
Mark J. Machina and Marciano Siniscalchi
760
To illustrate how this model can accommodate Ellsberg preferences in the Three-
Color Urn, keep the normalization U($100) = 1 and U($0) = 0, and suppose that the
decision-maker assigns probability 1/2 to each of the distributions
Then bet a
1
on red induces the same lottery P = {$100;1/3;$0,2/3} under
either measure, so we can identify it with the degenerate two-stage lottery {P,1}
to obtain W(α
1
) = V(P) = δ(1/3). A similar argument establishes W(a
4
) = V(P)
= δ(2/3).
Consider now the bet a
2
on black. Under distribution μ
1
it yields the lottery
P
1
= {$100,2/3,$0,1/3}, while under μ
2
it yields P
2
= {$100,0;$0,1}. ...