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It's not that your decision affects the others. That's messed up causality. It's that your decision shares a lot of its causes with other decisions in other people. If you take yours as typical of a particular subset, and decide not to vote, then that suggests that others in that subset might as well. Gathering a large bloc of equivalent voters raises the voting power from approximately 0 to... well, some nontrivial number. If it's really large, it's exactly 1 (voting power is not probability, so 1 is a legit answer).
It's not 'will be the same regardless of which side I come down on', like we're in a state
A |Luke votes & Joe votes> + B|Luke doesn't vote & Joe doesn't vote>
It's 'Is this a good plan of action? Let's look at its consequences. First order (if I do it): OK. Second order (if everyone does it): not OK.'
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