Infinite Prospects*

Abstract

Here's the plan. (Section 1) The St. Petersburg gamble cannot be assigned any fair value. (2) Standard arguments for orthodox expected utility theory, involving money pumps or regret, are also arguments against the rationality of preferences that give rise to the St. Petersburg gamble. (3) These arguments are doing something very different from familiar arguments for bounded utilities. (4) The structural requirement the arguments support is compatible with infinite utilities. (5) We describe a representation theorem, and explain how money pumps and regret are connected to the first point about fair values. (6) Some misgivings are expressed.

Expected choiceworthiness and fanaticism

“…So, if she's committed to (1), she won't be in a position to assert (2). Second, it seems rationally permissible to value certain goods, such as happy days of life, linearly (i.e., at constant marginal 22 Again, see McGee (1999) and Russell and Isaacs (2021) for arguments to this e ect.…”

“…By a 'live' moral theory I just mean one that gets included in the expected choiceworthiness calculation. I consider the proposal that we can exclude certain moral theories from the calculation on the basis of knowledge in §4.16 SeeMcGee (1999) andRussell and Isaacs (2021).…”

A St Petersburg Paradox for risky welfare aggregation

“…Given some widely accepted assumptions about the structure of individual welfare, Anteriority and Dominance conflict. (The conflict is closely related to puzzles arising from the possibility of unbounded value (Broome 1995;Russell and Isaacs, forthcoming) and of infinite populations (Vallentyne and Kagan 1997;Bostrom 2011). Neither possibility is assumed here.)…”