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Objective and subjective expected utility with incomplete preferences, working paper
, 2010
"... Abstract This paper extends the subjective expected utility model of decision making under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multiprior expected multiutility representations of preference relation under uncertainty. The paper als ..."
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Cited by 12 (3 self)
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Abstract This paper extends the subjective expected utility model of decision making under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multiprior expected multiutility representations of preference relation under uncertainty. The paper also introduces new axiomatizations of Knightian uncertainty and expected multiutility model with complete beliefs.
Cautious expected utility and the certainty effect
, 2013
"... Abstract Many violations of the Independence axiom of Expected Utility can be traced to subjects' attraction to riskfree prospects. The key axiom in this paper, Negative Certainty Independence JEL: D80, D81 Keywords: Preferences under risk, Allais paradox, Negative Certainty Independence, In ..."
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Cited by 2 (1 self)
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Abstract Many violations of the Independence axiom of Expected Utility can be traced to subjects' attraction to riskfree prospects. The key axiom in this paper, Negative Certainty Independence JEL: D80, D81 Keywords: Preferences under risk, Allais paradox, Negative Certainty Independence, Incomplete preferences, Cautious Completion, MultiUtility representation. * We thank Faruk Gul, Fabio Maccheroni, Massimo Marinacci, Efe Ok, Wolfgang Pesendorfer, Gil Riella, and Todd Sarver for very useful comments and suggestions. The coeditor and four anonymous referees provided valuable comments that improved the paper significantly. We greatly thank Selman Erol for his help in the early stages of the project. CerreiaVioglio gratefully acknowledges the financial support of ERC (advanced grant, BRSCDPTEA). Ortoleva gratefully acknowledges the financial support of NSF grant SES1156091.
Mathematical Social Sciences
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Familiarity Breeds Completeness
, 2013
"... This is a study of the representations of subjective expected utility preferences that admits statedependent incompleteness, and subjective expected utility preferences displaying noncomparability of acts from distinct sources. The notions familiar events and sources are defined and characterized. ..."
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This is a study of the representations of subjective expected utility preferences that admits statedependent incompleteness, and subjective expected utility preferences displaying noncomparability of acts from distinct sources. The notions familiar events and sources are defined and characterized. The relation greater familiarity on sources and increasing familiairity of a source are also defined and characterized.
Allais, Ellsberg, and Preferences for Hedging
, 2012
"... We study the relation between ambiguity aversion and the Allais paradox. To this end, we introduce a novel definition of hedging which applies to objective lotteries as well as to uncertain acts, and we use it to define a novel axiom that captures a preference for hedging which generalizes the one o ..."
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We study the relation between ambiguity aversion and the Allais paradox. To this end, we introduce a novel definition of hedging which applies to objective lotteries as well as to uncertain acts, and we use it to define a novel axiom that captures a preference for hedging which generalizes the one of Schmeidler (1989). We argue how this generalized axiom captures both aversion to ambiguity, and attraction towards certainty for objective lotteries. We show that this axiom, together with other standard ones, is equivalent to two representations both of which generalize the MaxMin Expected Utility model of Gilboa and Schmeidler (1989). In both, the agent reacts to ambiguity using multiple priors, but does not use expected utility to evaluate objective lotteries. In our first representation, the agent treats objective lotteries as âambiguous objects,â and use a set of priors to evaluate them. In the second, equivalent representation, lotteries are evaluated by distorting probabilities as in the Rank Dependent Utility model, but using the worst from a set of such distortions. Finally, we show how a preference for hedging is not sufficient to guarantee an Ellsberglike behavior if the
Universal interactive preferences
"... represent preliminary reports on work in progress and should therefore be neither quoted nor referred to in published work without the written consent of the author. Universal interactive preferences ..."
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represent preliminary reports on work in progress and should therefore be neither quoted nor referred to in published work without the written consent of the author. Universal interactive preferences
Risk, Ambiguity, and StatePreference Theory
, 2010
"... The statepreference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling “smooth” ambiguityaverse preferences. It does not require reference to objective probabilities, persona ..."
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The statepreference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling “smooth” ambiguityaverse preferences. It does not require reference to objective probabilities, personalistic consequences, or counterfactual acts, and it allows for statedependence of utility and unobservable background risk. The decision maker’s local beliefs are encoded in her risk neutral probabilities (her relative marginal rates of substitution between states) and her local risk preferences are encoded in the matrix of derivatives of the risk neutral probabilities. This matrix plays a central but generally unappreciated role in the modeling of risk attitudes in the statepreference framework. It can be computed by inverting a bordered Slutsky matrix and vice versa, it generalizes the ArrowPratt measure for approximating local risk premia, and its structure reveals whether the decision maker’s risk preferences are ambiguityaverse as well as risk averse. Two versions of the smoothambiguity model are analyzed — the sourcedependent risk aversion model and the secondorder uncertainty (KMM) model — and it is shown that in both cases the overall premium for local uncertainty can be decomposed as the sum of a risk premium and an ambiguity premium.
Optimal Aggregation of Uncertain Preferences
"... A paradigmatic problem in social choice theory deals with the aggregation of subjective preferences of individuals — represented as rankings of alternatives — into a social ranking. We are interested in settings where individuals are uncertain about their own preferences, and represent their uncert ..."
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A paradigmatic problem in social choice theory deals with the aggregation of subjective preferences of individuals — represented as rankings of alternatives — into a social ranking. We are interested in settings where individuals are uncertain about their own preferences, and represent their uncertainty as distributions over rankings. Under the classic objective of minimizing the (expected) sum of Kendall tau distances between the input rankings and the output ranking, we establish that preference elicitation is surprisingly straightforward and nearoptimal solutions can be obtained in polynomial time. We show, both in theory and using real data, that ignoring uncertainty altogether can lead to suboptimal outcomes. 1
Expected MultiUtility Representations
, 2011
"... This paper axiomatizes expected multiutility representations of incomplete preferences under risk and under uncertainty. The von NeumannMorgenstern expected utility model with incomplete preferences is revisited using a “constructive” approach, as opposed to earlier treatments that use convex anal ..."
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This paper axiomatizes expected multiutility representations of incomplete preferences under risk and under uncertainty. The von NeumannMorgenstern expected utility model with incomplete preferences is revisited using a “constructive” approach, as opposed to earlier treatments that use convex analysis.