TY - JOUR

T1 - Satan, Saint Peter and Saint Petersburg

T2 - Decision theory and discontinuity at infinity

AU - Bartha, Paul

AU - Barker, John

AU - Hájek, Alan

PY - 2014/3

Y1 - 2014/3

N2 - We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a 'limit choice' whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.'s Satan's apple, and give a general characterization of it. In these examples, repeated dominance reasoning (a paradigm of rationality) apparently gives rise to a situation closely analogous to having intransitive preferences (a paradigm of irrationality). Indeed, the agents in these examples are vulnerable to a money pump set-up despite having preferences that exhibit no obvious defect of rationality. We explore several putative solutions to such problems, particularly those that appeal to binding and to deliberative dynamics. We consider the prospects for these solutions, concluding that if they fail, the examples show that money pump arguments are invalid.

AB - We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a 'limit choice' whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.'s Satan's apple, and give a general characterization of it. In these examples, repeated dominance reasoning (a paradigm of rationality) apparently gives rise to a situation closely analogous to having intransitive preferences (a paradigm of irrationality). Indeed, the agents in these examples are vulnerable to a money pump set-up despite having preferences that exhibit no obvious defect of rationality. We explore several putative solutions to such problems, particularly those that appeal to binding and to deliberative dynamics. We consider the prospects for these solutions, concluding that if they fail, the examples show that money pump arguments are invalid.

KW - Decision-theoretic paradoxes

KW - Infinite decision theory

KW - Money-pump arguments

UR - http://www.scopus.com/inward/record.url?scp=84893961829&partnerID=8YFLogxK

U2 - 10.1007/s11229-013-0379-9

DO - 10.1007/s11229-013-0379-9

M3 - Article

SN - 0039-7857

VL - 191

SP - 629

EP - 660

JO - Synthese

JF - Synthese

IS - 4

ER -