By Brewer M. J.

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12 Dc f−g Dr g−f f g f−g f Di g−f g An illustration of an extension of desirability involving lexicographic utility. , of the type fc ≔ f + ????f , with f some real-valued gamble. 30) is preserved. Another way could consist of defining separate but connected strict and nonstrict preference orders, and not derive one from the other. 3, we saw that coherent sets of desirable gambles form a partial order under inclusion. This carries over to coherent extensions of assessments that avoid partial loss.

Darkly-filled dots are closure points of interest belonging to ; white-filled ones do not belong to . For each, we indicate which gamble f it depicts, explicitly or as a vector (f (a), f (b), f (c)). 6 Illustrations of derived coherent sets of desirable gambles. c 8 INTRODUCTION TO IMPRECISE PROBABILITIES is defined by (Γ1 h)(a) = (Γ1 h)(b) = h(d) and (Γ1 h)(c) = h(c); Γ2 from ({c, d}) to ({a, b, c}) is defined by (Γ2 h)(a) = 34 h(d), (Γ2 h)(b) = 14 h(d) and (Γ2 h)(c) = h(c). 3 Conditional sets of desirable gambles We may be interested in obtaining an uncertainty model for the situation in which the experiment’s outcome belongs to a conditioning event B ⊆ .

36), starting from a simple set of strictly desirable gambles. 1 that the corresponding set of marginally desirable gambles P is a hyperplane. 5 From lower previsions In the previous section, we have given the correspondence between simple coherent sets of strictly desirable gambles and lower previsions defined on the set of all gambles (). However, lower previsions are usually elicited on a gamble-by-gamble basis.