X Collusion-Resistant Tournament Design to Create and Disseminate Knowledge in Formal Sciences

We solve the problem of collusion in massive online tournaments (of formal scientific communities) which, surprisingly, has a simple yet rather counterintuitive solution. The solution requires that we collect the participants’ side-choices of whether they want to be proponent or opponent of a given claim, leading to the concept of a forced player or a devil’s advocate. In the presence of side-choice and forced players, we have succeeded in finding a broad class of collusion-resistant and incentive-compatible mechanisms for tournaments. We model the ranking of participants using three axioms NNEW (Non-Negative Effect for Winning), NPEL (Non-Positive Effect for Losing) and the crucial axiom called collusion-resistance (CR). We prove that any ranking function satisfying the three axioms must be based on a special kind of loss, called a fault. Those faults provide an elegant implementation of CR. We are used to building meritocracy based on winning. But in the world of side-choosing games, surprisingly, the standard approach does not work in general for any tournament. There is a simple alternative and we have two theorems to prove it: The Representation Theorem and the Meritocracy Theorem. Version 2/9/2015.