Probabilities as Similarity-Weighted Frequencies

Billot, Antoine; Gilboa, Itzhak; Samet, Dov; Schmeidler, David

doi:10.1111/j.1468-0262.2005.00611.x

Cited by 61 publications

(55 citation statements)

References 4 publications

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“…However, we will explain, that for unrestricted non-disjoint databases -with common, but differently precise pieces of information -the normative appealing spirit of averaging beliefs conflicts with a simultaneous care about precision and cautiousness in the belief formation 4 .…”

Section: Introductionmentioning

confidence: 94%

Cautious Belief Formation

Bleile

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe provide an axiomatic approach to a belief formation process in an informational environment characterized by limited, heterogenous and differently precise information. For a list of previously observed cases an agent needs to express her belief by assigning probabilities to possible outcomes. Different numbers of observations of a particular case give rise to varying precision levels associated to the pieces of information. Different precise information affects the cautiousness and confidence with which agents form estimations. We modify the Concatenation axiom introduced in Billot, Gilboa, Samet and Schmeidler (BGSS) (Econometrica, 2005) in a way to capture the impact of precision and its related perceptional effects, while still keeping its normative appealing spirit. We obtain a representation of a belief as a weighted sum of estimates induced by past cases. The estimates are affected by cautiousness and confidence considerations depending on the precision of the underlying observed information, which generalizes BGSS. The weights are determined by frequencies of the observed cases and their similarities with the problem under consideration.

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Section: Introductionmentioning

confidence: 94%

Cautious Belief Formation

Bleile

2014

SSRN Journal

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“…Billot et al (2005) provide an axiomatization of the same formula in the case that the random variable under discussion may assume at least three distinct values. 6 Gilboa et al (2007) extend this axiomatization to the assessment of a density function of a continuous variable.…”

Section: Axiomatic Derivationsmentioning

confidence: 99%

On the definition of objective probabilities by empirical similarity

2009

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We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.

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“…In order to illustrate the basic idea and plausibility of such a two stage belief formation process we modify the doctor example of BGSS. 5 According to Simon (1959, p.272) perception and cognition intervene between subjective view and the objective real world. In this context perception is often referred to as a "filter", where filtering can not only be seen as a passive, but also as an active selection process involving exclusion of almost all that is not within the scope of attention.…”

Section: The Impact Of Data and Experience On The Formation Of A Probmentioning

confidence: 99%

“…In this way, it is usually assumed that agents incorporate and take into account all available pieces of information 4 . However, the assumption of full attention and consideration of all available information requires that agents are aware of it, perceive it (unbiased) and eventually are able to process it without any cognitive and psychological constraints 5 .…”

Section: The Impact Of Data and Experience On The Formation Of A Probmentioning

confidence: 99%

Limited Attention in Case-Based Belief Formations

Bleile

2014

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract An agent wants to derive her belief over outcomes based on past observations collected in her database (memory). There is well establish evidence in the psychology and marketing literature that agents consistently fail (or choose not) to process all available information. An agent might be constraint to pay attention (recall) and consider only parts of her potentially available information due to unawareness, cognitive or psychological limitations or intentionally for effort-efficiency. Based on this insight, we axiomatize a two-stage belief formation process in which in a first step agents filter ((un)intentionally) the available information. In a second step individuals employ the remaining observations to express a belief. We impose cognitively and normatively desirable properties on the filtering process. The axioms on the belief formation stage describe the relationship between databases and their induced beliefs. The axiomatized belief induced by a filtered databases is representable by a similarity weighted average of the estimations induced by each past attentiongrabbing observation. An appealing application is a satisficing filter that induces a filtered belief that relies only on past experiences that are sufficiently relevant for a current problem. For the specific situation that agents (are able to) always pay attention to all available information, our axiomatization coincides with the axiomatization of a belief formation in Billot et al. (Econometrica (2005)). Terms of use: Documents in

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Probabilities as Similarity-Weighted Frequencies

Cited by 61 publications

References 4 publications

Cautious Belief Formation

Cautious Belief Formation

On the definition of objective probabilities by empirical similarity

Limited Attention in Case-Based Belief Formations

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