My Current Forecast of the 2010 House Election Sanford C. Gordon September 29, 2010
Veteran election handicappers like Charlie Cook and Stuart Rothenberg, who categorize individual races as tossups, likely Democrat, Solid Republican, etc., tend to have an amazing track record forecasting individual races. So I wondered if I could aggregate those rankings to tell us about what is likely to happen in November.
The basic idea is to treat the outcome of each current House race as the result of a weighted coinflip. So, for example, suppose that in the past, Democrats have won seats classified as leaning Democrat 93% of the time. Then our best estimate of the chance that the Democrat will win in a leaning Democrat district in the current race should be in the neighborhood of 93%.
We let a computer flip the coins for each congressional district (depending on its classification) to come up with a hypothetical election outcome. Then, we repeat the exercise, say, 10,000 times, to see what sorts of outcomes are more or less likely. (The full details of the procedures are available here.)
Below are bar charts summarizing the outcomes of 10,000 simulations using rankings from the Cook and Rothenberg Political Reports (as of late September).

Using the Cook rankings, the procedure projects an expected Republican caucus of 215 seats  shy of the 218 necessary for a majority, but still representing a large gain (37 seats). Using the Rothenberg rankings, the prediction is 213 seats (a 35 seat gain).
As the graphs indicate, there is a substantial amount of uncertainty surrounding these predictions. So the more useful question is, What is the probability that the Republicans obtain a majority in the House? The simulation using the Cook rankings suggests that the probability is now at about 37%; using the Rothenberg rankings, it is 14%.
I will periodically update this forecast between now and Election Day.
Sanford C. Gordon is Associate Professor of Politics, New York University. 
Updated Cook–Based and RothenbergBased Projections Now Diverge Substantially from Each Other Sanford C. Gordon October 15, 2010
Cook and Rothenberg have each made significant alterations to their lists of House races in play in 2010. In late September, my forecasts based on each differed by only two seats. Now the spread is now substantial: the forecast based on Cook’s 10/12/2010 rankings anticipates a Republican majority caucus of 221 seats (remember, you need 218 for a majority). The one based on Rothenberg’s 10/8/2010 yields an expected caucus size of 215 seats. The estimated probability of a Republican House using Cook is now at 63%; the figure using Rothenberg is 24%. (See the histograms below.)
A few notes of interest:
 The Cookbased forecast is now very close to others, particularly Nate Silver’s. As of writing, Silver’s model puts the probability of a Republican takeover at 72%.  The confidence interval on the Cookbased forecast is enormous. The model suggests that with 95% probability, the Republican seatshare will be somewhere between 203 and 238 seats. So there is a lot of uncertainty in the forecast now.  I find this odd: although Cook Political Report have moved a lot of Democratic seats into dangerous territory since the beginning of the month, their aggregate prediction has not changed: then and now, they state that their outlook is for a Republican net gain of at least 40 seats. It seems that the individual seat rankings are consistent with that outlook; before, they were not. (I have wonky discussion of this in section 6 of my paper here.)

MidOctober Cook and Rothenberg Rankings Now Both Yield a Forecast for a Republican House, but the Odds Are Close to Even Sanford C. Gordon October 21, 2010
Cook and Rothenberg have each continued to move seats rankings as the election approaches. For the first time, since I started doing this last month, my Cookbased and Rothenbergbased aggregate forecasts suggest a greater than 50 percent chance of a Republican house. Interestingly, however, the probability of a Republican takeover based on the Cook rankings has shrunk  this is because in past years, Cook updated his rankings around October 20, so the new forecast is calibrated on projections from prior elections closer to election day. The probability of a Republican takeover using the Cook rankings is now 55% (the overunder is 219 seats), while the probability of a Republican takeover using Rothenberg is 57% (with an overunder of 218 seats).
As before, there is a lot of uncertainty in these rankings, as depicted in the graph below. I suspected that these two forecasts would converge as the election approached, and this appears to be the case.
Intrade has its Republican control future selling at 87.8 per share, which, at least based on this methodology, seems awfully high to me. Nate Silver’s forecast this morning was 75% odds of Republican control. 
Final PreElection Take on the 2010 House Elections Sanford C. Gordon November 1, 2010
In the two weeks or so since I last updated this page, Cook and Rothenberg have updated their seat ratings, making the situation look considerably more dire for the Democrats than in midOctober. So, now, if you run the numbers, a Republican takeover appears to be a near certainty no matter whose rankings you use. I wrote a little script to plot a graph of how my method's forecasts have varied over the course of the 100 days leading up to the election. The solid line in the figure shows the expected number of Republican seats, with the gray area surrounding it capturing the margin of error. The dashed line is the probability of a Republican takeover. The horizontal line is at 218 seats (necessary for a Republican majority).

As the figures indicate, my method predicted that the Republicans would remain in the minority until earlytomid October, in which it started to show the Republicans more likely than not to win control.
Now here's the thing: the numbers are the numbers, but in my gut I actually believe the forecasts from late September/early October more than I believe the current ones. I am concerned that there may be some confirmation bias: raters believe this is going to be a wave for Republicans, and so may be unconsciously shading the ratings in a Republican direction. The national numbers continue to look terrible for the Dems, but do they really look that much worse than they did three weeks ago to justify the dramatic shift that the graph indicates?
In any event, does this mean that I am sure that the Democrats will hold the House? Absolutely not. Even three weeks ago, my forecast anticipated a strong (although less than 50%) likelihood the Republicans may take over.
One other thing: Adam Bonica, a stellar former graduate student of mine and now a postdoc at Princeton, has come with a really cool take on using campaign contributions in much the same way I use expert ratings: as forecasts whose accuracy can be calibrated with past performance. The advantage of his method over mine is that while I (currently) use two expert raters, his method basically uses however many contributors are in his dataset, i.e., thousands. His method predicts the Democrats hold the House with an anticipated loss of 1940 seats.
