INTRODUCTION
John Broome provides an influential account of fairness according to which fairness requires that claims are satisfied in proportion to their strength.Footnote 1 According to this account, if two people have equal claim to some divisible good, fairness demands that each person receives half of the good. However, in the case of indivisible goods, it is not possible to satisfy directly each person's claim. Instead, Broome advocates the use of weighted lotteries as a surrogate for direct proportional satisfaction, so that each person's chance of winning the lottery is directly proportionate to the strength of her claim.
Pace Broome, we argue that fairness does not require the proportional satisfaction of claims. First, we argue that it is almost impossible to fairly calculate values for the weights of claims in weighted lotteries. Call this the Calculation Objection. Second, we argue that Broome rejects the best method of fairly calculating these reasons. Call this the ‘Self-defeating’ Argument. These arguments motivate our claim that the use of weighted lotteries is unfair. It follows that fairness does not require weighted lotteries. Since the proportional satisfaction of claims requires weighted lotteries, it follows that fairness does not require the proportional satisfaction of claims.
BROOME’S THEORY OF FAIRNESS
In this section, we elucidate Broome's account of fairness, that fairness requires the proportional satisfaction of claims.Footnote 2 His account can be broken down into three constitutive points:
(i) Claims are moral reasons.
(ii) The satisfaction requirement: all claims must be satisfied.
(iii) The proportionality rule: claims must be satisfied in proportion to their strength.
First, we outline Broome's arguments for (i)−(iii). We then examine Broome's solution to the problem of proportionally satisfying candidates’ claims when distributing indivisible goods, namely the use of weighted lotteries. Broome holds that weighted lotteries allow the candidates’ claims to be satisfied by a surrogate. Thus, Broome argues that the proportional satisfaction of claims requires weighted lotteries.Footnote 3 Given that fairness requires the proportional satisfaction of claims, it follows that fairness requires weighted lotteries. We shall examine each aspect of this argument in this section.
The requirements of fairness
When distributing divisible or indivisible goods amongst a group of candidates, each candidate will have reasons why she should receive the good. Some of these reasons can be weighed against each other, whilst some of them dictate what ought to be done. Broome distinguishes between three kinds of reasons why a candidate should receive a good:Footnote 4
(a) Teleological reasons.
(b) Rights-based reasons.
(c) Claims.
Teleological reasons claim that goods should be distributed in whichever way would produce the maximum overall benefit or minimize overall harm. These are not reasons that are owed to anyone and they can be weighed against each other. If goods are distributed with concern only to teleological reasons, then each candidate's teleological reasons would be weighed against other candidates’ teleological reasons and whoever's reasons outweigh the others' reasons would receive the good. One might use this teleological approach to the distribution of goods and simply give the good to the ‘better’ candidate.
Rights-based reasons act as side-constraints on how goods should be distributed and they determine what ought to be done. For example, suppose that a candidate has a right to some good because that good is her income. The question of weighing reasons against each other does not occur when rights-based reasons are involved. Whilst rights-based reasons can acknowledge a teleological approach to distribution, these reasons overrule teleological reasons. The side-constraint theory holds that if a candidate has a rights-based reason for a good, he should simply have it.
However, Broome holds that fairness is interested in the third kind of reasons. Claims are reasons which hold that a candidate is owed the good, but they do not act as side-constraints, like rights-based reasons. This is to say that when a candidate has a claim to a good, she is owed that good but there remains the question of examining the other candidates’ claims. Broome motivates the notion that there is an intuitive distinction between claims and the other kinds of reason by considering the following situation:
Dangerous Mission: Someone has to undertake a dangerous mission. The mission is so dangerous that the person who undertakes it will almost certainly die. The people who are available to undertake the mission are equal in all respects except for one candidate, who has ‘special talents that make her more likely than [the] others to carry out the mission well (but no more likely to survive)’.Footnote 5
Each candidate has a claim not to be sent on the mission, that if they were sent on the mission, they would probably die. Furthermore, sending the talented candidate will increase the likelihood of the mission's success. This is a reason to send that individual.
If one were simply to take a teleological approach to the candidates’ claims and weigh them against each other, then the claim of the talented candidate would be overridden by the claims of her peers. The talented candidate is more likely to complete the mission successfully than her peers. Given that each candidate's claim is equal, the claims would cancel each other out and the teleological approach would send the talented candidate on the mission based on her skill set. Broome holds that this is clearly unfair. Furthermore, the teleological approach would still produce an unfair result, even when the candidates’ claims are not equal. If the good is simply awarded to the candidate with the strongest claim, then the other candidates will still have their claims overridden.
As a result, Broome argues that ‘everyone's claim to a good should, prima facie, be satisfied’.Footnote 6 Call this the satisfaction requirement. Thus, if a candidate has a claim to a good, the candidate must at least receive part of the good. Additionally, Broome argues that fairness requires that every claim should be satisfied in proportion to its strength. By this, Broome means that equal claims should receive equal satisfaction, stronger claims should receive greater satisfaction than weaker claims, and, given the satisfaction requirement, those weaker claims require some satisfaction.Footnote 7 It stands to reason that a claim should not be satisfied any more or any less than its strength allows. Thus, Broome argues that fairness requires the proportional satisfaction of claims.
Surrogate satisfaction
The distribution of indivisible goods poses a problem for Broome's theory of fairness. Consider a case where a heart is to be distributed between two candidates, who have identical claims to the heart. Given the nature of indivisible goods, the claims of one candidate will not be satisfied. If Broome's account of fairness is correct, that fairness requires every claim to be proportionally satisfied, then some kind of unfairness is inevitable. It will do no good to cut the heart in two and give each candidate half of the heart. Nor should the good be distributed to the candidate with the stronger claim, since this would be as unfair as distribution according to teleological principles. How, then, should the heart be distributed?
Broome holds that the requirements of fairness can be partially achieved by satisfying the candidates’ claims using a surrogate.Footnote 8 In the heart case, each candidate is assigned a probability of winning the good in a lottery, where the probability is proportionate to the strength of the candidate's claim. In this case, each candidate is given a 50 per cent chance of winning the heart. The good is distributed to whoever wins the lottery. The lottery acts as a surrogate which partially satisfies every candidate's claim. This is fairer than simply giving the good to the person with stronger claims and it explains the intuitive fairness of lotteries. Thus, Broome holds that fairness requires weighted lotteries in the distribution of indivisible goods.
CALCULATING LOTTERIES
In this section, we consider Brad Hooker's objection to Broome's account of fairness and present our own objections against Broome. Whilst we partially agree with Hooker, we hold that his argument does not go far enough against Broome. Consequently, we present our own twofold argument. First, we demonstrate that the problem of calculating a lottery undermines Broome's theory. Second, we argue that Broome has already ruled out the most plausible solutions that might deal with our first objection.
Hooker's objections
Brad Hooker agrees that fairness can require the proportional satisfaction of claims in cases of divisible goods.Footnote 9 However, he argues that in cases where claims are unequal and the good is indivisible, fairness does not require the proportional satisfaction of claims. Hooker asks us to consider the following situation:Footnote 10
Case 1: There are two candidates, who both have claim to a medicine. The first candidate, Candidate 1, needs the medicine otherwise she will die. The second candidate, Candidate 2, needs the medicine otherwise she will lose a finger. Furthermore, for the medicine to be helpful, it must be distributed in its entirety.
Both candidates have claims for the medicine and the claim of the first candidate strongly outweighs the claim of the second candidate. Hooker argues that if we were to hold a lottery to decide who should receive the medicine, we would be acting unfairly towards the first candidate. In some cases of indivisible goods and unequal claims, it seems clear that overriding the weaker candidate's claim for the good is not unfair. If we hold a lottery that proportionally satisfies the claims of both candidates and the lottery rewards the second candidate with the good, a great unfairness would have occurred.
Whilst Hooker's argument goes some way in showing how fairness does not require the proportional satisfaction of claims, we do not think it goes far enough. There are two serious problems with Broome's account of fairness that Hooker does not consider: (I) the calculation objection, and (II) the ‘self-defeating’ argument. The calculation objection argues that it is almost impossible to calculate the appropriate weights for the lottery and incorrectly calculated lotteries are unfair. Given the calculation objection, one might suggest the use of an authority or a rule in order to calculate the lottery correctly. However, the ‘self-defeating’ argument demonstrates that this is false, as Broome already rules out the possibility of using authorities or rules. We think that these problems are far more effective in showing that fairness cannot require weighted lotteries. It follows that if fairness cannot require the use of weighted lotteries and that the proportional satisfaction of claims requires the use of weighted lotteries, then fairness cannot require the proportional satisfaction of claims.
The calculation objection
Whilst Broome argues that weighted lotteries are required for the proportional satisfaction of claims, he provides no account of how unequal claims can be accurately weighted. In a situation where there are two candidates who each have a claim to an indivisible good, and the claims of two candidates are exactly equal and we know that their claims are exactly equal, a weighted lottery would be viable. However, such a situation is incredibly rare. It is more than likely that the claims will be unequal. This is to say that one candidate will have stronger claims than the other candidates. Broome explicitly states that the good cannot simply be given to the better candidate:
Simply weighing claims against each other may not seem enough. Weighing up is the treatment we would naturally give to conflicting duties owed to a single person. Applying it between different people may not seem to be giving proper recognition to the people's separateness. In particular, weighing up claims does not seem to give proper attention to fairness.Footnote 11
[In cases of indivisible good], the candidates’ claims cannot all be equally satisfied . . . So some unfairness is inevitable. But a sort of partial equality in satisfaction can be achieved. Each person can be given a sort of surrogate satisfaction. By holding a lottery, each can be given an equal chance of getting the good. This is not a perfect fairness, but it meets the requirement of fairness to some extent.Footnote 12
Instead, the satisfaction requirement for fairness can be achieved through surrogate satisfaction in a weighted lottery. Stronger claims are given more weight whilst weaker claims are given less weight.
However, this will not do. Consider the example of the patients awaiting medical treatment, where the first candidate will die if she does not receive the good and the second candidate will lose a finger if she does not receive the good. Broome argues that, in so far as fairness matters, one must still use a lottery to decide to whom the good should be distributed. Let us propose a lottery for Case 1. First, we must assume that the claims of each candidate are quantifiable. This is necessary if we are to run the required lottery. Second, we must assign percentages to each candidate, which represent the chance that candidate has of winning the lottery. We will not pretend that these percentages are not arbitrarily assigned because we simply do not know on what grounds we can weigh one claim against the other besides using vague terms like ‘this claim is stronger than that claim’ or ‘this claim is a lot stronger than that claim’. However, it seems appropriate that the first candidate is given a much higher weighting than the second candidate. Thus, we stipulate that Candidate 1 is given a 99 per cent chance of winning the lottery, while Candidate 2 is given a 1 per cent chance of winning the lottery.
But what if the situation is changed? How would one calculate the weights of claims if the conditions of the situation were altered? Consider the following situation:
Case 2: There are two candidates, who both have claim to a medicine. The first candidate (as before, Candidate 1) needs the medicine otherwise she will die. The second candidate, Candidate 3 needs the medicine otherwise she will lose her arm. Furthermore, for the medicine to be helpful, it must be distributed in its entirety.
In this case, Candidate 3 has a stronger claim than her counterpart Candidate 2 in Case 1. However, it is unclear exactly how the percentages of the lottery in Case 2 should be assigned. If we are agreed that Candidate 3 has a stronger claim than Candidate 2 (which we might not be; we deal with this objection below), she should be assigned a high chance of winning the lottery. The difficulty comes when one tries to calculate how much more an arm should count for than a finger. There does not seem to be an accurate way of calculating this difference. Presumably, fairness cannot require of an agent the impossible or the nearly impossible. Thus, we have reason to doubt that fairness can require us to calculate the percentages of weighted lotteries.
Obviously, this example can be extended to a large, potentially infinite, number of cases. Consider:
Case 3: A case just like Case 1 and Case 2, except Candidate 4 needs the medicine otherwise she will lose both her arms and both her legs.
In this case, the stakes are even higher for Candidate 4 than for Candidate 2 or Candidate 3. However, as high as the stakes may be, they are not comparable to what is at stake for Candidate 1: death.
By considering these cases, we have tried to motivate the worry that there is a serious difficulty in calculating the correct percentages of the lottery. When claims are unequal, it is unclear how one is meant to assign values to claims: it is nearly impossible for the calculation of a lottery to be carried out accurately.
The ‘self-defeating’ argument
It might be responded that by handing the process of assigning probabilities in a lottery to an authority or by formulating a set of rules that outline how probabilities should be assigned, we can limit the damage done by the calculation problem. In doing so, we would admit that the calculation objection carries significant weight. But, by using authorities or rules, we ensure that the probabilities would be assigned in a consistent manner. Thus, whilst the calculation problem remains a thorn in the side of Broome's theory, authorities and rules can partially proportionately satisfy candidates’ claims.
However, this is an approach that Broome himself would reject. Broome raises three arguments against the use of authorities in the teleological approach:Footnote 13
(i) The expense objection.
(ii) The burden objection.
(iii) The deliberate selection objection.
The expense objection argues that the job of assembling and assessing the information necessary for deliberation may be expensive and time consuming. When an authority makes a judgement about the weights of claims in a lottery, the costs of carrying out the process may be too great. This objection does not rely on fairness, but rather it appeals to economic factors in decision-making.
The burden objection holds that the responsibility of deciding who is to live and who is to die may be an intolerable emotional burden. In cases where the authority must decide which candidate is to live and which candidate is to die, it might be said that the weight of this burden is both unfair and too great for the authority to bear.
The deliberate selection objection is the strongest objection against the use of authorities. An authority might be biased in its decision or have a vested interest as to which candidate should receive the good. It is entirely possible that the authority may not actually succeed in picking the best candidates. This would be unfair to the candidates that do not receive the good.
One might argue that the implementation of a rule would resolve these objections. This is to say that if one can decide on a rule that will calculate the weight of the claims accurately, then one can avoid Broome's objections. This approach would resolve the problem of cost; whilst there might be some cost in getting the rule embedded in rulebooks and in people's thinking, there would not be any cost for each time the rule is used (or there would be far less cost than the costs to which Broome points). It would also overcome the burden objection. However, it does not resolve the problem of deliberate selection, for there could be bias when formulating the rule.
The objections that Broome raises against the use of authorities and rules are convincing, particularly the third objection, which states that the use of authorities and rules is potentially unfair. However, this same objection can be aimed at Broome's own theory of fairness. When implementing a weighted lottery, an authority or rule is needed to actually formulate the lottery itself. But Broome has ruled out the use of authorities and rules. In order for a lottery to be weighted in proportion to the relative strengths of competing claims, someone or some rule will be needed to calculate the relative strengths of competing claims. Furthermore, Broome argues that a lottery overcomes the first two objections and is preferable to a fixed rule because it is fairer.Footnote 14 However, we have shown how a weighted lottery is not fair. So, Broome's argument that lotteries are preferable to fixed rules does not work.
BRUSHING BROOME ASIDE
We have shown that there is a serious problem in calculating the weights of the lotteries. Furthermore, Broome argues against the use of authorities or rules in such decision procedures. However, the use of authorities or rules seems to be required for accurately calculating the weights of claims, so Broome undermines his own theory. By arguing that weighted lotteries cannot be calculated accurately and that the use of authorities and rules is unfair, we have reached the conclusion that weighted lotteries are unfair. Any result from a miscalculated lottery would be unfair because the claims of the candidates would not have been proportionally satisfied as Broome's theory of fairness requires.
Consider a situation in which the claims of two candidates are being compared where the first candidate is given a 65 per cent chance of winning the lottery and the second candidate is given a 35 per cent chance of winning the lottery. The lottery is run and the first candidate receives the good. Suppose, however, that later it is discovered that the lottery has been incorrectly calculated. This might be because a mistake was made in the original calculation (demonstrating the calculation problem) or it might be because the authority that decided the calculation purposefully weighted the first candidate's claim more than the second. This situation is clearly unfair to the second candidate according to Broome's own theory of fairness. If fairness requires that probabilities in a weighted lottery be proportional to the strength of claims, then we have here a case of unfairness. The probabilities of success in the weighted lottery given to the two candidates do not correspond to the relative strength of their claims. Furthermore, we hold that cases like these would be far from uncommon, given our objections. Given these reasons, we think that our objections show that Broome's theory of fairness must hold that weighted lotteries are unfair.
To conclude, Broome argues that the proportional satisfaction of claims requires weighted lotteries. If fairness requires the proportional satisfaction of claims, it follows from the transitivity of ‘requires’ that fairness requires weighted lotteries. However, we have argued that weighted lotteries are unfair according to Broome's theory of fairness. Fairness-all-things-considered cannot require something that is itself unfair-all-things-considered. This seems to go against the very nature of fairness. So, fairness does not require weighted lotteries. Therefore, we reject Broome's theory of fairness: fairness does not require the proportional satisfaction of claims.Footnote 15
