Utility Representation of an Incomplete Preference Relation

Ok, Efe A.

doi:10.1006/jeth.2001.2814

Cited by 183 publications

(98 citation statements)

References 26 publications

(28 reference statements)

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“…A close relative of the above representation concept is actually suggested also by Shapley and Baucells [24] (see Remark 3 below), and is studied in the context of utility theory under certainty by Ok [21]. This concept clearly carries a stochastic dominance flavor, and hence brings the expected utility theory one step closer to the theory of stochastic orders.…”

Section: Article In Pressmentioning

confidence: 78%

Expected utility theory without the completeness axiom

Dubra

Maccheroni²,

2004

Journal of Economic Theory

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276

235

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We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a welldefined sense. r

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Section: Article In Pressmentioning

confidence: 78%

Expected utility theory without the completeness axiom

Dubra

Maccheroni²,

2004

Journal of Economic Theory

Self Cite

276

235

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show abstract

“…Prior to Bewley, Aumann (1962), in the context of choice under uncertainty, was seminal and discussed when an incomplete preference relation could be represented by a utility function (on which see Richter, 1966 andPeleg, 1970). More recently, the representation question has reemerged using a tighter and more satisfactory definition of representation via sets of utility functions (Ok, 2002 andDubra et al, 2001). Cubitt and Sugden (2001) consider the consistency properties that choice functions satisfy when agents are assumed to be invulnerable to money pumps.…”

Section: Introductionmentioning

confidence: 99%

Incomplete preferences and rational intransitivity of choice

Mandler

2005

Games and Economic Behavior

106

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Do violations of classical rationality theory imply that agents are acting against their self-interest? To answer this question, we investigate whether completeness and transitivity necessarily hold when agents choose outcome rationally-that is, their choice sequences do not lead to dominated outcomes. We show that, because of the danger of money pumps and other manipulations, outcome rationality implies that agents must have transitive psychological preferences. Revealed preferences, on the other hand, must be complete since agents can be forced to choose from any set of options. But these justifications of transitivity and completeness cannot be combined. We show that if psychological preferences are incomplete then revealed preferences can be intransitive without exposing agents to manipulations or violating outcome rationality. We also show that a specific case of nonstandard behavior, status quo maintenance, is outcome-rational in the simple environments considered in the experimental literature, but not in more complex settings.

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“…Theorem 1 thus makes do with weaker conditions than the Efe A. Ok (2002) result on representing an incomplete preference relation with a (possibly infinite) set of utility functions. Juan Dubra et al (2001) show that an expected utility representation of possibly incomplete preferences on lotteries also requires no extra assumptions beyond the standard.…”

Section: Psychologies and Orderings Of Psychologiesmentioning

confidence: 99%

Cardinality versus Ordinality: A Suggested Compromise

Mandler¹

2006

am econ rev

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Ordinal utility theory permits only those assumptions on utility functions that are preserved under increasing transformations. The rationale for this rule is that any assumption P not preserved under increasing transformations cannot be verified with observations of choice behavior: if a utility u satisfies P, there will exist another utility uЈ that does not satisfy P but that represents the same preferences as u. Nonordinal assumptions therefore seem to be needlessly restrictive: given a nonordinal assumption, one may always make a weaker assumption with the same implications for choice behavior. According to this view, the only role for cardinal utility is the normative one of representing interpersonal comparisons of utility.Ordinalism's first targets were diminishing marginal utility (DMU) and concavity, which had long served as arguments for why consumer preferences should be convex. Neither DMU nor concavity is preserved by increasing transformations and hence neither is an ordinal assumption. The pioneer ordinalists such as Kenneth Arrow (1951) claimed that diminishing marginal utility is tantamount to assuming that utility is cardinal. Arrow's position remains predominant: either an assumption on utility is ordinal or it is cardinal (see, e.g., Andreu Mas-Colell et al., 1995, chap. 1). This paper will take sets of utility functionswhich we call psychologies-as primitive; this will define a finer gradation of properties of utility that allows for intermediate standards of measurement. In this framework, ordinal utility theory takes the psychology consisting of all increasing transformations of any given utility function as primitive and lies at one end of the measurement spectrum.1 Cardinal utility theory takes the psychology consisting of all increasing affine transformations of a given utility as primitive; since this is a smaller set of utility functions, cardinality is a stronger (more restrictive) theory than ordinality. Ratio scales which take still smaller psychologies as primitive (the functions generated by all increasing linear transformations) are also common, particularly outside of economics. But in addition to these well-known measurement scales, there is an infinity of intermediate cases. Diminishing marginal utility and concavity lie precisely in the middle ground between cardinality and ordinality. The psychology consisting of all concave utility representations of a given preference relation is larger than any cardinal psychology it intersects, but smaller than any ordinal psychology it intersects. Concavity thus presupposes an intermediate standard of measurement and does not deserve its strongly nonordinalist reputation. Compared to a cardinal psychology, a concave psychology is easier to assemble in that an agent does not have to make as many utility

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Utility Representation of an Incomplete Preference Relation

Cited by 183 publications

References 26 publications

Expected utility theory without the completeness axiom

Expected utility theory without the completeness axiom

Incomplete preferences and rational intransitivity of choice

Cardinality versus Ordinality: A Suggested Compromise

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