The thing with even number districts behaving differently is known in PR: since with an even number of seats any election near 50/50 (assuming a two party race here, which isn't exactly the case in any country that uses PR outside of Malta and they use STV which is different although the same thing does tend to happen) the seats split equally while with an odd number of seats someone must come out with the most.
What it probably does is actually empower bigger states more than a full national popular vote would do: since . For example using D'Hondt PR (and not factoring in the majority bonus in this; the same principle applies though) in order to swing an electoral vote in a three vote state you need to swing a hell of a lot of votes (in a straight two-candidate race the quota to get an electoral vote in a three vote state would be 25%; so outside of DC they'd all split 2/1 unless one candidate had a total landslide and got over 75% of the vote) while in California you'd need 1.8% of the vote to get a seat; so its much easier to pick off a few seats with a relatively small swing of the vote): so in small states that are 60% for one candidate why would the parties bother campaigning since they know what the distribution is going to be?
Alexander Hamilton's version of the 12th Amendment would have provided that presidential electors be elected by electoral district drawn by Congress (e.g. a state with one representative would have three electoral districts) and that the mode of election be specified by Congress, and that the electors designate presidential and vice presidential votes.
Hamilton's proposed 12th Amendment
Had this been adopted, there wouldn't be any questions about national popular vote, since nobody would be adding up the votes, anymore than they total the national popular vote for Congress.
A modern version would provide that:
Electors be apportioned among the United States and their territories based on the Citizen Population over age 18. An elector would represent between 20,000 and 50,000 persons.
Electors be chosen by the voters eligible to vote for the larger house of a legislature, with time, manner, place regulations set by the legislature, subject to a congressional override (e.g. same rules as apply to the election of Congress).
Electors would meet as a single national body, perhaps electronically linked; and would determine a president and vice president by majority vote. If no candidate received a majority on the initial vote, voting would continue by rounds among the (up to Top 10), with one eliminated on each round.
Here's the thing: this would basically mean that America would run Presidential elections in the same way that countries - hell; in some respects this is exactly the way that most European countries run with respect of picking their head of government, except that they are electing their parliament while you're elected a nonsense chamber full of thousands of people.
