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Attitudes toward uncertainty and randomization: An experimental study
, 2011
"... Subjects are randomizationloving if they prefer random mixtures of two bets to each of the involved bets. Various approaches appeal to such preferences in order to explain uncertainty aversion. We examine the relationship between uncertainty and randomization attitude experimentally. Our data sugge ..."
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Subjects are randomizationloving if they prefer random mixtures of two bets to each of the involved bets. Various approaches appeal to such preferences in order to explain uncertainty aversion. We examine the relationship between uncertainty and randomization attitude experimentally. Our data suggests that they are not negatively associated: most uncertaintyaverse subjects are randomizationneutral rather than loving. Surprisingly, a nonnegligible number of uncertaintyaverse subjects even seems to dislike randomization.
Ambiguity in the small and in the large
, 2012
"... This paper considers local and global multipleprior representations of ambiguity for preferences that are (i) monotonic, (ii) Bernoullian, i.e. admit an affine utility representation when restricted to constant acts, and (iii) locally Lipschitz continuous. We do not require either Certainty Indepen ..."
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This paper considers local and global multipleprior representations of ambiguity for preferences that are (i) monotonic, (ii) Bernoullian, i.e. admit an affine utility representation when restricted to constant acts, and (iii) locally Lipschitz continuous. We do not require either Certainty Independence or Uncertainty Aversion. We show that the set of priors identified by Ghirardato, Maccheroni, and Marinacci (2004)’s ‘unambiguous preference’ relation can be characterized as a union of Clarke differentials. We then introduce a behavioral notion of ‘locally better deviation ’ at an act, and show that it characterizes the Clarke differential of the preference representation at that act. These results suggest that the priors identified by these preference statements are directly related to (local) optimizing behavior.
A previous version of this paper circulated under the title “Uncertain Probabilities vs. Uncertain
, 2011
"... Ellsberg’s experiment involved a gamble with no ambiguity (N) and a gamble where the prize that could be won is objectively known, but the winning probability depends on the (ambiguous) urn’s composition (P). We extend this by including a gamble where the winning probability is objectively known, bu ..."
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Ellsberg’s experiment involved a gamble with no ambiguity (N) and a gamble where the prize that could be won is objectively known, but the winning probability depends on the (ambiguous) urn’s composition (P). We extend this by including a gamble where the winning probability is objectively known, but the prize depends on the urn’s composition (C), and also gambles where both the probability and the prize depend on the urn’s composition, and can either be correlated positively (D) or negatively (M). Among transitive subjects who
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
Objective Lotteries as . . .
, 2011
"... We derive axiomatically a model in which the Decision Maker can exhibit simultaneously both the Allais and the Ellsberg paradoxes in the standard setup of Anscombe and Aumann (1963). Using the notion of ‘subjective’, or ‘outcome ’ mixture of Ghirardato et al. (2003), we define a novel form of hedg ..."
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We derive axiomatically a model in which the Decision Maker can exhibit simultaneously both the Allais and the Ellsberg paradoxes in the standard setup of Anscombe and Aumann (1963). Using the notion of ‘subjective’, or ‘outcome ’ mixture of Ghirardato et al. (2003), we define a novel form of hedging for objective lotteries, and introduce a novel axiom which is a generalized form of preferences for hedging. We show that this axiom, together with other standard ones, is equivalent to a representation in which the agent reacts to ambiguity using multiple priors like the MaxMin Expected Utility model of Gilboa and Schmeidler (1989), generating an Ellsberglike behavior, while at the same time, she treats also objective lotteries as ‘ambiguous objects,’ and use a fixed (and unique) set of priors to evaluate them – generating an Allaislike behavior. We show that this representation is equivalent to one in which the agent evaluates lotteries using a set of concave rankdependent utility functionals. A comparative notion of preference for hedging is also introduced.
Recursive Vector Expected Utility
, 2011
"... This paper proposes and axiomatizes a recursive version of the vector expected utility (VEU) decision model (Siniscalchi, 2009). Recursive VEU preferences are dynamically consistent and “consequentialist.” Dynamic consistency implies standard Bayesian updating of the baseline (reference) prior in th ..."
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This paper proposes and axiomatizes a recursive version of the vector expected utility (VEU) decision model (Siniscalchi, 2009). Recursive VEU preferences are dynamically consistent and “consequentialist.” Dynamic consistency implies standard Bayesian updating of the baseline (reference) prior in the VEU representation, but imposes no constraint on the adjustment functions and onestepahead adjustment factors. This delivers both tractability and flexibility. Recursive VEU preferences are also consistent with a dynamic, i.e. intertemporal extension of atemporal VEU preferences. Dynamic consistency is characterized by a timeseparability property of adjustments—the VEU counterpart of Epstein and Schneider (2003)’s rectangularity for multiple priors. A simple exchangeability axiom ensures that the baseline prior admits a representation à la de Finetti, as an integral of i.i.d. product measures with respect to a unique probability µ. Jointly with dynamic consistency, the same axiom also implies that µ is updated via Bayes ’ Rule to provide an analogous representation of baseline posteriors. Finally, an application to a dynamic economy à la Lucas (1978) is sketched.