Abstract
We present a decision theory which models and axiomatizes a decision-making procedure. This procedure involves two steps: in the first step, for each action, some specific event which can bring about a relatively high payoff with a relatively high probability or a relatively low payoff with a relatively high probability is selected as the positive or negative focus, respectively; in the second step, based on the foci of all actions, a decision maker chooses a most-preferred action. Our model handles decision making with risk or under ambiguity or under ignorance within a unified framework. Our model resolves several anomalies, including the St. Petersburg, Allais, and Ellsberg paradoxes, and violations of stochastic dominance.
Highlights
The expected utility (EU) theory axiomatized by von Neumann and Morgenstern (1944), and the subjective expected utility (SEU)theory axiomatized by Savage (1954) are the foundation of decision under risk and uncertainty
The hypothetical experimental findings reported by Allais (1953) and Ellsberg (1961) show that people systematically violate the axioms proposed by von Neumann and Morgenstern for the EU and by Savage for the SEU
We define and characterize the negative evaluation system (NES), exhibit how framing affects the choice between the positive evaluation system (PES) and the NES in the context of the Asian disease problem, resolve the example of violations of stochastic dominance given and list the mathematical symbols used in NES
Summary
The expected utility (EU) theory axiomatized by von Neumann and Morgenstern (1944), and the subjective expected utility (SEU). In PES, the event which makes an action generate the highest payoff is the positive focus of this action because it is the most attractive (salient) event for this action; the DM chooses such an action that produces the highest payoff from among all positive foci This procedure is exactly the same as decision making under ignorance with the maximax criterion. We define and characterize the NES, exhibit how framing affects the choice between the PES and the NES in the context of the Asian disease problem, resolve the example of violations of stochastic dominance given and list the mathematical symbols used in NES. It should be emphasized that instead of conducting new experiments, we utilize well-documented and reliable experimental data
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