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Stuart_Armstrong comments on Arrow's Theorem is a Lie - Less Wrong
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This voting system fails Pareto efficiency. Given three alternatives A, B and C, which I love, like, and hate respectively, I would vote 10-10-0. Get a second person like me, and we have options A and B equal even though we both prefer A.
And yes, this is a rational way of voting, if my dislike of C trumps any difference between A and B, and if I didn't know the preferences of the other voter.
Again, that's not what Pareto efficiency means; it means that the voting algorithm will rank A higher if everyone votes A higher than B. Going by your definition, no voting algorithm could ever be Pareto efficient, because everyone could just lie and say they preferred B to A when it's actually the reverse.