In response to a summary by Alfred G. Cuzán of election forecasts, I wrote,

The Democrats in 2006 matched the Republicans in 2004 in seats. But in average district vote, the Democrats did much better, with nearly 55% of the average district vote: far better than the Republicans’ share even in 1994, and comparable to the Democrats’ average district vote during the 1980s. See Figure 1 of this paper
or here for the quick version.

Jim Campbell then wrote:

If you are going to look at the vote, don’t be misled into looking at the average district vote. The total vote division is what should matter democratically. The average district vote over-weights the “rotten-borough” or cheap seats that are consistently in the Democrats’ column. Imagine an EVENLY divided nation that happened to be organized with a lot of lopsided, low-turnout Democratic districts and fewer, high-turnout Republican tipping districts. The average district vote would look like the nation favored the Democrats; but as the premise stated, it is really an EVENLY divided nation.

No question that the Republicans may have some other distributional advantages that partly offset (or in some elections, more than offset) the Democratic cheap seat advantage. But when it comes to comparing the mean district vote percentage and the total national vote
percentage, the cheap seats difference quite consistently produces a higher Democratic mean
district vote percentage than their total vote percentage.

I wrote:

Clearly reasonable people can (and do) disagree on this! We prefer the average district vote for reasons discussed on page 8 in our paper. It depends on whether you want to count nonvoters as being represented.

Finally, Jim wrote,

I [Campbell] agree that reasonable people disagree about this. Nevertheless, I am still not sure how we represent the unrevealed choices of nonvoters in this. It amounts to some kind of (mostly) unintentional proxy voting–something that we would not countenance if done overtly. We have a tough enough time counting/representing the revealed choices of actual voters.

I agree. It’s a missing data problem, and also a problem of defining how we would want to summarize preferences if complete data were available (in this case, if we actually knew the preferences of everyone, voters and nonvoters). Also relevant is representation of people who are not eligible to vote (children, noncitizens, convicts)–their preferences aren’t quite relevant, but they are still being represented.

P.S. Steve Ansolabehere adds,

One unmentioned problem in all of this discussion is the fact that many states do not tally votes for candidates who run unopposed. Also, absentees and other ballots commonly go uncounted in races clearly decided by the election day totals. The total vote number commonly used does not itself measure total votes or nationwide vote shares. Eleven states do not even certify the total turnout in the state.