Ordinal Subjective Foundations for Finite-domain Probability Agreement
نویسنده
چکیده
Normative study of probability-agreeing orderings of propositions, much of it rooted in a false but evocative conjecture of Bruno de Finetti, has typically sought to abstract credal rationality claims familiarly made for numerical probabilities. It is now known that some probability-disagreeing orderings, e.g. possibilistic order, syntactically restate probability-agreeing orderings, and so share in any ordinal probabilistic ‘rationality.’ This paper explores what remains normatively distinctive about subjective probability agreement. A multiset partial ordering, characteristic of all transitive elementary orderings, helps provide succinct, apprehensible necessary and sufficient ordinal conditions for probability agreement.
منابع مشابه
Scale or Translation Invariant Additive Preferences
A self-contained proof is presented of the fact that any increasing, continuous preferences over contingent payoffs that admit a (possibly state-dependent) additive representation are scale (resp. translation) invariant if and only if they take the form of CRRA (resp. CARA) expected utility, with the probabilities and coeffi cient of risk aversion uniquely determined as part of the representati...
متن کاملMeasurement-Theoretic Foundations of Preference Aggregation Logic for Weighted Utilitarianism
Harsanyi [4, 5] develops expected utility theory of von Neumann and Morgenstern [21] to provide two formalizations of utilitarianism. Weymark [22, 23] refers to these results as Harsanyi’s Aggregation and Impartial Observer Theorems. In this paper, we are concerned only with Aggregation Theorem. Sen [6] argues that von Neumann-Morgenstern expected utility theory is an ordinal theory and, theref...
متن کاملCountable Additivity and Subjective Probability
While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti’s central argument against countable additivity and provide a new Dutch book proof of the principle, to argue that if we accept the Dutch book foundations of subjective probability, countable additivity is a...
متن کامل(Rethinking The) Foundations of Subjective Probability
For simplicity, I’ll talk about finite, logically omniscient, opinionated agents who make definite judgments regarding all propositions (or pairs thereof) in some algebra B. I will consider three kinds of judgments: Qualitative. S believes p [BS(p)]. S disbelieves p [DS(p)]. Comparative. S is strictly more confident in p than q [p S q]. S is strictly more confident in q than p [q S p]. S is “do...
متن کاملAnalytical bending solution of fully clamped orthotropic rectangular plates resting on elastic foundations by the finite integral transform method
This study presents exact bending solution of fully clamped orthotropic rectangular plates subjected to arbitrary loads resting on elastic foundations, based on the finite integral transform method. In this method, it is not necessary to determine the deformation function because the basic governing equations of the classical plate theory for orthotropic plates have been used. A detailed param...
متن کامل