Many people seem to think that their vote doesn’t matter much, because unless their vote happens to be the one that breaks a perfect tie then the outcome of the election would’ve been the same whether or not they voted. This is dumb.
There aren’t any real exact ties once you get more than a few hundred votes. There is too much noise in the system. Some votes are mis-read, some ballots are lost. Some people accidentally punched the wrong hole or read the wrong name, some ballots are hard to make out, and sometimes simple counting errors are made. How many times have you counted up the cards in your deck and not gotten the number you expected? Not often, but occasionally. Even computers can be glitchy.
There errors are random and so they don’t make much difference to the final count – they basically balance out over the long run. But they make getting an exact count impossible. If a vote is close enough to be within a tenth of a percent or so, it is essentially an irreconcilable tie. And let’s face it, when the population is THAT evenly split between candidates, an election is of no use. You might as well flip a coin, it’d be just as fair.
So an individual vote is not important because it might be the magical vote that actually makes the difference. Each vote is important because it gives its side a little more weight in this balance. The further the result is from a 50/50 split, the more clear and meaningful it is. If your vote pushes your favored side from 54.32% to 54.33%, that has made the result that much better for you. Go vote, because in the end the actual person sitting in the seat may not make a huge difference, but the weight of public support for one side or the other helps steer the future.