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Parity, Clumpiness and Rational Choice


Some philosophers believe that two objects of value can be ‘roughly equal’, or ‘on a par’, or belong to the same ‘clump’ of value in a sense that is fundamentally different from that in which some objects are ‘better than’, ‘worse than’, or ‘equally as good as’ others. This article shows that if two objects are on a par, or belong to the same clump, then an agent accepting a few plausible premises can be exploited in a money-pump. The central premise of the argument is that value is choice-guiding. If one object is more valuable than another, then it is not permitted to choose the less valuable object; and if two objects are equally valuable it is permitted to choose either of them; and if two objects are on a par or belong to the same clump it is also permitted to choose either of them.

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1 Chang Ruth, ‘The Possibility of Parity’, Ethics 112 (2002), pp. 659–88.

2 Carlsson Erik, ‘Parity Defined in Terms of Betterness’, Hommage à Wlodek: Philosophical Papers Dedicated to Wlodek Rabinowicz, ed. Ronnow-Rassmussen T. et al. . (Lund, 2007), argues that Chang's concept of parity can be defined in terms of betterness. Carlson's definition is interesting, but for our present purposes it does not matter whether it captures Chang's original intentions or not.

3 Parfit Derek, Reasons and Persons (Oxford, 1984), p. 431; Griffin James, Well-Being (Oxford, 1986), pp. 96–8.

4 Hsieh Nien-He, ‘Equality, Clumpiness and Incomparability’, Utilitas 17 (2005), p. 184.

5 Hsieh, ‘Equality, Clumpiness and Incomparability’, p. 182.

6 Scanlon Thomas M., What We Owe To Each Other (Cambridge, Mass., 1998).

7 In conversation, August 2005.

8 Schick Frederick, ‘Dutch Bookies and Money Pumps’, The Journal of Philosophy 83 (1986), p. 117.

9 McClennen Edward F., Rationality and Dynamic Choice (Cambridge, 1990).

10 Rabinowicz Wlodek, ‘Money Pump with Foresight’, Imperceptible Harms and Benefits, ed. Almeida Michael J. (Dordrecht, 2000), pp. 123–54.

11 Chang Ruth, ‘Parity, Interval Value, and Choice’, Ethics 115 (2005), pp. 346–7.

12 Chang, ‘Parity, Interval Value, and Choice’, p. 347.

13 See e.g. Chang Ruth, ‘Introduction’, Incommensurability, Incomparability and Practical Reason (Cambridge, Mass., 1997) and ‘Parity, Interval Value, and Choice’.

14 This objection was suggested to me by Eric Carlsson and Tor Sandqvist in conversation.

15 See e.g. Sen Amartya, ‘Internal Consistency of Choice’, Econometrica 61 (1993), pp. 495521.

16 Email correspondence, 11 September 2005.

17 Email correspondence, 12 September 2005.

18 The condition that no object is a member of more than one clump is not explicitly mentioned by Hsieh, but I shall nevertheless assume that he accepts this condition – otherwise it would of course be trivial to construct a money-pump.

19 Hsieh, ‘Equality, Clumpiness, and Incomparability’, p. 184.

20 Hsieh, ‘Equality, Clumpiness, and Incomparability’, p. 186.

21 I would like to thank Erik Carlsson, Sven Danielsson, Ruth Chang, Nicolas Espinoza, Nien-he Hsieh, Wlodek Rabinowicz, and Tor Sandqvist for fruitful discussions and helpful comments. My work on this article has been generously supported by a grant from the Swedish Rescue Services Agency.

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  • ISSN: 0953-8208
  • EISSN: 1741-6183
  • URL: /core/journals/utilitas
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