User talk:Jmather25

Restating of dictator definition
I may be misunderstanding Arrow's theorem, in which case I'd be happy if someone cleared this up. It seems to me that the proof on this page indicates that SOME cases of votes in a society result in a dictator. However, the formal definition says this dictator must exist for all inputs, not just a subset. I think the formal definition should say:

There is no $i ∈ {1, …, N}$ such that there exists some $(R1, …, RN) ∈ L(A)N$ where $a$ ranked strictly higher than $b$ by $Ri$ implies $a$ ranked strictly higher than $b$ by $F(R1, R2, …, RN)$, for all $a$ and $b$.