Hit the Target: Allais Paradox

This work revisits the Allais paradox through a target-first decision model. We show that apparently irrational choices emerge naturally once decisions are framed relative to achieving or not achieving a concrete target. The binary mechanism (target reached or not) explains why very large certain payoffs suppress consideration of risky alternatives. However, our framework is not purely binary: it also models what happens after binary decisions, how new targets emerge, and how behavior unfolds in marginal cases where the target is near but not fully decisive. By introducing a sensitivity parameter θ and formalizing the trade-off between probability loss and prize increase, we derive clear criteria for acceptance or rejection of gambles. The model therefore unifies “certainty effects,” “jackpot attraction,” and intermediate behaviors within a single, simple formulation.