Counting in Arrow's theorem

Question

I seem to be really confused with the counting system in Arrow's theorem. Can I have a simple explanation how they determine the outcome? I can't determine the outcome using rules from my notes. It says the roles are 1) If all vote the same that would be the outcome. 2) the ranking of A over B doesn't depend on other candidates and it depends how they are ranked compared to each other. But then what if 1/2 of the votes put A over B and the other half B over A?

What is the algorithm that gives you the out come?

By way of example: Suppose that we have three candidates A B C and two voters. So we get two votes ABC and BAC what's the outcome?

Answer 1

Arrow's impossibility theorem is not about any particular way to determine the outcome. The theorem says that no matter which fixed rule you select for transforming voters' preference orderings into a result, at least one of the following strange results can happen:

• One candidate can win over another even though every voter prefers the other candidate to the one who won.
• The ranking between A and B can change even if all voters keep their preferences between A and B constant (in other words, tactical voting is possible).
• There's a single voter whose ballot is the only one that matters for the result.

(with a few additional technical assumptions omitted).