> Speaking of rounding errors, you shouldn't vote, either.

Quite a few philosophers of politics and radicals would agree with that statement; from SEP[0]:

>There is some debate among economists and political scientists over the precise way to calculate the probability that a vote will be decisive. Nevertheless, they generally agree that the probability that the modal individual voter in a typical election will break a tie is small, so small that the expected benefit (i.e., p[V(D)−V(R)]) of the modal vote for a good candidate is worth far less than a millionth of a penny (G. Brennan and Lomasky 1993: 56–7, 119). The most optimistic estimate in the literature claims that in a presidential election, an American voter could have as high as a 1 in 10 million chance of breaking a tie, but only if that voter lives in one of three or four “swing states,” and only if she votes for a major-party candidate (Edlin, Gelman, and Kaplan 2007).

Chances are, you can use the time to do other things, things that gain you more benefit than "a millionth of a penny" (if we must use the economism of time = money).

[0] https://plato.stanford.edu/entries/voting/#1

I disagree with it too, but it follows from this silly theory of not taking any action unless it's the biggest possible action.

That's not at all the same comparison. An equal comparison would be where the president's vote counts at 1 trillion votes. In that case I wouldn't bother voting because even if everybody in the country votes for candidate A it'll mean nothing if the president votes for president B. The president's vote will always overpower everyone else's vote.