Concavity and additivity in diversity measurement

Re-discovery of an unknown concept

  • Eike B. Kroll
  • Bodo Vogt


Experimental economists have discovered various violations of expected utility theory and offered alternative models that can explain laboratory results. This study discovers a new violation in risky choices that cannot be explained by theories like Prospect Theory, Disappoint- ment or Regret Theory. In an experimental setting using a between- subject design, the influence of a dominated alternative on certainty equivalents is shown. One group of subjects was offered a series of choices between a lottery ticket with a 50-50 chance of winning and a sure payoff. A second group was offered the same choice plus a third alternative, that as it turned out was not chosen by any participant. As a result, the average chosen sure payoff in the second group was higher than in the first group. That means, by adding a dominated alternative to a choice set, the certainty equivalent of a lottery is in- creased.