Focus theory of choice and its application to resolving the St. Petersburg, Allais, and Ellsberg paradoxes and other anomalies

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.