When No Price is Right

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 whose values must be greater than every real number, and strict preferences betweenrandom quantities that are deemed closer in value thanevery positive real number. We also show how to extend anon-Archimedean preference to a larger set of random quantities. Therandom quantities that we consider include real-valued randomvariables, horse lotteries, and acts in the theory of Savage. In addition, we weaken the state-independent utility assumptions madeby the existing theories and give conditions under which the utilitythat represents preference is the expected value of a state-dependentutility with respect to a probability over states