Citizens Juries: One Solution for Difficult Environmental Questions," in Fairness and Competence in Citizen Participation, ed. Ortwin Renn, Thomas Webler, and Peter Wiedemann (Boston: Kluwer, 1995), 157-74; James S. Fishkin, The Voice of the People: Public Opinion & Democracy (New Haven, CT: Yale University Press, 1995); and Anna Coote and Jo Lenaghan, Citizens' Juries: Theory into Practice (London: Institute for Public Policy Research, 1997). For surveys of the uses of lotteries, see Vilhelm Aubert, "Chance in Social Affairs," Inquiry 2 (1959): 1-24; Jon Elster, Solomonic Judgments (New York: Cambridge University Press, 1989); and Neil Duxbury, Random Justice: On Lotteries and Legal Decision-Making (Oxford: Clarendon Press, 1999).
2.
DeLong, Refutation of Arrow's Theorem, 8.
3.
For further discussion of this topic, see Peter Stone, "Conceptualizing Lotteries" (Working Paper No. 16, Political Concepts: A Working Paper Series of the Committee on Concepts and Methods, International Political Science Association, 2007).
4.
It is thus possible both for a lottery to be "fair" and for it to be "unfair" to use that lottery to make a particular decision. The word "fair" is here used in two different ways. See Kornhauser and Sager, "Just Lotteries," as well as Stone, "Why Lotteries Are Just," 279n.
5.
Cf. the distinction between "strong" and "weak" uses of the lottery drawn by Dowlen, Political Potential of Sortition.
6.
Goodwin uses the term "sortition" as synonymous with "random selection." In the next section, I shall use the term in a more restrictive manner.
7.
Goodwin, Justice by Lottery, 54-55.
8.
Ibid., 55-56.
9.
Presumably, there is little reason to be concerned about "corruption" that results in the same decision as an uncorrupted process-assuming it even makes sense to speak of "corruption" in such cases.
10.
Some political theorists misunderstand this point. Robert Goodin, for example, recognizes the importance of avoiding bad reasons to impartiality. But his treatment of the topic does not seem to acknowledge the possibility of impartially discriminating between people for good reasons. See Robert E. Goodin, Reasons for Welfare: The Political Theory of the Welfare State ( Princeton, NJ: Princeton University Press, 1988).
11.
John Broome offers a different account of the relationship between lotteries and fairness. He argues that when the reasons for favoring different candidates are of unequal strength, a weighted lottery should be used, with different candidates receiving the good with probabilities proportionate to the strength of the reasons in their favor. But Broome does not offer independent justification for this understanding of fairness. On the contrary, he writes that "Sometimes a lottery is the fairest way of distributing a good, and my theory explains, better than any other theory I know, why this is so. That is the main evidence I offer for it." See Broome, "Fairness," 87. The strength of his entire understanding of fairness thus stands or falls on the basis of the plausibility of his account of allocation by weighted lottery. My understanding of fairness is incompatible with that of Broome, but space prohibits further consideration of the topic here.
12.
I assume here that indeterminacy involves indifference, or complete equality in all relevant ways between the options at hand. But indeterminacy can arise in other ways. It could be that the reasons for favoring the different claimants are incommensurable. In such a case, different moral values are at stake, some favoring one claimant, others favoring another, and there is no basis for trading these values off against one another. But philosophers continue to debate whether incommensurability is a real phenomenon, and if it is what the implications are for reasoned decision making. For a sample of the debate, see Ruth Chang, ed., Incommensurability, Incomparability, and Practical Reason (Cambridge, MA: Harvard University Press, 1997). I ignore these complications here.
13.
Jon Elster dubs this delusion hyperrationality; see Elster, Solomonic Judgments.
14.
Dael Wolfle , "Chance, or Human Judgment?" Science, February 27, 1970, 1201.
15.
The argument is not completely clear, as Wolfle also asserts a version of D2. In arguing against the use of lotteries in university admissions processes, he claims that "To choose students by a random process is to deny the ability of the faculty to select those applicants who show greatest promise or who appear most likely to benefit from higher education." Wolfle, "Chance, or Human Judgment?" 1201. Here Wolfle claims that random selection would ignore relevant differences between candidates. But this is fully compatible with the claim that, where no such differences exist (because two or more students are equally promising or stand to gain equally) a lottery would be required.
16.
For a more elaborate defense of this claim, see Stone, "Why Lotteries Are Just."
17.
On Athens, see J. W. Headlam, Election by Lot at Athens, 2nd ed. (New York: Cambridge University Press, 1933) and Mogens Herman Hansen, The Athenian Democracy in the Age of Demosthenes, 2nd ed. (Norman: University of Oklahoma Press, 1999). On Venice, see Robert Finlay, Politics in Renaissance Venice (New Brunswick, NJ: Rutgers University Press, 1980). On Florence, see John M. Najemy, Corporatism and Consensus in Florentine Electoral Politics, 1280-1400 (Chapel Hill, NC: University of North Carolina Press, 1982). On the disappearance of sortition from the modern era's list of approved political institutions, see Bernard Manin, The Principles of Representative Government (New York: Cambridge University Press, 1997).
18.
The argument applies, in reverse, if political office holding is regarded as a burden to be avoided, rather than a benefit to be desired. If citizens have an equal right to avoid this burden, then a lottery is once again the only fair way to allocate it. More generally, lotteries can be used to allocate burdens for the same reasons they can be used to allocate benefits. This is because the absence of a bad can be treated as a good. See Sher, "What Makes a Lottery Fair?" on this point.
19.
See Elster, Solomonic Judgments, 110-11. Dowlen (2008) identifies the need to prevent corruption as the primary reason for selecting political officials (including jurors) by lot. Corruption here means both ordinary cases of bribes and threats and the more potentially dangerous case of rule by factional or partisan interest. Dowlen's account of "arationality" as the key desirable property of lotteries is similar to my own account of the sanitizing effect of lotteries, although he does not apply it to lotteries not involving political office.
20.
Is a fair lottery, in which all outcomes are equally likely, the best way to eliminate incentive problems? Clearly, only an equiprobable lottery has the ability to sanitize decision-making processes. If one were to use a weighted lottery, which favored some outcomes over others, then one would need reasons for favoring certain outcomes over others, and so reasons would indeed be playing a role in the lottery. But there may be times when the best way to align incentives is to rely on weighted probabilities. This is made clear in the field of game theory. Equilibrium behavior sometimes requires randomization, but that randomization need not imply performing all actions with equal probability.
21.
Finlay, Politics in Renaissance Venice, 90.
22.
Ibid., 141-42.
23.
My emphasis; ibid., 32.
24.
Manin, Principles of Representative Government, 64.
25.
Finlay, Politics in Renaissance Venice, 107, 197.
26.
John Adams, "Letter to John Penn," in The Works of John Adams, ed. Charles Francis Adams ( Boston: Little, Brown and Co., 1851 ), 4: 205.
27.
See Ted Becker, Paul Szep and Dwight Ritter, Un-Vote for a New America (Boston: Allyn and Bacon, 1976); Barnett and Carty, Athenian Option; and Callenbach et al., Citizen Legislature/People's Parliament.
28.
This makes random sample an ineffective means of advancing the goal of descriptive representation for six- or twelve-member juries, which are too small to ensure that the law of large numbers takes effect. But there is a limit to how well such a small body can represent any reasonably diverse population, and so the lottery may well be the best option available. American law reflects this by largely confining its attention, not to the representativeness of the final jury, but to the representativeness of the pool of candidates from which juries are drawn.
29.
This argument receives further development in Peter Stone, "Voting, Lotteries, and Justice," Polity 40, no. 2 (2008): 246-53.
30.
If the list of characteristics to be represented is small, then a stratified random sample will work as well. Such a sample guarantees the inclusion of every possible combination of characteristics in proportion to its presence in the larger population. But stratified sampling becomes difficult very rapidly as the number of possible combinations increases. If, for example, one wanted a sample to reflect both sexes, five racial categories, and seven religions, then one would need to divide the population into 2 * 5 * 7 = 70 different weights.
31.
This argument presupposes, of course, that it is normatively desirable for the jury to be representative of the entire community, and not of the subset of that community possessing above-average intelligence.
32.
See Edna Ullmann-Margalit and Sidney Morgenbesser, "Picking and Choosing," Social Research 44 (1977): 757-85; and Peter Stone, "Picking and Choosing Revisited" (Paper presented at the annual meeting of the Midwest Political Science Association, 2008).
33.
This argument presupposes that picking "at random" is not equivalent to deciding by lot. Intuitively, this presupposition makes sense. After all, one could presumably pick under any circumstances under which one could employ a coin toss. Why bother with the latter, if the former is readily available? One can defend this presupposition by noting that picking, unlike random selection, cannot guarantee that bad reasons will be kept out of the process. The agent might, after all, not consciously perceive any reason for selecting one option over another, and still pick on the basis of some unconscious bias (i.e., a bad reason). A coin toss or the like precludes this possibility. For a more complete version of this argument see Peter Stone, "Justice, Rationality, and Indeterminacy" (lecture, Duke University, Durham, NC, April 7, 2008), and Peter Stone, "Picking and Choosing Revisited."
34.
Elster, SolomonicJudgments, 107.
35.
Ibid., 109.
36.
See Stone, "Justice, Rationality, and Indeterminacy."
37.
It is quite possible for indeterminacy to arise at other stages in this decision-making process. A policy maker might, for example, compare the merits of selecting hemodialysis recipients on the basis of need versus allowing them to bid for the service on an open market. She might decide that the two are equally attractive, and that there are insufficient reasons for choosing between them. But this would not result in an argument for the policy maker to toss a coin, unless there was some reason to think the sanitizing effect was needed. (This effect might be necessary if, for example, the policy maker had a child in need of hemodialysis who was more likely to receive treatment under one allocation regime than under another. But if this were the case, it would probably be more sensible simply to let somebody else make the decision.)
