Dominance and transitivity

Abstract

This article describes a study of transitivity of preference and of transparent dominance with 220 participants who judged each choice problem 4 times. It shows how a true-and-error model with 2 error terms per choice problem can be applied to replicated data, to ask if violations of dominance or of transitivity are ‘real’ rather than due to random response errors. These models allow one to estimate the incidence of systematic violations and of error rates. The new data showed about 3% violations of transitivity, corrected for error. This incidence might be statistically significant, but a skeptic might dismiss it as too small to build a theory upon. Tests of dominance found violations with overall rates from 4% to 18%. As in previous research, violations of transparent dominance appeared almost exclusively among people who systematically prefer ‘safe’ gambles (with low ranges of outcomes) over ‘riskier’ gambles with higher expected values when the ‘safe’ gamble was dominated by the higher-ranged gamble. For those participants and choice problems, rates of violation were 28%–45%, corrected for error. It was theorized that these violations of dominance may be due to a subgroup of risk-averse participants using a strategy in this experiment to find ‘safe’ alternatives, without comparing outcomes between gambles.

Keywords

• risky decision making
• transparent dominance
• transitivity of preference