MCDM'20 - paper no. 4
EXTENDED CHOICE FUNCTIONALS - A CARDINAL FRAMEWORK FOR THE ANALYSIS OF CHOICE UNDER RISK
Somdeb Lahiri
Abstract:
We propose a framework that extends the one developed by Professor Amartya Sen (with Arrowian roots), for the analysis of choice under risk by an individual, hereafter referred to as a decision maker. The framework is based on the decision maker's state dependent numerical evaluations - referred to as utility, worth, or pay-off - of the alternatives. We provide several examples to illustrate meaningful possibilities in the model proposed here. The expected utility choice functional assigns to each given state- -dependent data profile (i.e., a pair consisting of a profile of state-dependent evaluation functions and a probability distribution over states of nature) the non-empty set of alternatives obtained by maximizing expected utility. A significant result in this paper, which illustrates the workability of our frameworks of analysis, is an axiomatic characterization of the expected utility choice functional using purely combinatorial techniques. Aim/Purpose: To use a minor extension of the Arrow-Sen model of social choice theory to study individual decision making/aiding under risk and with state dependent evaluation functions. Methodology: Combinatorics (theory of finite sets). Findings: Plausible decision-aids for decision making under uncertainty with state dependent evaluation functions. Research Implications: Exactly same model and results apply for the study of "weighted" multi-criteria decision making/aiding with state dependent evaluation functions. Contribution: Apart from useful decision-aids for managerial decision making under risk and operations research, we provide an axiomatic characterization of the expected utility choice functional.
Keywords:
risk, state-dependent evaluation, extended choice functionals
Reference index:
Somdeb Lahiri, (2021), EXTENDED CHOICE FUNCTIONALS - A CARDINAL FRAMEWORK FOR THE ANALYSIS OF CHOICE UNDER RISK, Multiple Criteria Decision Making (15), pp. 66-78
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