Security and potential level preferences with thresholds

The security level models of Gilboa [1988. A combination of expected utility and maxmin decision criteria. Journal of Mathematical Psychology, 32, 405-420] and of Jaffray [1988. Choice under risk and the security factor: An axiomatic model. Theory and Decision, 24, 169-200] as well as the security and potential level model of Cohen [1992. Security level, potential level, expected utility: A three-criteria decision model under risk. Theory and Decision, 33, 101-104] and Essid [1997. Choice under risk with certainty and potential effects: A general axiomatic model. Mathematical Social Sciences, 34, 223-247] successfully accommodate classical Allais paradoxes while they offer an interesting explanation for their occurrence. However, experimental data suggest a systematic violation of these models when lotteries with low probabilities of bad or good outcomes are involved. In our opinion, one promising candidate for the explanation of these violations is the assumption of thresholds in the perception of security and potential levels. The present paper develops an axiomatic model that allows for such thresholds, so that the derived representation of preferences can accommodate the observed violations of the original security and potential level models.