Algorithm competitions are economic systems to push the state-of-the-art of solving a computational problem. TopCoder and similar platforms are prominent examples. Our new competition design is desirable from two viewpoints. (1) We minimize the effort on the competition administration by distributing the work of evaluation among participants while avoiding unfair evaluation. (2) We minimize collusion so that the strong participants cannot be outnumbered by colluding participants. Our design is axiomatic in that we formulate axioms (including a collusion-resistant axiom) for ranking functions and prove a representation theorem. It shows that all ranking functions satisfying the axioms must have an elegant property useful for collusion-resistant mechanism design. Our design approach introduces a new class of games, called side-choosing games, a generalization of semantic games, a well-studied area in logic.

In addition to algorithm competitions, our system and its theoretical foundation is also useful to pushing the state-of-the-art in formal sciences and in education in formal sciences. Indeed, the system was developed in the context of education (Algorithms and Software Development Courses) to facilitate fair peer grading and focused communication among students.