While we're at it, let's also do away with the electoral college. And yes, I'm being serious.
Here is a simple example:
You have three states. The first one is 10x larger than the other two, and the voting outcome is as follows:
State A: 500,001 votes for candidate 1; 499,999 votes for candidate 2
State B: 49,999 votes for candidate 1; 50,001 votes for candidate 2
State C: 49,999 votes for candidate 1; 50,001 votes for candidate 2
State A gives ten electoral votes to candidate 1, and states B and C each give one electoral vote to candidate 2.
As you can see, even though candidate 2 received more actual votes than candidate 1, he/she winds up losing.
The winner-take all rule makes sense whenever there is just one state involved, but when you carry it over across multiple states, you wind up losing accuracy. Currently there are only two states, Nebraska and Maine, which actually implement proportional voting by splitting their electoral votes. But even then, that is not 100% perfect because there are an integer number of electoral votes which are based on population size, so there is still a rounding error.
The most accurate, and to me the simplest approach is to simply add up the actual votes from each state for each candidate, and only at the very end do you compare votes to see who is the winner.