We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby meansof a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.

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Abstract—In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, i.e., some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts ’ preferences can be expressed as incomplete fuzzy preference relations. As part of this decision model, we propose an iterative procedure to estimate the missing information in an expert’s incomplete fuzzy preference relation. This procedure is guided by the additiveconsistency (AC) property and only uses the preference values the expert provides. The AC property is also used to measure the level of consistency of the information provided by the experts and also to propose a new induced ordered weighted averaging (IOWA) operator, the AC-IOWA operator, which permits the aggregation of the experts ’ preferences in such a way that more importance is given to the most consistent ones. Finally, the selection of the solution set of alternatives according to the fuzzy majority of the experts is based on two quantifier-guided choice degrees: the dominance and the nondominance degree. Index Terms—Additive consistency (AC), aggregation, choice degree, group decision making (GDM), incomplete preference relations, induced ordered weighted averaging (IOWA) operator. I.

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Motivated by the empirical findings concerning the importance of one’s current situation on her choice behavior, the main objective of this paper is to propose a rational choice theory that allows for the presence of a status quo bias, and that incorporates the standard choice theory as a special case. We follow a revealed preference approach, and obtain two nested models of rational choice that allow phenomena like the status quo bias and the endowment effect, and that are applicable in any choice situation to which the standard (static) choice model applies.

This paper explores the implications of a simple and intuitive restriction on reference dependent preferences assuming the status quo serves as the reference point. The condition imposed rules out situations in which a decision maker has a choice between two prospects, selects one, subsequently changes her mind and selects the other – even if the change is costly. It is shown that a surprising number of models in a riskless and risky setting violate this behavioral assumption, including Cumulative Prospect Theory as well as any theory exhibiting local nonsatiation in which all reference dependent indifference surfaces are smooth. It is also shown that one can construct simple alternative models that do satisfy the condition, axiomatically derived or otherwise. These alternative theories take the form of maxmin representations over a set of expected (or Choquet-expected) utility differences, where utility difference is measured between the prospect evaluated and the reference point.

Multi-person decision making problems involve the preferences of some experts about a set of alternatives in order to find the best one. However, sometimes experts might not possess a precise or sufficient level of knowledge of part of the problem and as a consequence that expert might not give all the information that is required. Indeed, this may be the case when the number of alternatives is high and experts are using fuzzy preference relations to represent their preferences. In the literature, incomplete information situations have been studied, and as a result, procedures that are able to compute the missing information of a preference relation have been designed. However, these approaches usually need at least a piece of information about every alternative in the problem in order to be successful in estimating all the missing preference values. In this paper, we address situations in which an expert does not provide any information about a particular alternative, which we call situations of total ignorance. We analyze several strategies to deal with these situations. We classify these strategies into: (i) individual strategies that can be applied to each individual preference relation without taking into account any information from the rest of experts and (ii) social strategies,

We investigate the classical Anscombe-Aumann model of decision-making under uncertainty without assuming the completeness axiom. We deduce the exact nature of preferences in this setup, and give a simple example that shows why one cannot use state-independent utility functions to represent such preferences (even for those that are separable and monotonic). In turn, we distinguish between the dual traits of “indecisiveness in beliefs ” and “indecisiveness in tastes.” The former is captured by the Knightian Uncertainty model while the latter by the single-prior expected multi-utility model. We show how these dual models would jointly obtain on the basis of an ambiguity aversion property, and then show how each model may be deduced from this result in isolation. As an application, we provide a new characterization of the Anscombe-Aumann representation of a preference relation in which we obtain the completeness and monotonicity hypotheses as consequences of a standard ambiguity aversion axiom and completeness of risk preferences alone.

We develop the ordinal theory of (semi)continuous multi-utility representation for incomplete preference relations. We investigate the cases in which the representing sets of utility functions are either arbitrary or finite, and those cases in which the maps contained in these sets are required to be (semi)continuous. With the exception of the case where the representing set is required to be finite, we find that the requirements of such representations are surprisingly weak, pointing to the wide range of applicability of the representation theorems reported here.

After reviewing the evidence for status quo maintenance (SQM), I consider how to reconcile SQM with traditional consumer theory. Behavioural economists usually let agents’ preferences change as a function of their endowments, treating the same person with different endowments as a set of distinct agents. Many properties of preferences then become immune to empirical test and it becomes impossible to judge whether an agent’s decisions make the agent better or worse off. This impedes prediction of when decision rules are likely to change. SQM can alternatively be explained with unchanging preferences if preferences are incomplete. SQM is then consistent with self-interest and there is no reason why it should not persist.