The numbers fallacy: rescuing sufficientarianism from arithmeticism

ABSTRACT

This paper argues in defence of sufficientarianism that there is a general flaw in the most common critiques against it. The paper lays out sufficientarianism and presents the problems of indifference, of outweighing priority, and of discontinuity. Behind these problems is a more general objection to the abruptness of the sufficiency threshold relying upon an assumption regarding arithmeticism about value. The paper argues that sufficientarians need not accept arithmeticism about value and that the commonly held critiques of sufficientarianism are in fact instances of the numbers fallacy pertaining to the construction of numerical counterexamples that gain intuitive traction from ‘empty numbers’ – numbers without meaningful content in reference to the view under investigation. The paper concludes that we should remain sceptical about such use of numerical counterexamples, and while this does not by itself prove sufficientarianism correct, it is an important and novel contribution to its justification.

KEYWORDS:

• Sufficientarianism
• distributive justice
• thresholds
• thought experiments
• numerical cases

Acknowledgements

I am grateful to David V. Axelsen, Andreas Albertsen, Liam Shields, Robert Huseby, Tom Parr and an anonymous reviewer for useful comments on earlier versions of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that in Tables 2 and 3 the counterintuitive response is not exclusively sufficientarian. Leximin-prioritarians would give the same reply because of the absolute priority given to the worst-off, and thus while they deny threshold abruptness, they too reject continuity and outweighing priority. Moreover, as the cases are presented in Tables 2 and 3, egalitarians would have (pro tanto) reasons to prefer the same outcomes as sufficientarians because they contain more equality, but this is contingent upon the design of the example (e.g., it would be different if we added the choice of an equal distribution), and indeed many egalitarians are pluralists and would for that reason in fact side with utilitarians in these cases. For a useful overview, see Adler (2019).

2 I am grateful to an anonymous reviewer for this point.

3 Although I focus narrowly here on the discontinuity problem, Chung (2017) also holds an important positive contribution in making utilitarianism better equipped than traditional utilitarian views to incorporate the moral importance of meeting thresholds. I set this contribution to utilitarian theory aside here, as my focus is on the implications of the discontinuity problem for sufficientarianism. This leaves it open, essentially, whether sufficientarianism is all things considered preferable to something like Chung’s prospect utilitarianism. This is a discussion for another paper. For general reasons motivating sufficientarianism particularly, see Huseby (2020) and Nielsen (2018).

4 This is an application of sufficientarianism accepted by many contemporary relational egalitarians (see Anderson 1999; O’Neil 2008; Moles and Parr 2019; Schemmel 2021).

Additional information

Funding

This work was supported by Danmarks Frie Forskningsfond [grant number 4089-00020B] and Danmarks Grundforskningsfond [grant number DNRF144].