Peter Stone, The Luck of the Draw: The Role of Lotteries in Decision Making, Oxford University Press, 2011, 195pp., $49.95 (hbk), ISBN 9780199756100

Almost everybody is familiar with one or two instances of the use of lotteries for public decision-making: allocating immigration quotas or filling juries are, perhaps, among the most popular today, but it is indeed a very old practice that has been documented in Greece, Israel, and other ancient cultures. In other words, it is a deeply rooted tradition in Western politics and yet, until very recently, there has been no systematic account of its normative foundations and applications. The Luck of the Draw is one of very few attempts at finding some conceptual unity in the political use of lotteries. Peter Stone considers here the two main types of decision by lot: the allocation of scarce goods and the assignment of public offices. His take is clearly normative, despite the wealth of evidence on lotteries discussed in the book. Stone investigates when lotteries are desirable, in particular when they are fair.

Stone’s case for lotteries hinges on the conceptual systematization and clarification of what lotteries are and when it is fair to use them. This is achieved through two normative statements, the lottery principle and the just lottery rule. First, Stone contends that there is an encompassing rationale for every use of randomization in decision-making processes, what he calls the lottery principle. According to this principle (p. 37), we would be justified in requesting that a decision is made by lot if it prevents the decision maker from influencing the outcome on the basis of reasons. This is “the sanitizing effect” of lotteries: they screen off some reasons from the decision process, be they good or bad, because the outcome of the decision becomes unpredictable for the decision-maker. But, of course, lotteries seem only defensible in cases where bad reasons may affect decisions, either because there are no good ones or, if there are, we cannot filter the bad ones out. 

Stone analyses then under which circumstances we would be normatively justified in using lotteries in the allocation of goods. Again, there is a general justifying principle, the just lottery rule (p. 53): “under conditions of indeterminacy, if an agent must allocate a scarce homogeneous lumpy good amongst a group of parties with homogeneous claims, then the agent must do so using a fair lottery”. In other words, if there is a suitable division of a good which all parties are equally entitled to claim, but there is not enough of it for everybody, a fair lottery is the most impartial tie-breaker: it only takes into account the equal strength of the claims over it (p. 78). This is guaranteed by the sanitizing effect of the lottery principle, since in a random allocation every other reason (merit, desert, nepotism…) is simply left aside. If the lottery gives equal probability to equal rights over the good, the allocation procedure will be fair. According to Stone, the just lottery rule is grounded on Scanlon’s contractarian approach: in cases of indeterminacy, every other alternative allocation rule (be the outcome certain or uncertain, as in weighted lottery) will be reasonably rejected by the involved parties.

Apart from systematizing and clarifying the concept of a fair lottery for the allocation of scarce goods, Stone’s case rests on a critical examination of other normative approaches to lotteries and alternative allocation rules. As to the former, Stone takes issue with justifications of lotteries in terms of consent (Goodwin), equality of opportunities and equality of expectations (Kornhauser and Sager), as well as with alternative contractarian foundations (namely, Rawls and Harsanyi). Stone considers as well eight alternative allocation procedures (e.g., desert, queuing, etc). The discussion is often quick, but insightful too. 

Finally, Stone adds a chapter on the assignment of public responsibilities by lot (usually known as sortition). The author contends that there is no unifying principle to justify its many uses documented throughout history. Stone discusses instead three kinds of arguments for sortition: allocative justice –rehearsing the previous arguments–, incentive alignment and descriptive representation. The former exploits the capacity of randomization to screen off perverse motivations in politics, e.g., nepotism in the appointment of public officials. The latter draws on the virtues of lotteries to make assemblies representative in a statistical (descriptive) sense: a random draw in a population with certain relevant characteristics can provide a sample that faithfully represents the distribution of such characteristics in the whole. But, of course, in both cases there is a clear trade-off between the virtues of lotteries and their various side-effects (e.g., the exclusion of qualified candidates), so Stone does not consider any of these arguments conclusive. The Luck of the Draw ends with a long concluding chapter addressing nine loose ends. 

Even if the reader disagrees with Stone’s arguments, it must be granted that the two principles provide an excellent thread to organize a compact overview of political lotteries. In my view, the author is right in adopting impartiality as the key to his normative analysis: it is open to debate whether lotteries yield (e.g.) equality of opportunity, but there is a clear consensus on the role of randomization as a warrant of impartiality even in purely epistemic contexts: we want a randomized allocation of treatments to patients in a clinical trial, for example, to prevent physicians from giving one particular drug to the patients they feel would benefit more. Humanitarian as this may be, it would spoil a fair comparison between treatments. However, Stone argues as if the normative leverage of lotteries stems from the exclusion of reasons alone: in allocating scarce goods, it would not be reasonable to oppose a fair lottery, where reasons play no role. But the superiority of such lotteries (compared to other allocation methods) lays in that they do not just sanitize reasons, but conscious and unconscious biases of all sorts. Psychologists have documented at length how people acting with the best reasons unwittingly deviate from them in a systematic fashion: a physician allocating treatments may be sincerely convinced that he treated all patients the same; but the data often reveal otherwise. This is the impartiality bias: we tend to think that we are more neutral than we actually are. Hence, for purely strategic considerations, I will request a randomized procedure if, for whatever reason, I suspect that the allocation of a scarce good may be otherwise biased (e.g., Kadane & Berry 1997), even if the people in charge of the allocation were guided by the best reasons alone. An interest-based contractarianism may provide in this respect a broader foundation for the impartiality of lotteries than Scanlonian reasonability. But biases and interests are simply left aside in The Luck of the Draw.

Stone does a wonderful job in unifying the discussion of scarce good lotteries under the umbrella of impartiality. But fair lotteries as allocation mechanisms are often uncontroversial: whatever the reasons we have to accept them, there is experimental evidence showing that we tend to like them (e.g., Bolton et al. 2005). I would have liked to see a more thorough discussion of the limitations of impartiality in the justification of sortition. According to Stone, we would need a general account of political decision-making (p. 123) if we were to construct all-encompassing rules of justice for sortition. But my impression, at least, is that the justice of lotteries depends implicitly of the type of good we are drawing lots for. When treatments are randomized in a clinical trial, the resulting allocation is often corrected because it doesn’t look random enough (e.g., one treatment goes to men and the other one to women). Whatever we do, there is a potential source of bias in such cases: maybe the unbalanced allocation is in itself biased, but if we grant us an unrestricted right to correct it, we may end up biasing it anyway. Whereas in scarce good lotteries only a few allocations may seem unbalanced, the outcomes of sortition are much more open to controversy: as the randomized selection of criminal and civil juries in the United States shows, for instance, there is an endless supply of motives for defense attorneys to strike jurors. The impartiality of the procedure in lotteries of this sort does not always provide a good enough reason to accept the outcome.

In sum, it would have been interesting to explore empirically what makes a lottery acceptable, addressing them as a procedure to control subjective biases and not only as the implementation of general criteria of justice. However, the exploration of this latter is enough to make The Luck of Draw an excellent read.

Berry, Scott M., and Joseph B. Kadane. 1997. Optimal bayesian randomization. Journal of the Royal Statistical Society. Series B (Methodological) 59: 813-819.

Bolton, Gary E., Jordi Brandts, and Axel Ockenfels. 2005 Fair procedures: evidence from games involving lotteries. The Economic Journal 115: 1054-1076.

{Agosto 2012}

{Economics and Philosophy 29.1 (2013), 139-142}