It's an interesting theory, but the flip side is that with a winner-take-all, more is at stake because of each contest. So while you're right that we can imagine a 266-266 electoral college split with three one-electoral-vote disputes all over the country, where with a winner-takes-all system none of the disputes would matter, we could also imagine a 268-262 split with one 8-vote state being close, where a proportional-share system wouldn't have yielded any real controversy, since it would have given someone well over 269 votes in any event. How can we tell whether the number of close contests effect is likely to swamp the more at stake effect, or vice versa?An excellent point. (But notice that it is directed at the choice between proportional and winner-take-all allocation of electoral votes, not between the Electoral College and direct popular election - more on this below.)
To take the obvious historical example, suppose Florida had allocated its electoral votes proportionally in 2000, and hold all other states’ allocation systems constant. Not including Florida, Gore had 266 electoral votes to Bush’s 246. Florida had 25 electoral votes, and its popular vote was so close that – regardless of the recounting scheme – a proportional share system would have given Gore at least 12 of them. Gore would have won with at least 278 electoral votes. Given that margin, initiating a recount would have been pointless. (See the numbers here.)
But there are two important caveats: (1) We have to assume people would have voted in the same way under the two systems. But that’s not necessarily so; for instance, GOP voters in California might have a greater incentive to bother voting under a proportional-share allocation. (2) Holding the other states’ allocation systems constant is crucial. Supposing that all 50 states plus D.C. had used proportional-shares and that voting behavior were unchanged, my quickie calculations indicate that Bush would have gotten a bare majority of electoral votes. More importantly, in many (at least 12 by my reckoning) of the states, small changes in vote totals could have generated single-electoral-vote shifts in one direction or the other. In short, I think proportional allocation would have created even more controversy in 2000.
Nonetheless, Eugene’s theoretical point is correct: proportional allocation of electoral votes would generate offsetting effects, so it’s not clear whether it would increase or decrease the relevance of voting errors.
Eugene’s argument only addresses the choice between winner-take-all and proportional allocation of electoral votes within the Electoral College system. Would his point alter my main argument, which was that the Electoral College reduces the relevance of voting errors relative to a direct popular election? I think it might. We can imagine an election in which a popular vote would have generated a national margin of victory larger than the national margin of error, but with a disproportionate number of voting errors having occurred in states where the margin of victory was much closer. In such an election, the Electoral College would result in more relevant errors (and hence recounts) than would a direct popular election.
So what’s the bottom line? It depends. If aggregation tends to cancel out margins of error while magnifying the margin of victory, then a popular vote would be preferred for dispute-minimizing purposes. But if aggregation tends to cancel out margins of victory while magnifying the margin of error, the Electoral College looks better. My suspicion is that aggregation tends to cancel out margins of victory (look at the 2000 numbers: despite the very close national total, Bush and Gore each won by landslides in many individual states), and that would tend to support the Electoral College. But if margins of error also tend to cancel out in the aggregation process then it’s still unclear which system is better.