Query advantages from more than two debaters

Determine whether introducing additional provers beyond the standard two (e.g., a third debater) reduces Debate Query Complexity for any classes of Boolean functions under the deterministic, alternating-quantifier debate model, and characterise any resulting query-complexity advantages or limitations.

Background

The core debate model studied uses two competing all-powerful provers with alternating quantifiers and a query-bounded verifier to compute Boolean functions, leading to tight characterisations of DQC and a PSPACE/poly equivalence for logarithmic query complexity.

The authors note that the alternating quantifier structure generalises to more players, but whether adding more debaters yields genuine query-complexity improvements is unsettled. Establishing if and when multiple debaters provide advantages would refine the theoretical landscape of debate-based verification and could inform the design of more efficient oversight protocols.