Mixture solvability of affine preferences
= Mixture solvability of affine preferences
For three strictly ordered affine-utility values $u>v>w$, the middle lottery is indifferent to the mixture of the extreme lotteries with weight $p=(v-w)/(u-w)$ on the best one. This weight lies strictly between zero and one. It is the exact mixture-indifference property underlying cardinal utility comparisons.