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Focus Theory of Choice: Modeling Procedural Rationality and Resolving the St. Petersburg, Allais, and Ellsberg Paradoxes, Preference Reversals, the Event-Splitting Effect, and the Violations of Tail-Separability, Stochastic Dominance and Transitivity

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 outcome with a relatively high probability or a relatively low outcome 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 can account for many anomalies, including preference reversals, violations of stochastic dominance, violations of transitivity, the St. Petersburg, Allais, and Ellsberg paradoxes, the event-splitting effect, and the violation of tail-separability, and handles decision making with risk or under ambiguity or under ignorance within a unified framework.