The coin flip argument doesn’t work because your vote isn’t drawn from the same distribution as most votes. E.g. if 60% of voters vote for A and 40% for B, then A will win, but your coin flip only has 50% probability of picking A, so it’s 50-50 for you. (Or well, slightly better odds than 50-50 because your vote exerts a causal force on who wins, but unless the voting population is smallish this effect is negligible. And it disappears in the presence of an opponent.)
The coin flip argument doesn’t work because your vote isn’t drawn from the same distribution as most votes. E.g. if 60% of voters vote for A and 40% for B, then A will win, but your coin flip only has 50% probability of picking A, so it’s 50-50 for you. (Or well, slightly better odds than 50-50 because your vote exerts a causal force on who wins, but unless the voting population is smallish this effect is negligible. And it disappears in the presence of an opponent.)