Lotteries are fascinating, both to those who buy tickets to enter them and to the economists, political theorists, and philosophers who talk about them. Peter Stone's ambitious book attempts to generalize and unify earlier treatments by Jon Elster, Neil Duxbury, Oliver Dowlen, and others, offering a single master account of lotteries that cuts across the many and highly heterogeneous political and social contexts in which they have been used. The result is a careful and clear discussion. In the end, however, Stone's master principles are excessively abstract; the concrete variety of lotteries and their institutional uses turn out to be more interesting than the philosophical generalities that unite them.

Stone's generalized account of lotteries rests on what he calls the “lottery principle,” which holds that “[l]otteries make sense when and to the extent that it is important that reasons be kept out of decision-making” (p. 16). This is only a slight step beyond earlier work; Dowlen, for example, sees “arationality” as a key feature of lotteries (The Political Potential of Sortition, 2008). But Stone pursues his theme relentlessly, and clarifies the abstract conditions under which lotteries do and do not promote justice or social utility.

Two types of cases receive sustained attention. The first are allocative settings in which reasons run out and lotteries serve a tiebreaking function. If, for example, there are multiple equally deserving claimants for a single indivisible good, lotteries seem a natural device for allocating the good without any (further) reference to reasons, for there are none to be had. Stone goes on to argue that justice demands the use of lotteries in such cases. According to his “just lottery” rule, “[u]nder conditions of indeterminacy, if an agent must allocate a scarce homogeneous lumpy good amongst a group of parties with homogeneous claims, then that agent must do so using a fair lottery” (p. 53).

In a second class of cases, the problem is not that reasons run out but that there are both good and bad reasons in the picture; here, lotteries minimize the influence of bad reasons and thus serve a precautionary function. Stone argues that the best rationale for allocating political offices by lot, as in classical Athens, is that when the risk of allocation on the basis of bad reasons—corruption, partisanship, and the like—exceeds the likelihood of allocation on the basis of good reasons, it may be preferable to use a random mechanism that allocates on the basis of no reasons at all. Here, as Stone notes, there is an important trade-off between the benefits and costs of excluding bad reasons at the price of excluding good ones as well; in some environments, the trade-off will be worth it, but no a priori conclusions are possible. Still, Stone's treatment does clearly identify the relevant considerations.

All this is plausible and generally well argued. Even so, however, Stone's account is occasionally questionable or incomplete on its own terms. The questionable part is his critique of the standard economic account of allocative lotteries, stemming from Lewis Kornhauser and Larry Sager (“Just Lotteries,” Social Science Information 27 [1988]: 483–516). On this account, where not all deserving claimants can receive a lumpy good, lotteries equalize distributions by providing all parties with equal ex ante chances of obtaining the good. Stone criticizes this on the ground, among others, that the chance of obtaining a good cannot itself be a good, observing that “[o]ne cannot, after all, eat chances” (p. 62). Yet chances of obtaining a good are routinely traded on markets, where permitted by law and norms, and are thus a good in both the ordinary-language sense and the economic sense. It may be that one cannot eat chances, but one can often trade them for money with which to buy food. Where alienability of chances is prohibited, this will not be so, but then the problem is not that the chance of a good is not itself a good; rather, the chance is just an illegal good, and shadow markets or black markets may arise.

The incomplete part is that Stone does not clearly identify an important third class of cases: not cases in which reasons run out (the tiebreaking function of lotteries), or in which the threat of bad reasons is so great that it is better to decide without reasons (the precautionary function), but cases in which there is intractable disagreement about what even counts as a good or bad reason in the first place. In such cases, parties who each advocate different allocative criteria—need, merit, or whatnot—may converge on lotteries as a unanimous second choice. It is an open question whether this sort of account might not better explain cases like classical Athens than does Stone's precautionary account.

These are the sorts of questions that no ambitious book can avoid, however. The larger problem is that Stone's relentlessly abstract treatment drains all the juice out of his subject. Perhaps this is a matter of taste or academic style. Yet one suspects that even the philosophically inclined will feel that there is nothing counterintuitive or surprising about (for example) Stone's careful demonstration that a fair lottery has the virtue of “impartiality,” an effort that occupies the bulk of a whole chapter. The gain from this sort of conceptual clarification is small, while the loss is appreciable. The richness of Elster's treatment (Solomonic Judgments, 1989) derives from its grounding in the variety of political experience with lotteries and related decision-making mechanisms, and also from his unstated assumption that there is no single interesting property that characterizes lotteries. Stone gives us a single property that characterizes lotteries, but the principle must be stated so abstractly that it does not yield much progress. All of ethics can be unified under the principle “do the right thing,” yet the variety of ethical problems is not thereby illuminated or made more tractable. So too with lotteries, mutatis mutandis.