A theorem stating that, for any deterministic process of collective decision, at least one of the following three properties must hold: (i) the process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome; (ii) the process limits the possible outcomes to two options only; (iii) the process encourages agents to think strategically: once an agent has identified their preferences, they have no action at their disposal that would best defend their opinions in any situation.

A theorem dealing with deterministic ordinal electoral systems that choose a single winner, stating that for every voting rule, one of the following three things must hold: (i) the rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or (ii) the rule limits the possible outcomes to two alternatives only; or (iii) the rule is susceptible to tactical voting: in certain conditions some voter's sincere ballot may not defend their opinion best.