Option luck, gambling, and fairness Forthcoming in Ethical Perspectives 19,3 (2012), 417-443. Daniel Butt, University of Bristol1 1. Introduction This article takes its inspiration from an essay by G.A. Cohen, "Fairness and legitimacy in justice, and: does option luck ever preserve justice?", which was written for a Festschrift for Hillel Steiner (de Wijze, Kramer, and Carter, 2009), before appearing in the posthumously published collection On the Currency of Egalitarian Justice, and Other Essays in Political Philosophy (Cohen, 2011). It was, as Michael Otsuka notes in his Introduction to the latter volume, Cohen's last published word on the subject of luck egalitarianism. The essay showcases Cohen's characteristic analytical brilliance, but it is acknowlegedly inconclusive as to aspects of its central question, which concerns whether outcomes sanctioned by luck egalitarians as a result of individuals' decisions to expose themselves to option luck should be seen as just.2 My aim in this essay is to challenge, revise, and expand a central part of Cohen's argument, which concerns the question of whether the outcomes of gambles which are voluntarily undertaken, and are unambiguously classed as instances of option luck, are fair. The idea of "option luck" was developed by Ronald Dworkin in his influential account of liberal equality, and has come to play a central role in contemporary debates over what is commonly termed "luck egalitarianism". The key idea here is that egalitarian accounts of distributive justice should distinguish between two different ways in which luck might affect how well a person's life goes. Sometimes, people simply suffer good or bad fortune as a result of circumstances over which they have no control; at other times, they choose to make decisions which have the predictable effects of exposing themselves, in various different ways, to the vagaries of fortune. Thus Dworkin distinguishes between "brute luck" in the former case and "option luck" in the latter: "option luck is a matter of how deliberate and calculated gambles work out – whether someone gains or loses through accepting an isolated risk he or she should have anticipated and might have declined. Brute luck is a matter of how risks fall out that are not in that sense deliberate gambles." (Dworkin, 2000: 73). Dworkin argues that the cases are different, and, specifically, that equality does not require that the state reverse inequalities which stem from option luck. Cohen's article is a response to a claim 1 I would like to thank Hugh Lazenby, Patrick Tomlin, and two anonymous referees for Ethical Perspectives for extremely helpful comments. This article is dedicated to Jerry Cohen. 2 Cohen concludes, "So: back to the drawing board, later! I would still be there now, but Festschrifts have deadlines, and this one's has come." (2011: 143) 2 that he attributes to Dworkin which maintains that option luck, understood as deliberate and calculated gambles against a just background, always preserves justice. Cohen orients his discussion around what he calls "a paradigm case of putatively justice-preserving option luck", writing that, if option luck does not preserve justice in this case "then it never does, and we can then safely return a negative answer to the question that appears in my title". (Cohen, 2011: 132) In this article, I argue for the following claims. Even if we accept that Cohen is right to think that option luck does not preserve fairness, and thus justice, in the example he outlines, he is wrong to think that his strong conclusion, that option luck never preserves justice, follows, as he is wrong to think that his gambling example is a paradigm case of putatively fairness-preserving option luck. As such, there are a range of different examples where it can be coherently claimed that option luck gambles do preserve fairness, and hence justice. To defend Cohen's strong conclusion, one would need to maintain that option luck gambles never give rise to morally relevant differences between persons. There are at least plausible reasons why one might deny this claim. 2. Cohen's argument Cohen's argument draws on an analysis of four ideas that feature prominently in debates about the justice of distributions, but which are not, he claims, always properly distinguished from each other: justice; unanimity; fairness; and legitimacy, the latter of which he defines as "the property that something has when, to put it roughly, no one has a right to complain about its character, or, perhaps a little less roughly, when no one has a just grievance against it" (125).3 Cohen's key claim is that while option luck may give rise to outcomes which are legitimate, in the sense that no one has a just grievance against them, this does not lead to the conclusion that such outcomes are fair, since, as he puts it (paraphrasing Toni Morrison) "what's legitimate... 'ain't necessarily' fair" (125). His conclusion here is that it is not right to describe the results of option luck, and the outcomes of gambles specifically, as "fully just" or "entirely just", even if we accept that they should be allowed to stand since they result from choices which people have freely made. This is on account of what Cohen terms the "'different types of justice' proposal" (128), whereby there is more than one sense in which an outcome might be described as just: although "legitimacy justice" endorses the outcome of gambles, "fairness justice" does not (141). Quite how we should articulate the claim that an outcome can satisfy one criterion of justice but not another is open to question: it might be said 3 Cohen accepts that this is not a fully satisfactory explanation of the idea of legitimacy to which he is referring, but does note that the idea that one does not have a just grievance against an outcome means "as a minimum" that "we cannot complain if the outcome's reversal is not enforced". (2011: 129) 3 that option luck results in outcomes which are in a sense unjust, as not fair; or which are only partially just, as not fair; or it might be that we think the force of Cohen's argument is sufficiently strong that we do not want even to say that the outcomes of option luck are actually just, but simply hold that they are legitimate, and so should not be overturned.4 The latter conclusion (which Cohen appears to reject , and which in any case goes against the implication of his "different types of justice" proposal) would be the most dramatic, in theory, if not in practice, as it would mean that luck egalitarianism could not lay claim to the title of a "theory of justice". But even the conclusion that outcomes involving option luck gambles are generally unfair would be an obvious embarrassment for advocates of luck egalitarianism.5 Cohen maintains that the option luck case is relevantly similar to a different case where an inequality of resources emerges from an initially fair and equal distribution due to the unanimous consent of all parties, such as where all the members of a given group voluntarily decide to transfer half of each individual's resources to two specific members of the group. Cohen contends that the outcome in such a situation is legitimate, as a result of the legitimating force of the unanimity of the parties to the transaction, but not fair: [M]any would say, and I among them, that the upshot is unfair, and everyone must agree that it is not fair by the criteria that rendered the original distribution fair. Still, the result is legitimate, in the defined sense: no one has a right to complain about the outcome, since everyone voted for the transactions that brought the outcome about." (133) Cohen does not dispute the claim that unanimity in this case trumps equality, which is to say that it would be wrong, in an all things considered sense, to restore equality against the wishes of the parties involved in the exchange.6 But, he suggests, there are two ways in which we might understand the justice of the subsequent distribution. We might think either i or ii: i. The unequal outcome is not entirely just (because it is unfair) but it is legitimate. With respect to legitimacy, unanimous will trumps the value of fairness. 4 For consideration of this latter claim, see Cohen, 2011: 142. 5 So, for example, Jonathan Wolff argues that Arneson, Cohen, and Dworkin are all committed to what he calls "The Lexical Priority of Fairness Thesis", which holds that "Egalitarianism is constituted by a lexically prior notion of fairness" (2008: 103). 6 It is significant that all members of the group agree to this outcome. One could readily imagine a case for disallowing gift giving of this type between particular group members insofar as the subsequent inequalities had an appreciable effect on third parties not involved in the consensual exchange, as Cohen argues in Self Ownership, Freedom and Equality, in relation to Nozick's Wilt Chamberlain example (1995: 26-7). For discussion of luck egalitarianism and gift giving, see Lazenby (2010). 4 ii. The unequal outcome is both legitimate and entirely just. Unanimous will confers unqualified justice on an unequal outcome that would otherwise be an unjust outcome. (133) Position (ii) is attributed to Dworkin, and it is this position that Cohen seeks to oppose. He does so by outlining the following example: Imagine, then, two people, A and B, who are relatively identical with respect to their assets, their circumstances, their tastes, and so forth: they are, that is, identical in every respect that bears on distributive justice, and the distribution of goods between them is perfectly equal and perfectly just. Let's say that each has $100,000. Now one taste that A and B share is for gambling. And each gambles half of his assets against half of the other's, on a 50-50 toss. Dworkin would claim that the resulting distribution is entirely just, because of its origin in option luck against a backdrop of equality, and despite the fact that one of the people emerges with $150,000, which is three times the assets that the other one comes to have, and however dire the resulting state of that other person may be. (133) For Cohen, the reason why it might be said that the losing gambler has no complaint in this case stems from unanimity, not fairness. It is not because the decision to gamble renders the outcome fair, but simply because of the fact of the decision to gamble: he agreed to the procedure which befell him. The conclusion is that "option luck never preserves the justice that precedes its operation". (134) So whilst the preceding distribution is just in the sense of being fair, the most that can be said of the subsequent distribution is that it is just in the sense of being legitimate. 3. Fairness, and the problem with the paradigm example Cohen is explicit that he sees his gambling example as posing a crucial test for the justice of option luck affected outcomes: writing both that "if option luck does not preserve justice in the case upon which I shall focus, then it never does" (132) and that if option luck doesn't preserve justice in the entirely asymmetrical two-person gamble case, then it doesn't do so anywhere" (134). Cohen does not explicitly state why he uses an example of this form, but the reasons seem obvious, and are linked to the notorious problems that luck egalitarians face in practice in seeking to distinguish between option and brute luck (Lippert-Rasmussen, 2001; Vallentye, 2002; Otsuka, 2002; Sandbu, 2004). Cohen's approach here is far from unique in the literature – it is commonplace to find theorists utilising gambling examples as paradigm cases of option luck.7 The gambling example, as presented by Cohen, strips away everything that differentiates between the individuals other than the way they call the toss of the coin – they have the same assets, circumstances, and tastes, and are 7 There are many such instances, but see, for example, Arneson, 1990: 175-6; and Otsuka, 2002: 41. 5 "identical in every respect that bears on distributive justice" (132). It is true that this example, then, appears to be an unambiguous case of option luck as defined by Dworkin, who, as above, specifically speaks of deliberate and calculated gambles in defining the term. There is also certainly a sense in which the gamble in Cohen's example can be described as fair in terms of its procedure, in a way which does not simply rest upon the fact that it is the result of a voluntary decision by the parties involved. The gamble Cohen describes is, in statistical terms, a "fair bet", which is to say that it "pays its price or stake in expectation" (McCarty and Meirowitz, 2007: 38). On McCarty and Meirowitz's definition, a bet is fair if w = px1 + (1 – p)x2, where w is the stake, x1 and x2 are possible monetary outcomes, p is the probability of x1 and (1-p) is the probability of x2 (2007: 39). The key idea here is that the expected payoff of such a bet if repeated in the long run would be zero – the cost of the bet is likely to match the winnings one makes from the times one wins the bet. So there is no "edge" for either gambler here – neither A nor B has managed to get the upper hand by betting on a situation where the expected payoff is more favourable to one party than to the other. Even if A or B thinks that they have a good reason to believe that heads or tails is more likely to come up than the alternative, meaning that the odds actually favour them, they are incorrect. As such, the choice to gamble cannot be said to reflect any exercise of skill or good judgement, as whether A or B wins is purely a matter of chance, and so the bet is an example of what Rawls calls "pure procedural justice" (1999: 75). It is worth noting that while bilateral bets between individuals on questions such as a coin toss can be fair bets, real world bets on matters of pure chance which take place through commercial enterprises such as casinos and so forth are generally not fair in this statistical sense – such bets do not normally pay their stakes in expectation, due to the profit margin of the enterprise in question (such as the inclusion of green "zeroes" on roulette wheels which do not pay out to bets on either red or black). A similar point applies to betting with a commercial bookmaker – the odds compiled by bookmakers typically include a margin so that the bookmaker will make a profit on any given event whatever the result, so long as the market does not bet disproportionately on particular outcomes. If one bets at random with a commercial bookmaker, one would expect to lose money over time. There is then a sense, at least, in which such bets are unfair by definition, though this is not necessarily to say that they result in either unfair or illegitimate outcomes. In the case of bets on a bookmaker's book, one can hope that one a better sense of the true odds of the likely outcome of the bet than the bookmaker, sufficient either to make the bet fair, or actually to turn the tables in one's favour. Commercial bets where outcomes depend solely upon chance are straightforwardly, in a statistical sense, unfair – one has simply to hope that one gets lucky. 8 8 For relevant discussion, see Lippert-Rasmussen's account of "gambles proper" and "quasi-gambles" (2001: 555). 6 Cohen, then, has described a statistically fair bet, where the procedure is perfectly fair to both parties and where the outcome is solely a function of option luck, and cannot be attributed to brute luck. One can see how one could assume that such a gamble constitutes a compelling test case for the luck egalitarian – if the outcome of a fair gamble between equally situated parties is not fair, what hope is there for other gambles? Such an assumption would be mistaken. Not all gambles are alike – it is possible to maintain that the results of some gambles are fair, and so not necessarily unjust, regardless of whether one accepts that the outcome in Cohen's paradigm case is unfair. This is the central claim of this article, and if this is correct, then Cohen's strong conclusion – that option luck does not ever preserve justice, other than when it happens, by chance to do so, falls. This means that we need more information about the character of any given gamble in order to determine whether it results in a fair or unfair outcome. It is the particular features of this gamble which render its outcome unfair: ironically, it is possible to maintain from a luck egalitarian perspective that statistically unfair gambles can result in fair outcomes in a way that some fair gambles do not, precisely because the asymmetry between the parties to the gamble which renders the gamble unfair in a statistical sense is sufficient to render the outcome fair, if it is seen as constituting a morally significant difference between the gambling agents. The perfect procedural fairness of Cohen's example means that there can be no such morally significant difference between parties to the gamble – but this is not a general feature of option luck gambles. In order to make this case, I employ the following principle of fairness in relation to equality (PF1): PF1: An inequality is only fair if it results from some morally relevant difference between persons. This should be differentiated from the more demanding alternative principle (PF2): PF2: An inequality is only fair insofar as it corresponds to some morally relevant difference between persons. The use of PF1 instead of PF2 requires some explanation. The aim here is to develop an account of fairness which captures common intuitive beliefs about the importance of treating like cases alike, whilst allowing a greater degree of variation between like and unlike cases than is allowed under PF2. PF2 is (in Nozick's terms) a patterned principle, which holds that inequalities must be proportional to the extent of the morally relevant difference between individuals which licenses the inequality in question.9 PF1, however, is not patterned in the same way, merely maintaining that 9 So Nozick writes that a principle of distribution is patterned "if it specifies that a distribution is to vary along with some natural dimension, weighted sum of natural dimensions, or lexicographic ordering of natural 7 fairness can only be satisfied if the inequality can be traced back to morally relevant difference between persons – proportionality, on this account, is not a requirement of fairness. The basic motivating idea behind both principles is that fairness requires that inequalities be justified by reference to some kind of difference between persons which is deemed to be of moral significance. Such a claim does not itself constitute a full principle of distributive justice and does not maintain that unfair inequalities are impermissible in an all things considered sense, but it does deny that inequalities which emerge which do not satisfy its criterion should be seen as fair. This claim, or something close to it, is often taken to be a widely held and largely self-evident principle of fairness. Neil Levy, for example, writes that "people are... strongly committed to [a] simple principle of fairness... [which] states that agents do not deserve to be treated differently unless there is a desertentailing difference between them", and suggests, indeed, that it is "very possible that this principle of fairness is innate in the primate mind: it seems to be a principle of this sort that explains the behaviour of Capuchin monkeys when they reject unequal pay for the same work" (2011: 9-10). Both PF1 and PF2 are deliberately phrased in a more general way than in Levy's formulation, which specifically invokes desert, so as to leave open the question of what might constitute a morally relevant difference. Both PF1 and PF2 reflect the claim that it is unfair if factors which are arbitrary from a moral point of view affect distributive outcomes, but they diverge with regards to how they allow morally arbitrary differences to lead to inequalities.10 PF1 and PF2 differ, since PF2 implies that the extent of the inequality should depend on the extent of the morally relevant difference. So, if we were to say that an inequality between A and B was justified on account of A's being more deserving, or more talented, or more industrious than B, PF2 would hold that the extent of the permitted inequality should reflect the extent of the difference. Suppose, for example, that we said that Afua should be paid twice as much as Belinda on account of the fact that she works twice as hard. Here the degree of difference in outcomes is explicitly related to the degree of difference in performance: as such, we can say that the inequality corresponds to the difference between the persons. The numbers here are not important in themselves – it would be possible to put forward an account that said that people who worked 50% harder than others should be paid twice as much than them in a way which could satisfy PF2 (if, for example, we thought that working 50% harder meant that someone was twice as deserving). What is necessary for the realisation of PF2 is that there is some intelligible and consistent relation between morally relevant differences between dimensions" (1974: 156), and lists, as suggested candidates for the relevant dimensions, "to each according to his moral merit, or needs, or marginal product, or how hard he tries, or the weighted sum of the foregoing" (156-7). 10 Rawls famously argues in A Theory of Justice that his two principles of justice "express the result of leaving aside those features of the social world that seem arbitrary from a moral point of view." (1999, 14). 8 persons and inequalities of outcome. This means that the greater the morally relevant difference, the greater the justifiable inequality. One way to think about this is to consider the principles from the perspective of the theory of justice outlined by Aristotle in the Nichomachean Ethics. It is commonplace to attribute to Aristotle the principle that justice requires that like cases be treated alike: so, for example, John E. Coons writes that, "This formula of Aristotle is widely accepted as a core element of egalitarian moral and social philosophy" (1987: 59). However, whilst this principle constrains the set of cases where an inequality is allowed by justice, it does not address the question of the degree of inequality which is permitted when there is a morally relevant difference between persons. Aristotle's fuller account of distributive justice rests on his principle of proportional equality, which holds that inequalities should be proportionate to the extent of the difference between persons which justifies the inequality (Aristotle, 2000: Book V, III) As Stefan Gosepath writes: Proportional equality in the treatment and distribution of goods to persons involves at least the following concepts or variables: Two or more persons (P1, P2) and two or more allocations of goods to persons (G) and X and Y as the quantity in which individuals have the relevant normative quality E. This can be represented as an equation with fractions or as a ratio. If P1 has E in the amount of X and if P2 has E in the amount Y, then P1 is due G in the amount of X′ and P2 is due G in the amount of Y′, so that the ratio X/Y = X′/Y′ is valid. (2011) Any distribution which is proportional in these terms satisfies both PF1 and PF2, and is, in Nozick's sense, patterned. Luck egalitarianism evidently cannot satisfy PF2, and so is not a theory of proportional equality in Aristotle's terms, due to the acknowledged role of luck in determining distributions. Luck – as opposed to the decision to expose oneself to the effects of luck is a feature of the external world, and not of the agent. In order for luck egalitarianism to satisfy PF2, it would have to be the case that one held "being lucky" as a morally relevant difference, which seems ridiculous. However, the lack of fit of luck egalitarianism with the proportional account of fairness does not mean that it follows that luck egalitarianism necessarily departs from the idea that fairness requires that like cases be treated alike. At least some luck egalitarian outcomes can satisfy PF1, since PF1 simply requires that there be a morally relevant difference between persons if there is to be an inequality between persons, without saying anything about how the degree of the difference maps on to the degree of the inequality. So, for example, imagine a situation where a farmer treats her crops with a hitherto untested fertiliser, not knowing whether this will help them to grow, or cause them to die. She has willingly chosen to gamble, and as such the outcome will be a reflection of option luck. This choice to expose herself to option luck is, on the luck egalitarian account, morally 9 relevant, but there will be no necessary link between the degree of inequality which emerges as a result of her decision, and the degree to which she has chosen to expose herself to the vagaries of fortune. It is of course possible that the difference in choice will map onto the difference in outcome, but this would simply be a contingent effect of the workings of chance (reflecting Cohen's earlier claim that luck egalitarian outcomes can preserve fairness "by accident"). Under luck egalitarianism, some very risky strategies will pay small rewards, and some more conservative and risk-averse strategies will end up leading to massive payoffs. But the luck egalitarian can coherently maintain that there is a morally relevant difference between individuals who choose to expose themselves to differential degrees of risk. If one accepts that differences which emerge as a result of PF1, rather than PF2, are fair, then the door is open to affirming the proposition that Cohen denies: that luck egalitarianism sometimes preserves fairness other than by accident. It would be intelligible, on this account, to say that an outcome whereby the risk-taking farmer ends up with significantly more (or significantly fewer) crops than others was fair, in that it resulted from (though did not necessarily correspond to) a morally relevant difference between the farmer and others: namely, the decision to take a risk which others forewent. In my view, it is this idea of fairness which affords luck egalitarianism with a degree of initial intuitive plausibility – if, and insofar, as it is the case that luck egalitarian outcomes satisfy PF1, and if one believes that PF1 is an acceptable principle of fairness, then it looks as if luck egalitarian outcomes are fair. We can now turn to Cohen's paradigm example of inequality based on differential option luck. The problem with the example, simply stated, is this: the example is deliberately constructed to block any possibility of the outcome being affected by brute luck, but in stripping away these elements, Cohen removes any possibility of morally differentiating factors between the two parties. Unless one believes that all examples of option luck have this particular character, there is no reason to believe that the paradigm example successfully models all luck egalitarian outcomes. Even if one accepts, for the sake of argument, that Cohen has successfully identified a case where luck egalitarianism does not lead to fairness, and that there is therefore at least something unjust about inequalities which arise from such a process, it does not follow that this claim is generalizable to all luck egalitarian outcomes. Thus, his claim should be rephrased as maintaining that luck egalitarianism sometimes fails to preserve justice.11 It is then a further question to what extent luck egalitarianism would tend to result in just or unjust outcomes (or, more fully, outcomes which are in a sense just or unjust as unfair) in practice. 11 Cohen, it should be noted, explicitly distances himself from this more limited claim, noting that strong arguments in its favour have already been made by Lippert-Rasmussen and Otsuka (131-2). 10 The detail of Cohen's example is key here. He imagines two individuals who are, he states, "identical in every respect that bears on distributive justice", and who gamble half their assets against each other on the basis of the toss of coin. The argument is constructed in such a way that there cannot possibly be a morally relevant difference, of the kind outlined above, between the two individuals – the outcome of the bet is a result of option luck, since they have agreed to the bet, but once the bet is made, only luck determines the outcome. As such, the resulting inequality is unfair according both to PF1 and PF2, since there is no morally relevant difference between the two individuals, as there is no moral significance to calling "heads" or "tails" apart from the fact that it signifies agreement to submit to the outcome of the coin toss , and, stipulatively, both have made this agreement in identical fashion. In fact, it is possible to construct the example in such a way that there is not even a difference in how the parties call the coin toss – imagine that they both call "tails", having previously both agreed to the same tie-breaking resolution, which holds that in the event of such an outcome, an independent third party should be charged with settling the bet by devising a way of randomly choosing one of the two to receive the money, such as drawing lots. The point here is that, from the perspective of justice, a choice to gamble can perform different functions in different cases. In some cases, the choice to gamble may be seen as creating a morally relevant difference between persons, as it represents a differential willingness to expose oneself to risk. In other cases, where both parties choose to gamble and, as in this case, are both exposed to precisely the same degree of risk, it does not do this – here there is no differentiating factor, and so it is simply the voluntarily made choice to gamble which has a putatively legitimating effect on the outcome. In Cohen's example, the parties choose differently: one calls "heads", and one "tails". The content of this differential choosing is not morally significant, and so, Cohen argues, cannot lead to a fair inequality under either PF1 or PF2. But this example does not establish the stronger claim that the differential choices which lead to option luck derived inequalities are always non-relevant from a moral point of view, and so Cohen fails to show that all luck egalitarian outcomes violate PF1. In fact, all he strictly shows is that luck egalitarian outcomes fail to preserve fairness in a very narrow range of cases where there is either practically or literally no difference between the gambling parties – a fuller assessment of the fairness-preserving character of luck egalitarianism would have to say more about what constitutes a morally relevant difference. To show why this is the case, it is necessary to say more about the particular features of the gambling example he employs. 4. Three contingent features of the paradigm example Cohen's paradigm example has at least three notable features, which will not always be present in real world gambles. Specifically, it is a (i) zero-sum (ii) fair bet, where both parties have an (iii) equal 11 chance of winning. Each of these factors is important, as it is potentially significant when it comes to assessing whether a luck egalitarian gamble has led to a morally significant difference between persons. We will consider each in turn. i) Zero sum versus non-zero sum Gambles may be classed as zero sum or non-zero sum, depending on whether their outcomes make a difference to the overall amount of resources in the system. Real world betting, in contexts such as casinos, or where individuals make wagers with one another, are typically zero sum in character. Thus, for example, authorities on these forms of gambling can write as follows: Without great loss in generality, "gambling" can be defined as a monetary transaction between two parties based on the outcome of an uncertain event... Depending on who is right, one person will be wealthier by the amount staked (the winner) and the other party will be out of pocket by the same amount. Since the winner receives from the loser the amount wagered, the contest can be conceptualized as a zero-sum game and the activity can be labelled "zero-sum gambling". No wealth is created by zero-sum gambling; rather it is redistributed. (Walker, Schellink, and Anjoul, 2008: 11) Choosing to participate in a gamble of this sort is clearly an example of option luck as Dworkin defines the term: as stated previously , option luck is "a matter of how deliberate and calculated gambles turn out-whether someone gains or loses through accepting an isolated risk he or she should have anticipated and might have declined" (Dworkin 2000, 73). But not all examples of option luck are zero-sum gambles. There are many ways in which people can choose to take risks which do not have this narrow redistributive character – instead, they potentially make a difference to the total amount of resources in the system, and so have the potential to be wealth creating or diminishing in a quite different sense. One way to characterise this point is to describe the distinction between zero sum and non-zero sum bets as relating to that between interpersonal and impersonal gambles. There will always be a winner and a loser in an interpersonal gamble – one hopes, simply, to gain at another's expense. This is straightforwardly the case when we think of bets and related instances of gambling, but it may also be the case in some forms of competition between individuals – if I try a dive with a high degree of difficulty in the Olympic High Board final, I take a gamble, and if it comes off, I will benefit, to the disadvantage of my competitors who will then be ranked lower than they would have been had I chosen a more conservative strategy. By way of contrast, impersonal gambles need not involve a loss to other parties – if my gamble straightforwardly makes a difference to the amount of resources in the system, this might result in a gain to myself without any corresponding disadvantage for other individuals. In the real world, such choices are unlikely to have such isolated effects – if I invent a new more efficient form of electricity 12 production, for example, it may be that my actions lead to a greater net amount of energy available for consumption, but it also may be the case that I benefit at the expense of other electricity providers. A gamble, then, can have both interpersonal and impersonal effects, but it will always be strictly either zero sum or non-zero sum. ii) Fair versus unfair bets As described previously, the bet in Cohen's example is, in statistical terms, a fair bet, in that it pays its stake in expectation. In order to characterize a bet as fair or unfair, we need to know something of the probabilities involved and the risk to which the gambler is exposed, and this means that such characterizations typically only really make sense in zero sum contexts, where there will be a clear winner and a clear loser. Even then, it is only in particular situations, such as betting on a coin toss or a roulette wheel, that parties to the gamble will have enough accurate information about the odds to be able to say with confidence whether a bet is fair or unfair. In many other cases, interpersonal bets will be made precisely because of disagreement as to whether the odds favour one party or the other – the bet be occasioned by a disagreement as to the likelihood of a given outcome materializing. Other forms of gamble will be even more speculative, and will take place in a context of genuine uncertainty as to the probabilities of success or failure. The entrepreneur who starts an untested new business, or the school teacher who quits her job to try to write her debut novel, cannot realistically be said to have a good understanding of the likelihood that their gamble will come good – even if the individual thinks it on balance unlikely that their venture will succeed but is willing to take a chance on the possibility of gaining significant future rewards, their situation is not strictly analogous to that of a long odds gambler who places a sum of money on a single number on a roulette table. iii) Equal versus unequal chances of winning Not only is the gamble which Cohen describes a fair bet, it is also one in which both parties are exposed to exactly the same degree of risk. These are different things – one could have a fair bet with an unequal chance of winning (A and B bet on the throw of a die – A bets that the number will be 1 or 2 at odds of 2:1), or one could have an unfair bet with equal chances of winning (A and B bet on a toss of a coin – if heads, A pays B £100, if tails, B pays A £200). One way to describe this situation is to say that A and B are members of the same "luck cohort", since they have decided to expose themselves to identical amounts of risk. There are four ways in which one might characterise differences or similarities in risk exposure between two individuals within luck egalitarianism: Situation i) Neither A nor B gambles – members of same luck cohort 13 Situation ii) A gambles and B does not – members of different luck cohorts Situation iii) A and B both gamble, but A exposes herself to a higher degree of risk than B (for example, A bets that heads will come up on two successive coin tosses) members of different luck cohorts. Situation iv) A and B both gamble, and expose themselves to the same degree of risk – members of same luck cohort. A simple contrast between gamblers and non-gamblers does not capture, first, the fact that there is a sense in which deciding "not to gamble" itself represents a decision to expose oneself to a particular set of risks,12 and, second, that there can be differences between "gamblers" in terms of the differential risks to which they have chosen to expose themselves. 5. Assessing the paradigm example Taking these three contingent features of gambles together, we can see that Cohen's example has a very particular character. They key point is this: each of these features has the potential to either constitute or contribute to what could be said to be a morally relevant difference between persons, which could be thought to give rise to a justly differential outcome under PF1. The feature would constitute a morally relevant difference if it was thought that its presence alone was sufficient to count; it would contribute to such a difference if it counted when present along with another factor or factors. To see how this works in practice, consider the following examples: 1) An individual invests in a salvage company to finance an expedition to hunt for the wreck of a sunken ship, so as to recover its perishable cargo. Another individual declines the opportunity to invest. (non zero sum, different luck cohorts) 2) A company markets a new, experimental fertiliser, which is known to work on some crops, but not others. One farmer tries a batch on her carrot crop, another farmer on her potatoes The former doubles her yield, the latter loses her crop. (non zero sum, same luck cohorts) 3) Two individuals purchase lottery tickets. The first purchases twenty times more than the second, in order to have a twenty times greater chance of winning. (zero sum, different luck cohorts) All three cases involve gambles. It is open to the defender of luck egalitarianism to hold the line on any of these examples, and maintain that the difference between the individuals in question renders 12 Kasper Lippert-Rasmussen cites Marc Fleurbaey's claim that "in our (uncertain) world 'individuals never have the choice between a risky lottery and no risk at all, they essentially choose one global lottery" (2005: 82). 14 the outcome fair as a consequence of PF1. Any such an attempt would obviously have to engage with the detail of the example, and maintain that the difference in question possesses moral significance. Noting such a possibility is all that is necessary to show that Cohen's argument, as it stands, is incomplete; but, of course, whether this conclusion is significant then depends on whether the suggestion that there could be situations where option luck results in fair inequalities is plausible. The most straightforward way to maintain that option luck can give rise to fair inequalities is to maintain that decisions to expose oneself to differential degrees of risk are morally relevant under PF1: thus, the key question is whether the parties in question are members of different luck cohorts. Cohen's failure to include differential degrees of risk exposure in his paradigm example therefore crucially undermines his strong conclusion that option luck outcomes are never fair except by accident. On such an account, (1) and (3) would give rise to morally relevant differences, but (2) would not, and so the outcome in (2) would be unfair in the same way that, Cohen claims, the outcome in his paradigm example is unfair. Quite how these claims are to be expressed is an open question. Perhaps the most obvious way to express the idea, in everyday parlance, would be to say the individuals "deserve" the distributions which result from such gambles. Such a claim is controversial, however, as the meaning of desert in this context is disputed. If we see desert as corresponding strictly to, for example, the virtue of the agent, then the acknowledged role of luck in luck egalitarian distributions rules out the possibility that gamblers deserve the resources that stem from their lucky or unlucky choices -on such an understanding of desert, outcomes would have to satisfy PF2 rather than PF1. If we use desert more loosely, to indicate simply that a given outcome is a result of choices for which an agents is responsible, then it is possible to phrase the claim in terms of desert, but then we seem again to have replaced a concern for unanimity with that of fairness – on such an interpretation, the winner in Cohen's paradigm example deserves his good fortune. It is at least possible, however, to use desert here in a third way, to mirror a PF1 style claim about fairness, and this involves a recognition of the fact that the outcome stems from an action on the part of another individual which separates herself from others in a significant way – that it gives rise, in short, to a morally relevant difference between persons. Luck egalitarians cannot maintain that lucky impersonal gamblers deserve their good fortune, in the sense of desert as corresponding to the virtue of the agent. But they can nonetheless maintain that the decision to gamble, or not to gamble, is of moral significance. So the point of the claim that such outcomes are fair need not be that it reflects in proportional fashion the differential desert of the different parties, but it might be that it stems from a morally relevant – and thus, potentially, a desert-entailing – difference between them. Such a judgment would, then, be compatible with the aforementioned principle of fairness 15 articulated by Neil Levy, which holds that "agents do not deserve to be treated differently unless there is a desert-entailing difference between them". So a defender of the fairness of option luck outcomes can resist Cohen's critique in terms of PF1 so long as they are willing to maintain that there can be moral significance to individuals' decisions to expose themselves to differential risks. How strongly should this claim be expressed: is it always the case that differential voluntary exposure to risk is morally significant, or is this only the case depending on the nature of the gamble in question? It is possible, though certainly controversial, to maintain the latter position by drawing a distinction between zero sum and non-zero sum gambles. My suggestion is that it is easiest to make an intuitively forceful case for the fairness of option luck outcomes in relation to the sort of example described in (1) above, where some individuals, but not others, choose to take a risk which has the potential to contribute to the common good, by increasing the net amount of resources in the system. But this leaves unclear the question of whether it is the non-zero sum character of the gamble, or the differential degree of risk of the different parties, which leads to the intuitive reaction that endorses the fairness of the outcome. One can see why one might feel more strongly about the desirability, broadly speaking, of non-zero sum than zero sum gambles. Not all such gambles will successfully add to the net stock of resources in society, but it might well be believed that the net effect of allowing inequalities which result from such gambles is likely to do so. Clearly it is then a further question whether the unequally held introduction of new resources will indeed aid the common good, and different distributions are likely to be viewed differently by, for example, straightforward utility maximisers and prioritarians. But it may well be that at least some of the intuitive attraction of luck egalitarianism comes from considering such examples, and thinking that it is not just legitimate but fair to allow Pareto efficient inequalities which result from such risk taking to stand – that there would be something specifically unfair about confiscating and redistributing the proceeds, which would not be true in relation to the outcomes of zero-sum gambles. As such, it might be claimed that differential willingness to undergo a non-zero sum gamble is morally relevant in a way that willingness to undergo zero sum gambles is not, so that (1) is fair but (3) is not.13 Of course, many will want to deny outright the claim that the 13 It might also be noted here that insofar as a gamble aims to generate new resources, it poses less of a challenge to the principle of equality than a gamble whose sole aim is to gain resources at another's expense. This is not to deny that wealth creating gambles against a backdrop of initial equality have an inegalitarian aspect. If successful, they do result in a situation where the gambler has more resources than those who did not gamble (assuming that the fruits of the gamble are not then redistributed). It may be significant, however, that the improved position of the successful gambler has not come about as a direct result of losses suffered by another (albeit consensual) party, even though it is possible that the relative inequality in holdings that results may leave the non-gambler in a worse off position overall than if the gamble had not taken place. A 16 tendency of such gambles to contribute to the common good is sufficient to confer fairness, rather than (at most) legitimacy upon their outcomes, not least on account of the sort of argument which Cohen himself puts forward when critiquing the claim that inequalities that arise under Rawls's Difference Principle on account of their propensity to advance the interests of the least advantaged members of society should be seen as just (Cohen, 2008). On such a view, it is one thing to maintain that such activity is desirable, and so should be permitted, but quite another to hold that the desirability of the practice confers fairness upon its outcomes. Nonetheless, there is at least scope for such a move, and so, again, the particular characteristics of Cohen's example – in this case, its being zero sum rather than non-zero sum, undermines his strong conclusion relating to all option luck outcomes. In summary, one might maintain that a differential willingness to expose oneself to risk is morally relevant, or one may insist that this is only so when the general tendency (rather than the specific instance) of people exposing themselves to risk in this way serves morally good ends. Either belief would provide a reason for maintaining that luck egalitarianism can preserve fairness other than by chance. What then, finally, of type (2) examples, where we have individuals who are in the same luck cohort in relation to non-zero sum gambles? The most obvious response to this example is to maintain that the differential outcomes the two farmers enjoy are not fair – to argue that the choice as to crop treatments is analogous to the calling of heads or tails in the coin toss, and so to accept that the force of Cohen's paradigm example, though zero sum in nature, carries over to non-zero sum gambles. Accepting this claim poses a significant problem for the fairness of luck egalitarian outcomes: it suggests that the apparent fairness which is derived from considering examples where individuals choose to expose themselves to differential degrees of risks is not indicative of luck egalitarianism as a whole. Even if fairness were to be maintained in such cases, there would seem to be unfairness in terms of how people in the same luck cohorts face differential life prospects, as there does not appear to be a morally relevant difference between them, violating both PF1 and PF2 – even if we believed it to be desirable that the outcomes of such gambles should be allowed to stand in an all things considered sense. To reject this conclusion, one would have to maintain that the crop decision is different from the coin toss decision, not because of any quality of the individual farmer which leads to the decision to treat carrots rather than potatoes (after all, both farmers may have used a coin toss to decide which crops to treat), but simply in virtue of the content of the decision: namely, it being a decision which has the actual effect of making a difference to overall Cohenite way to express this thought would be to hold that zero sum gambles, in particular, threaten the egalitarian ethos of a just society. See Cohen, 2008. 17 production, and so which potentially serves a morally good end. For many, such a move will simply be to stretch fairness, and, specifically, the idea of a morally relevant difference too far. But there is at least the possibility of such an argument being made. Imagine a society fully regulated by Rawls's two principles of justice, in which there are two individuals, identical except for their differential degree of native talent. Suppose that the application of the Difference Principle means that the more talented individual ends up with a greater share of primary goods then the less talented, and that this is justified by reference to the fact that allowing this inequality maximises the position of the least well off member of society. Does this application of the Difference Principle satisfy PF1? One could obviously deny that it does, maintaining that the difference between the two individuals is arbitrary from a moral point of view, as it does not reflect anything for which they are personally responsible, But one might seek instead to maintain that the difference in talent becomes morally relevant when it contributes to an improvement for the least advantaged members of society. As in the case of endorsing the fairness under PF1 of (2), this is obviously controversial, as it asserts that a feature of an individual can constitute a morally relevant difference on account of its effects, even though the fact that it is the feature of one person and not another is itself a matter of luck. Even so, the possibility of this move is sufficient to show that arguments stemming from Cohen's paradigm example cannot capture all the claims which could plausibly be made about ways in which particular gambles can lead to unequal outcomes. 5. Conclusion It has been maintained that Cohen's argument that option luck never preserves "fairness justice " is not convincing. Even if one accepts the force of his argument in relation to the paradigm example, this is not generalizable to all cases of option luck. Luck egalitarian outcome are, from the perspective of fairness articulated by PF1, complicated sometimes they will be fair, and sometimes not, depending on one's account of what constitutes a morally relevant difference between persons. Cohen's strong claim, that option luck never preserves justice other than by accident, does not stand, but nor, if one accepts PF1, does the opposing strong claim that option luck always preserves justice, in the sense, at least, of "fairness justice". Whether this is a technical point that applies only to unusual examples of zero sum, fair gambles where each party has an equal chance of winning, or whether this undermines the claim to fairness of a wide range of luck egalitarian outcomes will, again, depend on one's particular account of what constitutes a morally relevant difference between persons. In practice, luck egalitarian outcomes would be messy: legitimacy justice would be accompanied by fairness justice in some cases, but not in others, and depending on our account of morally relevant differences, there may well be many cases where we simply would not know 18 whether outcomes were fair or not. So long as legitimacy justice is nonetheless present, it looks as if the outcomes should not be straightforwardly reversed (or, at the very least, that individuals do not have a just grievance if they are not reversed), but Cohen does entertain some possibilities as to how outcomes which only have legitimacy justice may not warrant full protection from the state. Towards the end of his article, he offers a number of suggestions as to possible practical implications of this argument in a section entitled "Does it Matter?" (140-2). One thought concerns the legitimacy of taxation in different circumstances. He writes that, if we accept that the result of option luck gambles are merely legitimate, and not fair, then: ...with respect to rights of bequest, it might matter whether a given lump of cash was or was not acquired by gambling. If it was the fruit of a fair gamble, then you might have less right to bequeath it than if it was the product of your labor, and, correspondingly, we might think that the proceeds of gambling are more legitimately taxable than some other types of income. (141) It may well be that to say this as a general statement about gambles and gambling is too quick. The argument of the preceding sections allow us to see that there are coherent arguments which seek to differentiate between different types of gambles, and afford them a different moral status. Under PF1, the results of some gambles will be fair and legitimate, whilst others will be simply legitimate. Thus one can readily imagine, for example, a luck egalitarian who was prepared to accept Cohen's argument when it came to the taxation of the fruits of certain types of gamble, such as zero sum interpersonal bets, but who was much less willing to countenance such intervention in relation to non-zero sum chances that individuals choose to take, which end up having positive outcomes. As has been stated, gambling, in a casino or betting shop sense, is often seen as being a paradigm example of option luck; verdicts upon which are readily generalizable to other types of gamble. This article has sought to cast doubt upon the justifiability of such a move. The result may well be that we end up believing that there is a justification for the taxation, control, or even prohibition of such forms of activity which does not extend to other instances of individuals freely choosing to make deliberate and calculated gambles. Bibliography Aristotle (2000) Nicomachean Ethics (trans. Roger Crisp). 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