We also don't elect presidents based on who people "tried to vote for." Bush won the first count, and he won the automated recount. It should never have progressed further than that. 7 of 9 justices agreed that the ad-hoc recount that applied different standards to different counties violated the equal protection clause.
Moreover, we have no way of knowing whether Bush or Gore "won" Florida. Voting is a mechanism for measuring something. Like any method of measurement, it has a margin of error. The margin between Bush and Gore was so close that it was almost certainly smaller than the error in the voting mechanism itself. The scientifically right answer would have been to exclude Florida (and, in fact, several other states decided by very small margins) from the sampling process.
