A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision theory might be (...) supplemented; the role of simulations of such infinite games; the role of small probabilities, and of idealization, in decision theory; tolerance about practical norms; and alternative ways of understanding decision theory's job description. (shrink)

This paper evaluates a recent method proposed by Jeremy Gwiazda for calculating the value of gambles that fail to have expected values in the standard sense. I show that Gwiazda’s method fails to give answers for many gambles that do have standardly defined expected values. However, a slight modification of his method (based on the mathematical notion of the ‘Cauchy principal value’ of an integral), is in fact a proper extension of both his method and the method of ‘weak expectations’. (...) I show that this method gives an appropriate value when the ‘tails’ of the gambles that are eliminated in the truncation are ‘stable’, but that the value is not appropriate when the tails are not stable. I do not attempt to give an argument for the use of this method, but just note that it is more general than Gwiazda’s method, and is mathematically quite natural. (shrink)

Countenancing unbounded utility in ethics gives rise to deep puzzles in formal decision theory. Here, these puzzles are taken as an invitation to assess the most fundamental principles relating probability and value, with the aim of demonstrating that unbounded utility in ethics is compatible with a desirable decision theory. The resulting theory frames further discussion of Expected Utility Theory and of principles concerning symmetries of utility.

Theories that use expected utility maximization to evaluate acts have difficulty handling cases with infinitely many utility contributions. In this paper I present and motivate a way of modifying such theories to deal with these cases, employing what I call “Direct Difference Taking”. This proposal has a number of desirable features: it’s natural and well-motivated, it satisfies natural dominance intuitions, and it yields plausible prescriptions in a wide range of cases. I then compare my account to the most plausible alternative, (...) a proposal offered by Arntzenius :31–58, 2014). I argue that while Arntzenius’s proposal has many attractive features, it runs into a number of problems which Direct Difference Taking avoids. (shrink)

This paper is a response to Paul Bartha’s ‘Making Do Without Expectations’. We provide an assessment of the strengths and limitations of two notable extensions of standard decision theory: relative expectation theory and Paul Bartha’s relative utility theory. These extensions are designed to provide intuitive answers to some well-known problems in decision theory involving gaps in expectations. We argue that both RET and RUT go some way towards providing solutions to the problems in question but neither extension solves all the (...) relevant problems. (shrink)

Expected utility theory often falls silent, even in cases where the correct rankings of options seems obvious. For instance, it fails to compare the Pasadena game to the Altadena game, despite the latter turning out better in every state. Decision theorists have attempted to fill these silences by proposing various extensions to expected utility theory. As I show in this paper, such extensions often fall silent too, even in cases where the correct ranking is intuitively obvious. But we can extend (...) the theory further than has been done before---I offer a new extension, Invariant Value Theory, which deals neatly with those problem cases and also satisfies various desirable conditions. But other prima facie desirable conditions, including Independence, the theory violates. Is this a problem for the proposal? It may not be---in a new impossibility result, I show that no theory can satisfy Independence in full generality without violating several other conditions that together seem just as plausible. (shrink)