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evgenit comments on Arrow's Theorem is a Lie - Less Wrong
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I may have misunderstood something, but I don't think your system excludes pivotal voters. For example, with the aforementioned ten people, it is possible that everyone gave every alternative except B score 0, and alternative B got score 1 from every member of the group. If one of the members then changes her score for A to 10 and for B to 0, we have A(10) > B(9).
This does appear fixable with a scale tailored to the number of people and alternatives.
You've misunderstood the axiom of non-dictatorship: it requires that there not be a person who is always capable of determining the outcome.
It is impossible, given Pareto efficiency, for there to be no person sometimes capable of determining the outcome (i.e. pivotal voter), because a unanimously pro-A group, which must elect A, can be turned into a unanimously pro-B group, which must elect B, by repeatedly changing the preference of just one individual. (But not the same individual every time, of course.)
Oh, right. I should check before posting.
I don't quite see the second part, but thank you for the explanation.
In a world of black and white, if there's both a black place and a white place, then somewhere, black and white are right next to each other. If you can change an election where Epsilon wins to an election where Delta wins by changing a whole bunch of votes, then for some set of votes, you can do it by changing just one vote.