Hostname: page-component-7d684dbfc8-zgpz2 Total loading time: 0 Render date: 2023-09-24T07:56:04.382Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "coreDisableSocialShare": false, "coreDisableEcommerceForArticlePurchase": false, "coreDisableEcommerceForBookPurchase": false, "coreDisableEcommerceForElementPurchase": false, "coreUseNewShare": true, "useRatesEcommerce": true } hasContentIssue false

Parity, Clumpiness and Rational Choice

Published online by Cambridge University Press:  12 November 2007

University of


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.

Research Article
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


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

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)Google Scholar, 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. 431Google Scholar; Griffin, James, Well-Being (Oxford, 1986), pp. 96–8Google ScholarPubMed.

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

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

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

7 In conversation, August 2005.

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

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

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

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

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

13 See e.g. Chang, Ruth, ‘Introduction’, Incommensurability, Incomparability and Practical Reason (Cambridge, Mass., 1997)Google Scholar 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. 495521CrossRefGoogle Scholar.

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.