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  What makes a good imprecise belief?

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التوقيع : رئيس ومنسق القسم الفكري

عدد الرسائل : 1500

الموقع : center d enfer
تاريخ التسجيل : 26/10/2009
وســــــــــام النشــــــــــــــاط : 6

 What makes a good imprecise belief? Empty
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مُساهمة What makes a good imprecise belief?

There are, as we have seen, certain structural properties that are necessary conditions on rational belief. What exactly these are depends on your views. However, there are further ways of assessing belief. Strongly believing true things and strongly believing the negations of false things seem like good-making-features of beliefs. For the case of precise credences, we can make this precise. There is a large literature on “scoring rules”: methods for measuring how good a probability is relative to the actual state of the world (Brier 1950; Savage 1971; Joyce 2009; Pettigrew 2011). These are numerical methods of measuring how good a probability is given the true state of the world.
For the case of imprecise probabilities, however, the situation looks bleak. No real valued scoring rule for imprecise probabilities can have the desirable property of being strictly proper(Seidenfeld, Schervish, and Kadane 2012). Since strict propriety is a desirable property of a scoring rule (Bröcker and Smith 2007; Joyce 2009; Pettigrew 2011), this failing is serious. So further work is needed to develop a well-grounded theory of how to assess imprecise probabilities.
Frigg et al. (2014) suggest a first step in this direction. Building on work by Hagedorn and Smith (2009) they show that certain kinds of “nonprobabilistic odds” perform better in their toy betting models than do probabilistic odds. This is far from a complete story of assessing IP forecasts, however.

4. Summary

Imprecise probabilities offer a model of rational belief that does away with some of the idealisation required by the orthodox precise probability approach. Many motivations for such a move have been put forward, and many views on IP have been discussed. There are still several open philosophical questions relating to IP, and this is likely to be a rich field of research for years to come.
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What makes a good imprecise belief?

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