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IIRC voting rules for the company I hold the most equity in are that a board-opposed measure does not pass unless more than half of all voting shares vote in favor. Which is a significantly different measure than half of all votes cast. (Essentially any unvoted shares vote with the board.) Imagine if we needed half of all eligible voters to vote for a new candidate before we could change the president. (U.S.A)

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In the US regular voters can't change the president at all, I thought? Once they are in for the term, they are in for the term.

(There's an impeachment process. But that's not available for regular voters.)

Correct, but I'm trying to draw a parallel between regular, scheduled shareholder votes and regular, scheduled votes for elected officials. In the U.S we typically have around 60% of eligible voters participating in presidential elections. My analogy assumes that voting against the incumbent follows the same rules as voting against the board, in which case we would need something like 84% of cast votes to be for the challenger to avoid re-electing the incumbent. (Assuming I haven't gotten my math wrong.) I'll also go so far as to suggest voter participation is low in both cases but it isn't a very effective tool for changing policy. :-)

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