Is Evaluative Compositionality a Requirement of Rationality?

Abstract

This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities assigned to them)? The paper first outlines a certain simple response to the Pasadena game and identifies two problems with this response, the second of which is that it leads to a wholesale violation of evaluative compositionality.I then argue that rationality does not require decision makers to factor in outcomes of arbitrarily low probability. A method for making decisions which flows from this basic idea is then developed, and it is shown that this decision method (Truncation) leads to a limited-as opposed to wholesale-violation of evaluative compositionality. The paper then argues that the truncation method yields solutions to the problems posed by the Pasadena game and its relatives that are both attractive in themselves and superior to those yielded by alternative proposals in the literature.

Decision Theory Without Finite Standard Expected Value

“…We are thus agreeing withSeidenfeld et al (2009) andSmith (2014) in rejecting what Smith (2014: 465) calls 'the principle of compositionality': 'the value which a rational agent places [or at least should place] on a gamble is [solely] a function of the values which she places on the possible outcomes of the gamble, together with the probabilities assigned to those outcomes by the gamble'. W and SP1 assign the same probabilities to the same payoffs but are not equally valuable.…”

“…For additional discussion of Easwaran's approach, seeFine (2008),Sprenger and Heesen (2011) andSmith (2014).4 Actually, only one of us (Vallentyne) finds Finite Weak Expectations compelling. The other(Lauwers) finds it compelling for one-stage lotteries but not for compound lotteries (e.g.…”

Difference Minimizing Theory

“…Likewise, if a stochastically dominates a , then the area of the utility contour corresponding to a will 37. The proposal offered by Smith (2014) yields verdicts in an equally broad range of cases. But, like Hájek (2014), I find many of these verdicts implausible.…”

“…So far, discussions of this issue have generally favored the first option. For example, Seidenfeld et al (2009), Smith (2014), and Lauwers and Vallentyne (2016) all suggest we should reject Stochastic Equivalence and Stochastic Dominance, and thus reject views which entail those principles, like Difference Minimizing Theory. I disagree.…”

How to co-exist with nonexistent expectations

“…(...) Restrict decision theory to finite state spaces (...) Restrict decision theory to bounded utility functions." Nicholas J.J. Smith (2014), notably, defends a hybrid of these:…”