yields a concave dependence of the subjective probability upon the wager. Thus, the rhetorical function is concave, as required by RIA-based polarization. In our quantitative treatment of the experimental context, we use the simpler mean-variance approximation of expected utility, which is valid for small wagers (Eeckhoudt, Gollier, and Schlesinger 2005:11-12). It states that the expected util- ity of a gamble rises with the mean gain but diminishes with increasing uncertainty, operationalized as the variance. Consider a binary gamble with two mutually exclu- sive outcomes A and B , which an individual estimates to have respective probabilities p and q = 1 − p . Assuming p > 1 / 2, for a $1 wager on A , the mean gain is equal to 2 p − 1 and the variance is given by 4 p (1 − p ), as follows from a binomial distribution. The expected utility U ( w ) of a wager w is then U ( w ) = (2 p − 1) w − 4 αp (1 − p ) w $^{2}$, where α is an individual’s risk aversion; a larger α representing greater sensitivity to uncertainty. Note that for a fixed w the variance is greatest for p = 1 / 2 so that increasing p has the dual effect of increasing the mean gain while decreasing the vari- ance around it, thereby enabling w to increase as an accelerating function of p . More precisely, finding the maximum expected utility by setting the derivative of U with respect to w equal to zero yields the optimal wager as a function of probability: We need not take the second derivative of Equation 1 to recognize that it is an accelerating function of p (for p > 1 / 2) given that w → ∞ as p → 1. The inverse transformation, which defines the rhetorical function, therefore yields probability as a concave function of the wager. For p < 1 / 2, outcome B is more likely and one should replace p by q in Equation 1 in order to avoid negative wagers. However, if we employ the artifice of assigning negative wagers to bets on B , then we can extend 11 w = 2 p − 1 8 αp (1 − p ) . (1)