Imprecise probabilistic beliefs as a context for decision-making under ambiguity

Nehring, Klaus

doi:10.1016/j.jet.2008.05.009

Cited by 38 publications

(40 citation statements)

References 38 publications

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“…One way in which the DM can be proven wrong is by pointing out that there are compelling, objective reasons to exhibit the opposite preference. A similar condition appears in Nehring (2001Nehring ( , 2009, titled Compatibility.…”

Section: Relating Objective and Subjective Rationalitymentioning

confidence: 63%

Objective and Subjective Rationality in a Multiple Prior Model

2010

Econometrica

179

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A decision maker (DM) is characterized by two binary relations. The first reflects choices that are rational in an "objective" sense: the DM can convince others that she is right in making them. The second relation models choices that are rational in a "subjective" sense: the DM cannot be convinced that she is wrong in making them.In the context of decision under uncertainty, we propose axioms that the two notions of rationality might satisfy. These axioms allow a joint representation by a single set of prior probabilities and a single utility index. It is "objectively rational" to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is "subjectively rational" to choose f rather than g if and only if the minimal expected utility of f (with respect to all priors in the set) is at least as high as that of g. In other words, the objective and subjective rationality relations admit, respectively, a representation à la Bewley (2002) and à la Gilboa and Schmeidler (1989). Our results thus provide a bridge between these two classic models, as well as a novel foundation for the latter.

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Section: Relating Objective and Subjective Rationalitymentioning

confidence: 63%

Objective and Subjective Rationality in a Multiple Prior Model

2010

Econometrica

179

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“…However, following Nehring [10] and Ghirardato et al [4] we show that, given a standard assumption, from any preference relation defined over a restricted domain, one can extract a (maximal) Knightian preference component. Given a preference relation, this Knightian component is the unambiguous portion that lends itself to extension: the prudent rule can be reasonably applied to this component.…”

Section: 3mentioning

confidence: 76%

“…We argue that this is not the case though. Given a preference relation over H (that need not satisfy independence), we follow Nehring [10] and Ghirardato et al [4] and show that one can extract "the Knightian component" out of it. Given a preference over H, we derive an unambiguous preference defined as follows.…”

mentioning

confidence: 99%

Extension Rules or What Would the Sage Do?

Lehrer

Teper

2014

American Economic Journal: Microeconomics

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Abstract. Quite often, decision makers face choices that involve new aspects and alternatives never considered before. Scenarios of this sort may arise, for instance, as a result of technological progress, or from individual circumstances such as information acquisition and improved awareness. In such situations, simple inference rules, past experience and knowledge about historic choice problems, may prove helpful in determining what would be a reasonable action to take vis-a-vis a new problem. In the context of decision making under uncertainty, we introduce and study an extension rule, that enables the decision maker to extend a preference order defined on a restricted domain. We show that utilizing this extension rule results in Knightian preferences, when starting off with an expected-utility maximization model confined to a small world.

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“…The closely related ideas of probability intervals, upper and lower probabilities and comparative probabilities have a long history going back to at least Keynes, Koopman and Borel (see [24]), while use of sets of measures is advocated by, amongst others, Levi [14], [15], [16], Je¤rey [12], Good [8], Voorbraak [22] and Nehring [19]. But the literature contains quite a wide range of applications of the idea and it is useful to get some clarity on this.…”

Section: Interpretationsmentioning

confidence: 99%

“…Many authors argue that in these kinds of situation the agent is not merely in a state of uncertainty in the sense that they don't know for sure which colour ball will be drawn but can assign a probability to the prospect of each colour, but are rather in a state of ignorance in the sense that, such are the limits on what they know and can …nd out, that they have no non-arbitrary basis for assigning such a probability. See for instance, Voorbraak [22], Levi [16], Steele [21] and Nehring [18], [19].…”

mentioning

confidence: 99%

Revising incomplete attitudes

Bradley

2009

Synthese

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Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be changed are then characterised and compared with those found in AGM style models of attitude revision. Finally these models are employed to describe how agents make up their mind when deliberating.

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Imprecise probabilistic beliefs as a context for decision-making under ambiguity

Cited by 38 publications

References 38 publications

Objective and Subjective Rationality in a Multiple Prior Model

Objective and Subjective Rationality in a Multiple Prior Model

Extension Rules or What Would the Sage Do?

Revising incomplete attitudes

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