A consequence of complementary symmetry

Abstract

In this note the property of complementary symmetry is shown to imply the following consequence: If $x_{p}y$ is a binary prospect to win $x$ with probability $p$ and otherwise receive $y$, then the difference between the selling and buying prices of $x_{p}y$ will be equal to the difference between the selling and buying prices of the complement of this prospect, $y_{p}x$.