We show that in an environment of incomplete information, if individual preferences are sufficiently rich, then monotonicity and the Pareto property applied only when there is common knowledge of Pareto dominance imply (i) there must exist a common prior over the smallest common knowledge event and (ii) aggregation must be ex-ante utilitarian with respect to that common prior. This work builds ...

In the field of Artificial Intelligence many models for decision making under uncertainty have been proposed that deviate from the traditional models used in Decision Theory, i.e. the Subjective Expected Utility (SEU) model and its many variants. These models aim at obtaining simple decision rules that can be implemented by efficient algorithms while based on inputs that are less rich than what...

Following Richter (1966), we provide criteria under which a preference relation implied by a finite set of choice observations has a complete extension that can in turn be represented by a utility function. These criteria rely on a mapping over preference relations, the rational closure, which is a generalization of the transitive closure and is employed to construct the complete extension. We ...

This paper develops an extension of expected utility theory by introducing various restrictions; e.g., probabilities have only decimal (or binary) fractions of finite depths not greater than a given constant, the preference relation in question may be incomplete. The basic idea is separation between measurement of utility for pure alternatives and extension to lotteries involving more risks suc...

The ordinal consistency is the usual weak transitivity condition that a logical and consistent person should use if he/she does not want to express inconsistent opinions, and therefore becomes the minimum requirement condition that a consistent reciprocal preference relation should verify. In this paper, we define and study the ordinal consistency of an incomplete reciprocal preference relation...

In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of ...