Side-Choosing Games (SCGs)
SCGs are a new kind of games used to test the correctness of a claim
(e.g., a logical statement) via a two player game,
where one player tries to satisfy the claim and the other to dissatisfy it.
A success of one side is not a proof, but can be considered as an indication of the correctness/falseness of the claim, as well as of the skill of the player.
SCGs offer safe ways of
aggregating the ranks of many players via a tournament.
A useful family of ranking functions are collusion-resistant.
Collusion-resistance together with two natural monotonicity axioms
imply that the ranking functions belong to a simple class called
local fault-based counting.
Although theoretical, these results inform the design
of competitions to design better algorithms or to
find better solutions to precisely formulated, complex problems.
They also inform the design of structured student interactions
in formal science courses.