Ethical Theory and Moral Practice

, Volume 19, Issue 1, pp 59–69 | Cite as

Mixed Feelings About Mixed Solutions

  • Jan GertkenEmail author


The numbers problem concerns the question of what is the right thing to do in trade-off cases where one can save different non-overlapping groups of persons, but not everyone. Proponents of mixed solutions argue that both saving the many and holding a lottery to determine whom to save can each be morally right in such cases, depending on the relative sizes of the groups involved. In his book The Dimensions of Consequentialism, Martin Peterson presents an ingenious version of such an approach that avoids a commitment to interpersonal value aggregation, which is highly controversial and rejected by many philosophers for a number of reasons. I criticise Peterson’s proposal by first arguing that it cannot account for the idea that holding a lottery is morally wrong if differences in numbers are very large, and by second pointing out that it relies on implausible assumptions about what is good for an individual. Given the shortcomings of Peterson’s non-aggregationist version of a mixed solution, I next address the issue of how problematic a commitment to interpersonal aggregation really is. To this end, I present an aggregationist version of a mixed solution that is reason-based and bypasses most standard objections to interpersonal value aggregation. I conclude that although there is reason to be optimistic, it remains to be seen whether a mixed solution can be worked out in a fully satisfying way.


Interpersonal aggregation Mixed solutions Numbers problem Martin Peterson Reasons Separateness of persons 



I am grateful to Andreas Müller, Thomas Schmidt, Attila Tanyi, Martin van Hees and an anonymous reviewer for very helpful comments on earlier versions of this paper. I would also like to thank Martin Peterson and all participants of the workshop „The Dimensions of Consequentialism“ (16-17 November 2013, University of Konstanz) for a very fruitful discussion.


  1. Broome J (1990) Fairness. Proc Aristot Soc 91:87–101CrossRefGoogle Scholar
  2. Dancy J (2004) Ethics without principles. Oxford University Press, OxfordCrossRefGoogle Scholar
  3. Hirose I (2004) Aggregation and numbers. Utilitas 16:62–79. doi: 10.1017/S0953820803001067 CrossRefGoogle Scholar
  4. Kamm F (1985) Equal treatment and equal chances. Philos Public Aff 14:177–194Google Scholar
  5. Kamm F (1993) Morality, mortality volume I: death and whom to save from it. Oxford University Press, OxfordGoogle Scholar
  6. Kelleher JP (2014) Relevance and non-consequentialist aggregation. Utilitas 26:385–408. doi: 10.1017/S0953820814000144 CrossRefGoogle Scholar
  7. Liao SM (2008) Who is afraid of numbers? Utilitas 20:447–461. doi: 10.1017/S0953820808003269 CrossRefGoogle Scholar
  8. Lübbe W (2008) Taurek’s no worse claim. Philos Public Aff 36:69–85. doi: 10.1111/j.1088-4963.2008.00124.x CrossRefGoogle Scholar
  9. Meyer K (2006) How to be consistent without saving the greater number. Philos Public Aff 34:136–146. doi: 10.1111/j.1088-4963.2006.00059.x CrossRefGoogle Scholar
  10. Parfit D (1978) Innumerate ethics. Philos Public Aff 7:285–301Google Scholar
  11. Parfit D (2011) On what matters volume I. Oxford University Press, OxfordCrossRefGoogle Scholar
  12. Peterson M (2013) The dimensions of consequentialism. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. Saunders B (2009) A defence of weighted lotteries in life saving cases. Ethic Theory Moral Prac 12:279–290. doi: 10.1007/s10677-009-9157-7 CrossRefGoogle Scholar
  14. Scanlon T (1998) What we owe to each other. Harvard University Press, Cambridge MAGoogle Scholar
  15. Schroeder M (2007) Slaves of the passions. Oxford University Press, OxfordCrossRefGoogle Scholar
  16. Taurek J (1977) Should the numbers count? Philos Public Aff 6:293–316Google Scholar
  17. Temkin L (2012) Rethinking the good. Oxford University Press, OxfordGoogle Scholar
  18. 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 CrossRefGoogle Scholar
  19. Voorhoeve A (2014) How should we aggregate competing claims? Ethics 125:64–87. doi: 10.1086/677022 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Humboldt-Universität zu BerlinInstitut für PhilosophieBerlinGermany

Personalised recommendations