Indifference and incompleteness distinguished by rational trade

doi:10.1016/j.geb.2008.11.009

Games and Economic Behavior

Volume 67, Issue 1, September 2009, Pages 300-314

https://doi.org/10.1016/j.geb.2008.11.009 Get rights and content

Abstract

We use an agent's strict preferences to define indifference and incompleteness relations that identify the sequences of trades that are rational to undertake. If an agent makes sequences of trades of options labeled indifferent, the agent will never be led to an inferior outcome, but trades of options where no preference judgments obtain can lead to diminished welfare. For one-shot choices, in contrast, there can be no behavioral distinction between indifference and incompleteness. Applications include: an isomorphism for incomplete preferences that indicates when weak and strict preferences contain interchangeable information, a characterization of the (possibly incomplete) preference relations consistent with a one-shot choice function, and an equivalent definition of incompleteness that relies on the philosophical theory of incommensurability.

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^☆: I am grateful to an advisory editor and two referees for several valuable suggestions. I wrote this paper following heated arguments with Marco Mariotti about the relative merits of taking weak and strict preferences as primitive. In light of Section 5 and Observation 2, I no longer see any merit in either of our positions but my conversations with Mariotti were indispensable. We have agreed not to argue any further about the subject.

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Indifference and incompleteness distinguished by rational trade☆

Abstract

J. Econ. Theory

Games Econ. Behav.

Games Econ. Behav.

J. Econ. Theory

J. Econ. Theory

J. Econ. Theory

The construction of a utility function from expenditure data

Int. Econ. Rev.

Rational choice functions and orderings

Economica

Characterization of generalized weak orders and revealed preference

Econ. Theory