An extreme point characterization of random strategy-proof social choice functions: The two alternative case

We show that every strategy-proof random social choice function is a convex combination of strategy-proof deterministic social choice functions in a two-alternative voting model. This completely characterizes all strategy-proof random social choice functions in this setting.

► Focus on the two alternative case in voting games. ► The set of strategy-proof random social choice functions is a convex set. ► An SP random SCF is a convex combination of SP deterministic SCFs.