| Also ran across: > It states that for any deterministic process of collective decision, at least one of the following three properties must hold: > 1. The process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome; > 2. The process limits the possible outcomes to two options only; > 3. The process is open to strategic voting: once an agent has identified their preferences, it is possible that they have no action at their disposal that best defends these preferences irrespective of the other agents' actions. > […] Gibbard's theorem can be proven using Arrow's impossibility theorem. > Gibbard's theorem is itself generalized by Gibbard's 1978 theorem[2] and Hylland's theorem, which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of chance. * https://en.wikipedia.org/wiki/Gibbard%27s_theorem |