• decision-making under risk;
  • multiple trials;
  • rationality;
  • compromise effect


We report three studies showing that in prospective multiple-trial decisions people often select a mix of sure and risky options over pure bundles of either option. Such a preference is not ‘rational’ because a mixed option cannot be the EV-maximizing choice. Experiment 1 confirmed a mixed-option preference for gains but not for losses. Showing a graph of the multiple-trial outcome distribution reduced but did not eliminate this effect, suggesting that it is not due purely to a failure to aggregate correctly over the multiple trials. Experiment 2 replicated the mixed option preference using a wider range of problems. Experiment 3 compared choices in the trinary choice conditions used in Experiments 1 and 2 with binary choices between pairs of the multiple-trial sure, mixed, and risky options. In the binary choice condition the mixed option was no longer the modal choice, suggesting that the strong mixed option preference found in the trinary choice conditions is mainly due to a compromise effect. However, the binary choice probabilities did show violations of strong stochastic transitivity in a pattern that suggested a slight bias toward the mixed option. Copyright © 2006 John Wiley & Sons, Ltd.