# Prerationality as Avoiding Predictably Regrettable Consequences

*Peter Hammond*

CRETA Online Discussion Paper Series from Centre for Research in Economic Theory and its Applications CRETA

**Abstract:**
Following previous work on consequentialist decision theory, we consider an unrestricted domain of finite decision trees, including continuation subtrees, with : (i) decision nodes where the decision maker must make a move ; (ii) chance nodes at which a â€œroulette lotteryâ€ with exogenously specified strictly positive probabilities is resolved ; (iii) event nodes at which a â€œhorse lotteryâ€ is resolved. A complete family of binary conditional base preference relations over Anscombeâ€“Aumann lottery consequences is defined to be â€œprerationalâ€ just in case there exists a behaviour rule that is defined throughout the tree domain which is explicable as avoiding, under all predictable circumstances, consequences that are regrettable given what is feasible. Prerationality is shown to hold if and only if all conditional base preference relations are complete and transitive, while also satisfying both the independence axiom of expected utility theory and a strict form of Anscombe and Aumannâ€™s extension of Savageâ€™s sure thing principle. Assuming that the base relations satisfy non-triviality and a generalized form of state independence that holds even when consequence domains are state dependent, prerationality combined with continuity on Marschak triangles is equivalent to representation by a refined subjective expected utility function that excludes zero probabilities.

**Keywords:** Prerational base relations; rational planning; decision trees; regrettable consequences; Anscombeâ€“Aumann lotteries; preference ordering; independence axiom; sure-thing principle; subjective probability; subjective expected utility; Bayesian rationality; state independence JEL codes: D81 (search for similar items in EconPapers)

**Date:** 2022

**New Economics Papers:** this item is included in nep-mic, nep-ore and nep-upt

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https://warwick.ac.uk/fac/soc/economics/research/c ... _-_peter_hammond.pdf

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Journal Article: Prerationality as Avoiding Predictably Regrettable Consequences (2022)

Working Paper: Prerationality as Avoiding Predictably Regrettable Consequences (2022)

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