I’m giving a speech tonight at St. Olaf College in Northfield, Minn., (it’s nice to see some snow on the ground!) which has necessitated my taking a little bit of a step back and reviewing what happened two Tuesdays ago.

One thing that is reasonably clear is that Democrats performed a little worse than might be expected based on the performance of the economy alone. There are different formulas based purely on macroeconomic numbers, or some combination of the economic data and the number of seats that each party holds going into the election. Most of these would have projected a Democratic loss in the range of 30-50 seats in the House rather than the 60-plus seats that they will actually lose once all races are called. Democratic losses were also a little higher than what you might have expected based on President Obama’s mediocre-but-not-terrible approval rating, suggesting that voters may have been focused on the actions of the Democratic Congress in particular.

There have been various studies about the relationship between different roll call votes that Democratic House members took — in particular, their votes on health care, cap-and-trade, the stimulus package, and the extension of the TARP bailout — and their performance in the elections. All of these studies conclude that there seems to be something going on — Democrats who voted yea on certain controversial policies were punished by voters more than others. But there are differences of opinion about precisely which votes mattered more.

This is one of those times that I prefer a simpler, rather than a more complex, research design. Some of the studies, for instance, attempt to account for the quality of opposition that the Democrats faced based on their opponents’ fund-raising numbers. This seems mistaken since those fund-raising numbers are not independent of those votes that Democrats took, i.e. if a Democrat voted for health care in a district where the bill was unpopular, that may have helped the opponent to raise a lot of money. Other studies use the vote share that Democrats received in their races in 2008 as an input variable. This likewise seems somewhat problematic because it introduces a lot of noise related to whether the Republicans happened to have fielded a strong nominee in their district two years ago (or indeed, fielded a nominee at all), something which may have been somewhat haphazard in a year where Republicans were having difficulty finding candidates.

Instead, I’d prefer to take advantage of the fact that the relationship between Congressional and presidential voting became much stronger this year. That is, the vote share obtained by the Democrat was very strongly correlated with the percentage of the vote obtained by President Obama in the district in 2008, and John Kerry’s vote share in 2004.

Here, for instance, is a chart tracking the margin of victory (or defeat) for all Democratic incumbents who ran for re-election earlier this month, and who faced a Republican opponent. On the horizontal axis is the margin by which Mr. Kerry won or lost the district in 2004 (for various reasons, I slightly prefer using Mr. Kerry’s vote share to Mr. Obama’s in making these comparisons, but it makes hardly any difference). On the vertical axis is how Democrat did this year.

As you can see, the relationship is generally quite strong. You’ll also see, however, that there are a handful of red dots in the chart; these are Democrats (and there weren’t very many of them) who voted against the stimulus package.

What we’re looking for is whether the Democrats who voted against a policy outperformed those who voted for it, relative to the overall partisan orientation of the district. In terms of the graph, this would mean that the red dots appeared above the regression line, which is derived based on the performance of the Democrats who voted for the policy.

In this case — the stimulus package — the relationship isn’t terribly clear. Although the majority of the red dots appear above the line, it is by a small margin in some cases, and there are other examples of Democrats who voted against the stimulus and significantly underperformed in their districts. This relationship is not statistically significant — that is, there is no conclusive evidence that Democrats who voted for the stimulus were punished more by voters than those who didn’t.

On the other hand, there is a clearer relationship between Democrats’ votes on extending the TARP bailout and their performance in the midterms:

Here, all but one of the red dots appear above the regression line, and it is often by a significant margin. Democrats who voted no on the bailout seem to have done themselves a big favor.

Likewise, the relationship is pretty easy to spot in terms of how the Democrats voted on health care; the vast majority of the red dots (and there are more of them to look at since health care received considerably more Democratic opposition than the stimulus or the bailout) are above the regression line.

Cap-and-trade, however, is more of a mixed bag. Although this relationship is positive — meaning, Democrats who voted against cap-and-trade tended to do slightly better than those who voted for it — it isn’t particularly close to statistically significant, especially when one considers that many of the Democrats who voted against cap-and-trade also voted against the health care bill.

This simple analysis would conclude, then, that Democrats were punished by voters for their bailout and health care votes, but not to any particularly important extent for cap-and-trade or the stimulus package.

Indeed, I think this jibes pretty well with the polling on each of these issues. The bailouts were enormously unpopular from the get-go, and the Democrats managed to take the blame for them, even though they were initiated under George W. Bush’s administration. The 35 percent of midterm voters who blame the recession on Wall Street in exit polls nevertheless voted for Republicans 57-41.

The health care bill dominated the political discourse for nearly a year and was of course also quite unpopular, particularly with the types of voters — e.g. older, wealthier ones — who tend to vote more reliably in midterms.

On the other hand, the stimulus bill was reasonably popular at the time it was passed, and midterm voters were about evenly divided about whether it had helped, hurt, or had no effect on the economy, according to exit polls.

And cap-and-trade just didn’t receive that much attention compared to these other issues, except in a few districts where the economy is significantly dependent on fossil fuels. For that matter, cap-and-trade actually polls reasonably well, although the same polls suggest that most voters don’t know very much about it.

There are inherent limitations to this sort of analysis. It does seem fairly clear, however, that individual Democrats who voted against the health care bill — and the bailout extension — overperformed those who did in otherwise similar districts who voted for them, and it seems probable that these votes also damaged the electoral standing of Democrats over all.