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Paralleling research in perception, behavioral models of risky choice posit “psychophysical” transformations of material outcomes and probabilities. Prospect theory assumes a value function that is concave for gains and convex for losses, and an inverse S-shaped probability weighting function. But in typical experiments, form and content are confounded: Probabilities are represented on a bounded numerical scale, whereas representations of monetary gains (losses) are unbounded above (below). To unconfound form and content, we conducted experiments using a probability-like representation of outcomes and an outcome-like representation of probability. We show that interchanging numerical representations can interchange the resulting psychophysical functions: A proportional (rather than absolute) representation of outcomes leads to an inverse S-shaped value function for gains. This alternative value function generates novel framing effects, a common ratio effect for bounded gains, and a “framing interaction,” where gain-loss framing matters less for proportional outcomes. In addition, we show that an absolute (rather than proportional) representation of probability reduces sensitivity to large probabilities. These findings highlight the deeply constructive nature of the psychophysics of risky choice, and suggest that traditional models may reflect subjective reactions to numerical form rather than substantive content.