Here's a thought experiment. I'm not suggesting we do this, but it's an interesting thought experiment.
Imagine that voting for president works the same way it does right now, with one tiiiiiny little difference: any citizen can cast their vote in any one state (or county, or however you divide it).
So I could cast my vote for MA, where I live, or I could cast my vote in, say, Texas.
Put aside the idea of ideal behavior: people aren't ideal. Instead, think about how many people of what types you think would take advantage of this "switched voting", and what you think the effects might be as years pass and people get used to the idea. What sort of new groups do you think voters would create to try to leverage their votes?
I'll get things started: I think that most groups of independents (such as libertarians) would get together and agree to win a specific (low-population) state. "Green party wins Alaska!" would be hilarious...