Eight days (or five weeks, take your pick) after I pointed it out, the idea of a Democratic takeover of the House has crept into the national conversation. Yesterday, Rachel Maddow (citing us as evidence) discussed the possibility with Nancy Pelosi, who thinks the probability is about 60%. Clearly Pelosi’s duty out on the basketball court is to engage in trash talk. But this week, conservative stalwart Bill Kristol said:

an Obama +3 victory on Election Day [could] drag the Democrats to an edge in the congressional vote—and control of the House. In any case, based on current polling, I don’t think one can say that it’s now out of the question that we could wake up on the morning of November 7 to the prospect of … Speaker Nancy Pelosi.

There’s been continuing pushback on my analysis. The math I used is fairly simple – and it needs to be covered before we get into any of the fine details, which have attracted so much notice.

First, some basic ideas.

Basic idea 1: Whoever wins the popular Congressional vote will control Congress. Here is a plot of House seat margin, plotted against national House popular-vote margin, for 1946-2010.

I have shaded in the regions where one party both won the popular vote and took (or kept) control of the House. Note that 32 out of 33 elections fall inside the shaded regions. Considering that the House is determined by 435 separate elections, many in convoluted districts, how can this be?

Most of you know that in the Presidential race, the winner of the popular vote usually wins the election – but not always. When it doesn’t happen, it’s because the Electoral College is “lumpy”: most states’ electoral votes will go entirely to Obama or to Romney, whether the win is by 1% or 30%. House elections are like that too, except that there are 435 of them, making the “lumps” really small.

It is only when the national-vote margin gets to less than 1% that Basic Idea 1 breaks down. Even then, it failed only once out of four elections – in 1996, when the margin was 0.3%.

Basic idea 2: Generic Congressional preference polls can be used to predict the November popular vote outcome. I won’t revisit the whole argument. I outlined it here, here, and here. It consists of two parts: (a) In September and October of on-years (e.g. 2004, 2008), these polls tend to move slightly towards the Presidential winner. (b) By Election Eve, an average of polls ends up very close to the actual vote.

Based on these two ideas, the Democrats’ current narrow lead suggests that this November, they are favored to re-take the House. To turn this to a probability, we have to consider the exact Democratic-Republican margin today and the range of possibilities for movement. This is not a complicated calculation. It leads to the estimate I gave last week.

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Here are some objections I have encountered, along with my replies.

Objection 1: Incumbents have an advantage. This might be true, but the question is: how much? I made a rough estimate that incumbency is worth an equivalent of about 1.3% of popular vote for the party in power. Even that might be an overestimate, considering Basic Idea 1 above.

Another issue with the incumbent argument is that it is in the same category as “fundamentals”-based arguments that political scientists put into their predictive models. In other words, it is a cause that drives voting preference – which is measured by the generic Congressional preference poll. And if it is already baked into the measurement we have in hand, it does not need to be further accounted for.

Objection 2: Redistricting has tilted the playing field. In many statehouses, Republicans have controlled the post-Census redistricting process. In Slate, Dave Weigel has claimed that gerrymandering makes the House safe for Republicans.

I do not have much patience for this kind of qualitative argument. Also, Slate‘s editorial policy is to be contrary – even if it means being wrong. Again, the real question is: exactly how large is the “structural” advantage? Most of the data in the graph above came during a period of prolonged Democratic dominance. If you look at it, any structural advantage for them was no more than 1% of national popular vote – and it’s likely to overlap with the incumbency advantage. After only one cycle of redistricting, it is doubtful that Republicans can match even this small number.

How can redistricting accomplish so little? One answer is that from year to year, elections are uncertain. You can pack a lot of your opponents into a few districts, but if your own districts are only 55% for your own party, a 10-point swing can knock you out of office. And the swing from 2010 to 2012 is currently about 9 points. Another answer is that redistricting is sometimes done to protect specific incumbents – which results in packing one’s own party members into a district. On average, the whole thing could well be a wash.

As an exercise, I suggest that you go to Pollster.com’s House summary page. Mouse over the “leaning Republican” and “leaning Democratic” seats. You’ll find a lot of small margins. Even a 5-point swing in either direction would make a big difference.

Objection 3: Professional prognosticators say it won’t happen. It has been pointed out that the Cook Report, Stu Rothenberg, and others disagree with me – and that they are often right. Well, let’s look at that. Here is how they (and I) did in 2010:

There I am in the middle of the pack, not far from Larry Sabato. Collectively, forecasters underpredicted the Republican victory, with an average error of about 12 seats. And that was on Election Eve. We got away with it because the midpoint of the likely range was far from a tie. Nearly all of us correctly said the Republicans would take over the House, so we got little grief.

This year, the midpoint is close to a tie. And every prediction has some uncertainty, which prognosticators usually do not report. Misunderstanding uncertainty is a conceptual error that I discussed a few days ago. The bottom line is that the pundits’ margin of error allows the possiblity of a Democratic or a Republican House.

Objection 4: 74% is such a large probability. You are crazy! Actually, it is not large (and I am not crazy, mostly). The probability is a logical consequence of my estimate that the national election margin midrange will be between D+0% (tie) and D+8%. People don’t mind that. Turn it into a probability, and they freak out.

“74% probability” and “D+0% to D8%” are mathematically equivalent. And 74% is not that significant. Many responders have an unclear understanding of the relationship between a confidence interval in vote margins and a win probability.

Generally, any probability in the the 20-80% range is a knife’s edge situation. Under current conditions, the Democrats are favored to take the House…but there is a 26% chance that they will not. Why do you think Bill Kristol is sounding an alarm about the House, but not the Senate? The Senate has slipped away from the Republicans – but not the House. The probability I have given can change – but in which direction? This uncertainty is contained in my calculation.

For example, a recent single Bloomberg poll says R+2%, hopeful for the GOP. However, generic polls are noisy data. Even the median jumps around a bit. Like you, I wait for more information.

Objection 5: District-level polls will tell us what’s going on with more precision. In fact, this is true. In the last Presidential year, 2008, district polls predicted a likely outcome of 254-260 D. The actual outcome was 257 D, right in the middle of the range. As this year’s district polls come, we’ll learn much better what’s going on.