Pfanzagl Exchanges Diagnose a Continuity Anomaly Pertinent to Allais' Problem

The principle of choice often expressed as a continuity axiom recommends a single ordering of both riskless and risky prospects. An analytical device contributed by Pfanzagl is extended here to show that riskless versus risky monetary comparisons ought to be more nuanced, even from a perspective sympathetic to the usual axioms. Allais’ example illustrates a related point to oppose the usual theory. Although the continuity difficulty is genuine, the consequences of conceding frank normative tolerance of some riskless-risky continuity violations on the specific grounds revealed are not catastrophic for the orthodox axioms.