WLODEK RABINOWICZ
PREFERENCE STABILITY AND SUBSTITUTION OF
INDIFFERENTS: A REJOINDER TO SEIDENFELD
ABSTRACT. Seidenfeld (Seidenfeld, T. [1988a], Decision theory without ‘Inde-
pendence’ or without ‘Ordering’, Economics and Philosophy 4: 267-290) gave
an argument for Independence based on a supposition that admissibility of a
sequential option is preserved under substitution of indifferents at choice nodes
(S). To avoid a natural complaint that (S) begs the question against a critic of
Independence, he provided an independent proof of (S) in his (Seidenfeld, T.
[1988b], Rejoinder [to Hammond and McClennen], Economics and Philosophy
4: 309-315). In reply to my (Rabinowicz, W. [1995], To have one’s cake and eat it
too: Sequential choice and expected-utility violations, The Journal of Philosophy
92: 586-620), in which I argue that the proof is invalid, Seidenfeld (Seidenfeld,
T. [2000], Substitution of indifferent options at choice nodes and admissibility:
A reply to Rabinowicz, Theory and Decision 48: 305–310 this issue) submits
that I fail to give due consideration to one of the underlying assumptions of his
derivation: it is meant to apply only to those cases in which the agent’s preferences
are stable throughout the sequential decision process. The purpose of this note is
to clarify the notion of preference stability so as meet this objection.
KEY WORDS: Decision theory, Sequential decisions, Independence, Backward
induction, Preferences, Indifference, Preference stability, Tiebreaks
A REJOINDER TO SEIDENFELD
Teddy Seidenfeld’s influential argument for Independence (Seiden-
feld, 1988a) was based on the following substitution principle:
(S) Admissibility of an option in a sequential decision problem is
preserved under substitution at choice nodes of indifferent options.
McClennen (1988) has objected to the use of this principle in an
argument for Independence. According to him, this would be ques-
tion begging. A theorist who rejects Independence denies that ad-
missibility of options is invariably preserved under substitution of
indifferents at chance nodes. Why would he need to accept that
substitution of indifferents at choice nodes is any less problematic?
Theory and Decision 48: 311–318, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.