If everyone thought, as you assert, that an individual vote does not matter, then they would not vote; therefore both the quantitative and qualitative meaning/value of the "votes" (plural) would change too. They are inextricably bound; you are just viewing things through a statistical lens but that is not the only one that is valid. Grow up. Your attitude is poison and if more people thought like you we would have lost democracy long ago.

Furthermore the act you describe of taking the time to vote based on the issues, even when a particular candidate or proposition goes against the voter's normal worldivew, is not irrational, it is doing one's civic duty to be informed. The vote is the inflecion point at which that civic duty materializes most clearly; but it is part of a larger, always-ongoin process in which the citizens and the state are in a dialogue with each other; and the citizens are in dialgue with other citizens.

If there were no impetus to vote, then the dialogue itself becomes somewhat irrelevant; therefore the voting is what anchors the abastract to the concrete world of here-and-now. Your again, extremely small-minded, view of the world can not account for this.