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Article Excerpt
1. Introduction
When James Watson and Francis Crick submitted to Nature their groundbreaking paper relating DNA structure to protein synthesis, they faced a choice. In what order were their names to be listed? Would it be "Watson and Crick," or "Crick and Watson?" They resolved the matter by tossing a coin. (1)
Watson and Crick--I shall use the same ordering of names that they did--faced a problem of justice in placing their names on their seminal paper. There was something of value to be had--top billing on a groundbreaking paper. Either Watson or Crick, but not both, could enjoy this good. Each scientist could give good reasons for listing his name first; both had, after all, worked hard to produce the results contained in the paper. Thus, each had a claim to the good. If the claim of one had been clearly stronger than that of the other, then justice would have required that the superior claimant receive the good. Had, for example, Watson done more work on the project, a case could have been made for "Watson and Crick" on the basis of merit. Alternatively, if Watson had been more well-established, and therefore less in need of a boost in reputation, then grounds of need might have recommended the ordering "Crick and Watson." (2) In short, had a uniquely strong claim existed, the use of a coin toss would have made no sense.
In this case, however, the reasons that could be given on behalf of "Watson and Crick" were just as good as the reasons for "Crick and Watson"; neither man's claim to top billing was stronger than the other's. As a result, claim strength proved indeterminate in deciding who ought to receive the good. In effect, there was a tie. Some sort of tiebreaking procedure was needed to resolve this indeterminacy. Hence the coin toss.
The case of Watson and Crick is not an aberrant example. There are many allocative decisions in which considerations of justice prove indeterminate. (3) People need organ transplants, and society is reluctant to decree one life to be more valuable than another. Would-be emigrants from the Third World wish to enter the United States in numbers far greater than that country would realistically consider admitting; most of them have no better claim to admission than any of their rivals. Troops are needed in times of war. Young men (and possibly women) must be called to service, but not all are needed; exemptions are available, and there's often no particular reason to give these exemptions to some rather than others. Ties must be broken in all of these cases, and so tiebreaking is anything but a marginal phenomenon. Moreover, while nonacademics may dismiss the Watson and Crick case as trivial, nobody can treat lightly such topics as organ transplantation or military conscription. Sometimes, the resolution of indeterminacy is literally a matter of life and death.
But although ties must be broken when considerations of justice prove indeterminate, it remains true that not all tiebreakers are equally just. True, tossing a coin was not the only option available to Watson and Crick. They could have rolled a die, with an even number leading to "Watson and Crick" and an odd number leading to "Crick and Watson." Alternatively, they could have drawn from a deck of cards, with the high card (or low card) granting the right to be listed first. But suppose Crick had proposed an alphabetical listing. Or imagine that Watson had proposed a listing by age, from youngest to oldest. (Watson was born in 1928; Crick was born in 1916.) Few would defend such tiebreakers as just. In short, the demands of justice do not end once the candidates with the strongest claims to a good have been identified. These demands must also be satisfied when one of these candidates is chosen as the ultimate recipient of the good.
This raises the question of how to distinguish just from unjust tiebreaking procedures. Philosophers concerned with justice have devoted surprisingly little attention to this question. Rather, they have assumed that some paradigmatic tiebreaking procedures--coin tosses, balls drawn from an urn, drawn straws--are just. They have attempted neither to define the class of just tiebreaking procedures more precisely nor to explain why all and only all the procedures in this class should be counted as just. (4)
There have been few efforts to break this rather surprising philosophical silence. The most prominent of these efforts is George Sher's classic paper "What Makes a Lottery Fair?" (5) Sher uses the term lottery to describe any tiebreaking device that could be used to resolve indeterminacies with respect to the allocation of goods. He then sets out to distinguish between fair lotteries, which can be used to resolve indeterminacies justly, and unfair lotteries, which cannot. Sher defends a broad definition of a fair lottery, one that would encompass coin tosses, such as that used by Watson and Crick, but also many other procedures. But Sher not only offers a definition of a fair lottery; he provides an argument as to why it is just to use a fair lottery to break ties in this manner.
Since the publication of Sher's seminal paper, there have been only a few sustained efforts to examine the relationship between lotteries and justice. (6) While this literature has produced valuable results, it has failed to confront systematically the complete problem posed by Sher. Some works attempt to explain why justice might require resort to a lottery, while relying upon an intuitive understanding of what a lottery is. Others grapple with the problem of defining a fair lottery, but take for granted the relationship between lotteries and justice. Few connect together the tasks of definition and defense, and none confront Sher's argument systematically. Has Sher provided an adequate definition of a fair lottery? And has he successfully linked fair lotteries to justice? This paper offers answers to these two questions.
Section 2 lays out Sher's definition of a fair lottery and explains why he believes justice requires using such a lottery as a tiebreaker. In section 3, I argue that Sher's definition suffers from three critical failings. It fails to guarantee that a fair lottery will even exist; it fails to include all potential tiebreaking devices that intuition suggests should count as fair lotteries; and it allows the extent of the class of fair lotteries to depend upon arbitrary factors. In section 4, I point out where Sher's definition goes wrong and offer two corrections. Section 5 concludes by suggesting why justice might demand that ties be broken using a fair lottery satisfying the definition I endorse. It also draws lessons from my disagreement with Sher regarding contractarianism and justice.
Before proceeding, a small terminological problem is worth settling. A tiebreaking procedure--a method for resolving indeterminacy--is needed whenever there is a set of people with maximally strong claims that is larger than the quantity of goods to be distributed. Each of the persons in this set has a claim that is as strong as the claim of every other person in the set; moreover, each person in the set has a stronger claim than anyone outside of the set. (7) Some of the people outside of this set may have weaker claims; others may not have claims at all. (In effect, their claims are of "zero" strength.) A healthy person has no claim to an organ transplant, whereas a moderately sick person may have a weak claim. It is cumbersome to reiterate all of this each time I must refer to an individual in this set, and so I shall refer to each such individual as a strongest claimant. This terminology is a little misleading. One normally takes the adjective "strongest" to denote uniqueness; if there is a strongest claimant, then that seems to imply that this person is also the strongest claimant. (8) I do not intend this implication. It is the fact that there are multiple strongest claimants--more than there are goods to go around-that prompts the need for tiebreaking in the first place. This is not the neatest terminological solution, but it will have to do.
2. Sher on Fair Lotteries
"It is generally agreed," writes Sher, "that when two or more people have equal claims to a good that cannot be divided among them, the morally preferable way of allocating that good is through a tie-breaking device, or lottery, which is fair." Sher aims to discover "(a) exactly what conditions...
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