Violations Of Stochastic Dominance Research Articles

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.

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.

Other-Regarding Preferences, Concerns for Others' Opportunities and Violations of Stochastic Dominance: A Choice-Theoretic Analysis

Decision makers with other-regarding preferences may care not just about others' outcomes but also about their opportunities. In social situations involving risk, this often results in their choices violating stochastic dominance, a property that underlies both expected and non-expected utility theories. We propose and axiomatize a model of other-regarding preferences, which we refer to as opportunity adjusted expected utility, that accommodates opportunity concerns and possible violations of stochastic dominance. Our model considers a set-up with a decision maker (DM) and another individual and characterizes the DM's preferences over allocation-lotteries through a representation that is based on (i) a baseline expected utility assessment and (ii) an adjustment that captures her attitude toward the other individual's opportunities.

Making trade-offs: a probabilistic and context-sensitive model of choice behavior.

The stochastic difference model assumes that decision makers trade normalized attribute value differences when making choices. The model is stochastic, with choice probabilities depending on the normalized difference variable, d, and a decision threshold, delta. The decision threshold indexes a person's sensitivity to attribute value differences and is a free estimated parameter of the model. Depending on the choice context, a person may be more or less sensitive to attribute value differences, and hence delta may be used to measure context effects. With proportional difference used as the normalization, the proportional difference model (PD) was tested with 9 data sets, including published data (e.g., J. L. Myers, M. M. Suydam, & B. Gambino, 1965; A. Tversky, 1969). The model accounted for individual and group data well and described violations of stochastic dominance, independence, and weak and strong stochastic transitivity.

Testing Critical Properties of Decision Making on the Internet

This article reviews recent findings that violate a broad class of descriptive theories of decision making. A new study compared 1,224 participants tested via the Internet and 124 undergraduates tested in the laboratory. Both samples confirmed systematic violations of stochastic dominance and cumulative independence; new tests also found violations of coalescing. The Internet sample was older, more highly educated, more likely male, and also more demographically diverse than the lab sample. Internet participants were more likely than undergraduates to choose the gamble with higher expected value, but no one conformed exactly to expected value. Violations of stochastic dominance decreased as education increased, but violations of stochastic dominance and coalescing were still substantial in persons with doctoral degrees who had read a scientific work on decision making. In their implications, Internet research and lab findings agree: Descriptive decision theories cannot assume that identical consequences can be coalesced.

Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment.

Decision field theory provides for a mathematical foundation leading to a dynamic, stochastic theory of decision behavior in an uncertain environment. This theory is used to explain (a) violations of stochastic dominance, (b) violations of strong stochastic transitivity, (c) violations of independence between alternatives, (d) serial position effects on preference, (e) speed-accuracy trade-off effects in decision making, (f) the inverse relation between choice probability and decision time, (g) changes in the direction of preference under time pressure, (h) slower decision times for avoidance as compared with approach conflicts, and (i) preference reversals between choice and selling price measures of preference. The proposed theory is compared with 4 other theories of decision making under uncertainty.