I think that your vote can count even if, in retrospect, it changed nothing, so long as votes are interchangeable and anonymous.

I think that's the crux of the issue. My take was to assign a mapping between people and votes such that your vote was in the "excess" portion and thus didn't matter. But just because such a mapping exists doesn't mean it is fair or valid to assign it. Instead I imagine it's a statistics problem where all mappings are possible, which leaves you with a non-zero but tiny "contribution" to electing the winner.

And if you voted for the loser? Then I think the contribution to voter turnout mentioned in the post comes into play. Again a only very tiny amount, but non-zero.

Then finally social issues likes signaling status and desire to belong to a group probably are pretty big factors, maybe bigger than the above "real" factors.

In the end I think it's possible to justify voting or not voting depending on your values, particularly how you value your time relative to these fuzzier benefits.