Abstract
The three most common responses to Taurek’s ‘numbers problem’ are saving the greater number, equal chance lotteries and weighted lotteries. Weighted lotteries have perhaps received the least support, having been criticized by Scanlon What We Owe to Each Other (1998) and Hirose ‘Fairness in Life and Death Cases’ (2007). This article considers these objections in turn, and argues that they do not succeed in refuting the fairness of a weighted lottery, which remains a potential solution to cases of conflict. Moreover, it shows how these responses actually lead to a new argument for weighted lotteries, appealing to fairness and Pareto-optimality.
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Notes
I assume any plausible weighted lottery will give the larger group a greater chance of being saved—though I discuss Hirose’s inverse lottery objection—but not necessarily a proportional chance. See the distinction between the General Weighted Lottery (GWL) and Procedure of Proportional Chances (PPC), below.
It is assumed throughout that these individuals are equal in all morally relevant respects.
This is (chance of being in the four) x (chance of the four being rescued) + (chance of being the one) x (chance of the one being rescued), or 0.8x0.8+0.2x0.2 (Otsuka 2006, p.124).
I owe this point to Adam Swift.
I thank Rainer Trapp for prompting this formalization.
References
Beitz C (1989) Political Equality. Princeton, Princeton University Press
Broome J (1984) Selecting people randomly. Ethics 95:38–55 doi:10.1086/292596
Broome J (1990) Fairness. Proc Aristot Soc 91:87–101 http://www.jstor.org/stable/4545128
Broome J (1998) Kamm on fairness. Philos Phenomenol Res 58:955–961 doi:10.2307/2653739
Crowder G (2002) Liberalism and value pluralism. Continuum, London
Hirose I (2004) Aggregation and numbers. Utilitas 16:62–79 doi:10.1017/S0953820803001067
Hirose I (2007) Weighted lotteries in life and death cases. Ratio 20:45–56 doi:10.1111/j.1467-9329.2007.00345.x
Hooker B (2005) Fairness. Ethical Theory Moral Pract 8:329–352 doi:10.1007/s10677-005-8836-2
Kamm F (1985) Equal treatment and equal chances. Philos Public Aff 14:177–194 http://www.jstor.org/stable/2265456
Kavka G (1979) The numbers should count. Philos Stud 36:285–294 doi:10.1007/BF00372632
Lawlor R (2006) Taurek, numbers and probabilities. Ethical Theory Moral Pract 9:149–166 doi:10.1007/s10677-005-9004-4
Otsuka M (2006) Saving lives, moral theory, and the claims of individuals. Philos Public Aff 34:109–135 doi:10.1111/j.1088-4963.2006.00058.x
Parfit D (1978) Innumerate ethics. Philos Public Aff 7:285–301 http://www.jstor.org/stable/2264959
Parfit D (1997) Equality and priority. Ratio 10:202–211 doi:10.1111/1467-9329.00041
Rawls J (1999) A theory of justice, revised edition. Harvard University Press, Cambridge MA
Sanders J (1988) Why the numbers should sometimes count. Philos Public Aff 17:3–14 http://www.jstor.org/stable/2265283
Saunders B (2008) The equality of lotteries. Philos 83:359–372 doi:10.1017/S0031819108000727
Scanlon T (1975) Preference and urgency. J Philos 72:655–669 doi:10.2307/2024630
Scanlon T (1998) What we owe to each other. Harvard University Press, Cambridge MA
Stone P (2007) Why lotteries are just. J Polit Philos 15:276–295 doi:10.1111/j.1467-9760.2006.00274.x
Taurek J (1977) Should the numbers count? Philos Public Aff 6:293–316 http://www.jstor.org/stable/2264945
Timmermann J (2004) The individualist lottery: how people count, but not their numbers. Analysis 64:106–112 doi:10.1111/j.1467-8284.2004.00468.x
Acknowledgements
Some of the ideas in this paper were first developed, in a different context, as part of my doctoral dissertation. Among the many debts incurred during that time, I must thank the supervision of David Miller, funding from the Arts and Humanities Research Council (UK), my examiners, Adam Swift and David Estlund, and participants in the Oxford Moral Philosophy Seminar (2nd June 2008), particularly John Broome.
My criticisms of Hirose were first aired at the Oxford University Centre for Ethics and Legal Philosophy workshop on Aggregation and Numbers (5th February 2005) and I thank the participants there for lively discussion. Finally, for further helpful comments on this paper, I thank Daan Evers, Johann Frick, Iwao Hirose, Toby Ord, Gerard Vong, and two anonymous referees for the journal.
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Saunders, B. A Defence of Weighted Lotteries in Life Saving Cases. Ethic Theory Moral Prac 12, 279–290 (2009). https://doi.org/10.1007/s10677-009-9157-7
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DOI: https://doi.org/10.1007/s10677-009-9157-7