Rakesh K. Sarin

Measurable Multiattribute Value Functions

This paper presents a theory of measurable multiattribute value functions. Measurable value functions are based on the concept of a “preference difference” between alternatives and provide an interval scale of measurement for preferences under certainty. We present conditions for additive, multiplicative, and more complex forms of the measurable multiattribute value function. This development provides a link between the additive value function and multiattribute utility theory.

Ranking with Partial Information: A Method and an Application

A method is presented for ranking multiattributed alternatives using a weighted-additive evaluation function with partial information about the weighting scaling constants, the method is applied to evaluate materials for use in nuclear waste containment. The paper derives conditions to determine whether a pair of alternatives can be ranked given the partial information about weighting constants, and presents an algorithm that partially rank-orders the complete set of alternatives based on the pairwise ranking information.

A Simple Axiomatization of Nonadditive Expected Utility

This paper provides an extension of L. J. Savages subjective expected utility theory for decisions under uncertainty. It includes in the set of events both unambiguous events for which probabilities are additive and ambiguous events for which probabilities are permitted to be nonadditive. The main axiom is cumulative dominance, which adapts stochastic dominance to decision-making under uncertainty. The authors derive a Choquet expected utility representation and show that a modification of cumulative dominance leads to the classical expected utility representation. The relationship of their approach with that of D. Schmeidler, who uses a two-stage formulation to derive Choquet expected utility, is also explored. Copyright 1992 by The Econometric Society.

Risk-value models

Abstract In this paper we propose a risk-value model for evaluating decisions under risk. In this model preference for a gamble is determined by its riskiness and its value or worth. In a simple form of the risk-value model, risk is measured by variance and value by expected returns. We discuss several other empirically more attractive forms of the risk-value model. We show that the risk-value model provides a framework for unifying the streams of research on risk judgments and on modeling choices. We explore the consistency of the risk-value model with both expected utility and non-expected utility preferences. Specifically, we show that if we define risk and value in appropriate ways, the rank order produced by the risk-value model will be consistent with a suitably chosen expected utility or non-expected utility model. We briefly discuss application of the risk-value model to the theory of finance and to social risk analysis.

Comparative Ignorance and the Ellsberg Paradox

We investigate the evaluation of known (where probability is known) and unknown (where probability is unknown) bets in comparative and non-comparative contexts. A series of experiments support the finding that ambiguity avoidance persists in both comparative and non-comparative conditions. The price difference between known and unknown bets is, however, larger in a comparative evaluation than in separate evaluation. Our results are consistent with Fox and Tverskys (1995) Comparative Ignorance Hypothesis, but we find that the strong result obtained by Fox and Tversky is more fragile and the complete disappearance of ambiguity aversion in non-comparative condition may not be as robust as Fox and Tversky had supposed.

Strength of Preference and Risky Choice

This paper provides conditions under which a utility function under risk can be legitimately interpreted to measure strength of preference between consequences. These conditions require that if a decision maker regards the preference difference between acts a and b to be the same as the preference difference between acts a ′ and b ′ for every state of the world, then the preference difference between a and b should be regarded as equivalent to the preference difference between a ′ and b ′. A key assumption is that a decision makers preference differences between acts given one state of the world should be independent of common consequences given other states of the world. Usefulness of this result is discussed.

Group Decisions with Multiple Criteria

We consider a decision problem where a group of individuals evaluates multi-attribute alternatives. We explore the minimal required agreements that are sufficient to specify the group utility function. A surprising result is that, under some conditions, a bilateral agreement among pairs of individuals on a single attribute is sufficient to derive the multi-attribute group utility. The bilateral agreement between a pair of individuals could be on the weight of an attribute, on an attribute evaluation function, or on willingness to pay. We investigate cases in which each individuals utility function is either additive or multiplicative. In the additive case, the group utility can be represented as the weighted sum of group attribute weights and group attribute evaluation functions. In the multiplicative case, the group utility takes a more complex form.

Revealed Likelihood and Knightian Uncertainty

Nonadditive expected utility models were developed for explaining preferences in settings where probabilities cannot be assigned to events. In the absence of probabilities, difficulties arise in the interpretation of likelihoods of events. In this paper we introduce a notion of revealed likelihood that is defined entirely in terms of preferences and that does not require the existence of (subjective) probabilities. Our proposal is that decision weights rather than capacities are more suitable measures of revealed likelihood in rank-dependent expected utility models and prospect theory. Applications of our proposal to the updating of beliefs and to the description of attitudes towards ambiguity are presented.

Technical Note—Single Machine Scheduling with Controllable Processing Times and Number of Jobs Tardy

Sensitized and unsensitized transparent film material in sprocket-hole punched form is provided together with means to indicate the area encompassed by a frame such that the film material can then be utilized in still projection devices. In one preferred embodiment a sheet of film material is formed with a plurality of sprocket-hole punched strips separated from each other by perforations in the sheet.

Preference Conditions for Multiattribute Value Functions

This paper examines conditions on preferences that simplify the assessment of multiattribute value functions for use in the analysis of multiobjective decision problems. It is shown that when these conditions hold the value function must have a simple analytic form. A procedure is presented for testing whether the conditions hold and determining the value function when the conditions are found to be valid.