In this paper, we show how to represent a non-Archimedean preference over a set of random quantities by anonstandard utility function. Non-Archimedean preferences arise when somerandom quantities have no fair price. Two common situations give riseto non-Archimedean preferences: random quantities...

In this paper, we show how to represent a non-Archimedean preference over a set of random quantities by a nonstandard utility function. NonArchimedean preferences arise when some random quantities have no fair price. Two common situations give rise to non-Archimedean preferences: random...

<Para ID="Par1">We extend a result of Dubins (Ann Probab 3:89–99, <CitationRef CitationID="CR8">1975</CitationRef>) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the...</citationref></para>

We extend de Finetti’s (1974) theory of coherence to apply also to unbounded random variables. We show that for random variables with mandated infinite prevision, such as for the St. Petersburg gamble, coherence precludes indifference between equivalent random quantities. That is, we...

Savage's expected utility theory orders acts by the expectation of the utility function for outcomes over states. Therefore, preference between acts depends only on the utilities for outcomes and the probability distribution of states. When acts have more than finitely many possible outcomes,...

This essay considers decision-theoretic foundations for robust Bayesian statistics. We modify the approach of Ramsey, de Finetti, Savage and Anscombe and Aumann in giving axioms for a theory of robust preferences. We establish that preferences which satisfy axioms for robust preferences can be...

This investigation combines two questions for expected utility theory: 1. When do the shared preferences among expected utility maximizers conform to the dictates of expected utility? 2. What is the impact on expected utility theory of allowing preferences for prizes to be state-dependent? Our...