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Tyrrell_McAllister comments on Arrow's Theorem is a Lie - Less Wrong
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I had noticed that and edited my post, but too late for you to see, I guess. Sorry for the hasty conclusion.
No, "determinism" in Arrow's theorem means that the preference orders assigned by the algorithm cannot change unless the preference orders of the voters change. Randomness is one way that an algorithm could be nondeterministic, but it isn't the only way. Your system gives another way to be nondeterministic in the sense of Arrow's Theorem.
If you want to use the word "determinism" in that sense, then a far better definition would be "the voting outcome is not affected by anything other than the votes of the voters", which my system does hold to. As I said above, I haven't claimed to found a flaw in the mathematical proof of Arrow's Theorem, just a mismatch between the content of the theorem and how voting systems work in real life. Certainly, in real life, we should want to distinguish between "a vote between the Democrats, the Greens, and the Republicans", and "a vote between the Democrats, the Greens, and superintelligent UFAI", even if our preference order is the same in both cases.
Fair enough, but it's not a matter of how I want to use the word "determinism". That word in Arrow's Theorem has a certain technical meaning, and your system does not qualify as deterministic under that technical meaning.
You're making the case that determinism, in Arrow's sense, is not such the desideratum that it's usually made out to be. FWIW, I'm coming around to your point there.