Mechanism Design with Private Communication to Neutralize Fairness Constraints

We study mechanism design under auditable fairness mandates that constrain only the formal rule while allowing off-record private communication between the principal and agents. We model a two-layer environment: a formal rule that maps agents' reports to outcomes and must satisfy the mandate, and private advice in which the principal can provide type-contingent recommendations. We construct a format-preserving randomized encryption (FPRE): the principal randomizes over symmetry-constrained rules and pairs each realization with ''password''-like advice. Under FPRE, any Bayesian incentive-compatible social choice function (SCF) is implementable by symmetric formal rules; if the SCF is dominant-strategy incentive-compatible (DSIC), the resulting mechanism achieves DSIC. In contrast, constraints that embed predictable structures-such as strict monotonicity and continuity-cannot be neutralized. We also present an approximate version: continuity is compatible with it. Our results highlight a regulatory-scope insight: if auditors can verify only the format of the rule, format-type fairness does not bind, whereas structure-revealing mandates (i.e., strict monotonicity and continuity) hinder the ''encryption'' that sustains obedience to private advice.