We present an Axiom System and a Representation Theorem for a class of preferenceson l otteries which we cal l Rational Preference Orderings with a Discontinuity Structure, and whichimplies Expected Utility Theory as a continuous special case. Rational Preference Orderings witha Discontinuity Structure are based on so-cal l ed Security Level Eects, independently introducedby I.Gilboa and Y.-J.Jaray, and Potential Level Eects, introduced by M.Cohen, which formalizeparticular psychological attitudes towards the evaluation of uncertain outcomes. In this paper wepresent two main extensions of these mode is:1. We introduce the concept of a Discontinuity Structures which determines unambiguous lythe occurence of Security Level Eects and of a Potential Level Eects for a given preferenceordering. As a consequence our Representation Theorem provides an exact speci...caton of thediscontinuities in the Utility function.
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