Editing Arrow's impossibility theorem (section)

==== Setup ====

Assume there are ''n'' voters. We assign all of these voters an arbitrary ID number, ranging from ''1'' through ''n'', which we can use to keep track of each voter's identity as we consider what happens when they change their votes. [[Without loss of generality]], we can say there are three candidates who we call '''A''', '''B''', and '''C'''. (Because of IIA, including more than 3 candidates does not affect the proof.)

We will prove that any social choice rule respecting unanimity and independence of irrelevant alternatives (IIA) is a dictatorship. The proof is in three parts:
# We identify a ''pivotal voter'' for each individual contest ('''A''' vs. '''B''', '''B''' vs. '''C''', and '''A''' vs. '''C'''). Their ballot swings the societal outcome.
# We prove this voter is a ''partial'' dictator. In other words, they get to decide whether A or B is ranked higher in the outcome.
# We prove this voter is the same person, hence this voter is a [[Dictatorship mechanism|dictator]].