We can replace Continuity with the Archimedean property (or, ‘You would accept some chance of a bad outcome from crossing the street.‘) By my reading, this ELU idea trivially follows Archimedes by ignoring the part of a compound ‘lottery’ that involves a sufficiently small probability. In which case it would violate Independence, and would do so by treating the two sides as effectively equal when the differing outcomes have small enough probability.
We can replace Continuity with the Archimedean property (or, ‘You would accept some chance of a bad outcome from crossing the street.‘) By my reading, this ELU idea trivially follows Archimedes by ignoring the part of a compound ‘lottery’ that involves a sufficiently small probability. In which case it would violate Independence, and would do so by treating the two sides as effectively equal when the differing outcomes have small enough probability.