Continuity-preserving tie-breaking to relax anti-symmetry in Revelation Principle extensions

Develop a tie-breaking mechanism for indifference classes over distributions that preserves continuity of preferences, thereby relaxing the anti-symmetry assumption (A2) while retaining a valid utility representation needed to extend the Revelation Principle to real-valued bids.

Background

The paper extends the Revelation Principle and stable sampling to real bids under assumptions including anti-symmetry (A2). In realistic LLM preference models defined by continuous losses (e.g., KL divergence), indifference classes arise, violating anti-symmetry.

The authors note that simple lexicographic tie-breaking breaks continuity and utility representability. A continuity-preserving tie-breaking scheme would remove this obstruction and broaden the applicability of their Revelation Principle extension.