Unless there are overriding moral objections, one should make *instrumentally rational choices*—choices that best serve one’s ends full stop. *Expected utility *(*EU*)* theory* is generally accepted as a normative theory of (instrumentally) rational choice under risk. EU theory advises agents to rank their choice options (from least to most choiceworthy) according to their EU, where the EU of an option is a probability-weighted sum of each of its possible utilities.[1] According to Martin Peterson, today, nearly all decision theorists accept EU theory (Peterson, 2017, p. 66). As such, as long as that is the case, laypersons with respect to decision theory will be rationally required to accept EU theory.

Philosopher Johan Gustafsson has argued that choice options in a decision problem should be construed as sets of acts such that one could jointly intentionally perform, at any time *t*, all the acts in the set, but no additional acts (Gustafsson, 2014). One of the reasons given by Gustafsson is that if one construes choice options as individual acts, then one runs into the *Problem of act versions* (Bergström, 1966; Castaneda, 1968). Consider the following example:

It is raining outside, but Ann will feel invigorated if she takes a brisk walk around the block (10 utiles), more so than if she stays inside (2 utiles). However, Ann has an injured toenail which causes her a great deal of pain when she tries to walk with her rain boots on. She will therefore experience a great deal of pain if she goes out for a walk wearing her rain boots (–30 utiles), more so than if she stays inside wearing her rain boots (–2 utiles). Luckily, Ann has a very comfortable pair of shoes which do not cause her any pain. However, there is a problem: it is raining very hard and her feet will get soaked. Ann will experience considerable discomfort if she goes out for a walk not wearing her rain boots (–15 utiles), more so than if she stays inside not wearing her rain boots (0 utiles).

Let us suppose that Ann assigns probability 1 to the state of the world as described above. Although the utility of the act ‘Ann stays inside’ is lower than that of the act ‘Ann goes out for a walk’, the utility of at least one version of the act ‘Ann stays inside’—that is, ‘Ann stays inside and does not wear her rain boots’ (2 + 0 = 2 utiles)—is greater than the utility of all versions of the act ‘Ann goes out for a walk’—that is, ‘Ann goes out for a walk and wears her rain boots’ (10 + –30 = –20 utiles) and ‘Ann goes out for a walk and does not wear her rain boots’ (10 + –15 = –5 utiles). Thus, intuitively, Ann should stay inside. However, if choice options are construed as individual acts, then EU theory counsels Ann *not* to stay inside, but instead to go out for a walk.

Therefore, to be intuitively plausible, EU theory should be minimally cashed out as follows:[2]

For any agent, *S*, faced with any decision under certainty or under risk and for any number of mutually exclusive and jointly exhaustive options, or sets of acts, *a*, *b*, *c*, *d *and* e*, such that, for each set, *S* could jointly intentionally perform, at any time, *t*, all the acts in the set, but no additional acts,

*a*is more choiceworthy than*b*, for*S*, at*t*, if and only if the EU of*S*jointly intentionally performing*a*at*t*is greater than the EU of*S*jointly intentionally performing*b*at*t*, and*a*is just as choiceworthy as*b*, for*S*, at*t*, if and only if the EU of*S*jointly intentionally performing*a*at*t*is equal to the EU of*S*jointly intentionally performing*b*at*t*.

This implies the following derivative decision rule for individual acts:[3]

For any agent, *S*, faced with any decision under certainty or under risk and for any two mutually exclusive acts, *a* and *b*,

*a*is more choiceworthy than*b*, for*S*, at any time,*t*, if and only if*a*is logically entailed by every set of acts such that, for each set,*S*could jointly intentionally perform, at*t*, all the acts in the set, but no additional acts and such that, in accordance with EU theory, the set of acts would be more choiceworthy for*S*, at*t*than each set of acts such that*S*could jointly intentionally perform, at*t*, all the acts in the set, but no additional acts and such that the set of acts logically entails*b*, and*a*is just as choiceworthy as*b*, for*S*, at any time,*t*, if and only if*a*is not more choiceworthy than*b*, and*a*is logically entailed by every set of acts such that, for each set,*S*could jointly intentionally perform, at*t*, all the acts in the set, but no additional acts and such that, in accordance with EU theory, the set of acts would not be less choiceworthy for*S*, at*t*than each set of acts such that*S*could jointly intentionally perform, at*t*, all the acts in the set, but no additional acts and such that the set of acts logically entails*b*.

### Bibliography

Bergström, L. (1966). *The Alternatives and Consequences of Actions*. Stockholm: Almqvist & Wiksell.

Castaneda, H.-N. (1968). A Problem for Utilitarianism. *Analysis*, *28*(4), 141–142. https://doi.org/10.1093/analys/28.4.141

Gintis, H. (2018). Rational Choice Explained and Defended. In G. Bronner & F. Di Iorio (Eds.),* The Mystery of Rationality: Mind, Beliefs and the Social Sciences* (pp. 95–114). Springer. https://doi.org/10.1007/978-3-319-94028-1_8

Gustafsson, J. E. (2014). Combinative Consequentialism and the Problem of Act Versions. *Philosophical Studies*, *167*(3), 585–596. https://doi.org/10.1007/s11098-013-0114-x

Peterson, M. (2017). *An Introduction to Decision Theory*. Cambridge University Press. https://doi.org/10.1017/9781316585061

[1] For a defense of EU theory, see Gintis (2018).

[2] Inspired by Gustafsson (pp. 593–594).

[3] Inspired by Gustafsson (p. 595).

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