There are 435 districts, so this comes out to less than 20 respondents per district: so how can they really get all the estimates for the map? The short answer is that the estimates will be noisy but MRP does some smoothing based on district-level predictors. So the estimate for any district will end up being partially pooled toward estimates from other districts. Also, n=20 ain’t nothing. If something like 75 percent of people in each district support ENDA, then in a simple random sample of size 20, there’d be a 90 percent chance that you’d see between 12 and 18 Yes responses. To put it another way, if you’re trying to estimate something with high precision (for example, a 2 percent shift in vote opinion), you’ll need a large sample size. But if you’re trying to estimate something really easy (for example, a position where people are 3:1 in favor), a small sample will do the trick.
The math isn’t quite as simple as I stated above: surveys have “nonresponse” and need to be adjusted to match the population (that’s the “poststratification” step in MRP), but the basic idea holds.
P.S. When I earlier posted on this, some commenters brought up primary elections and others talked about the intensity of preferences.
Regarding primary elections: Yes, Republican Congress members have to worry about the attitudes of conservative Republican primary election voters. But that’s not the whole story, as they also try not to go counter to vast majorities of the people in their districts. To put it another way, general attitudes in the district are relevant, and with 70-80 percent support overall, I don’t think primary voters can be as opposed as all that.
Regarding the issue of intensity of support: The suggestion is that voters who oppose gay rights feel more strongly about the issue than voters who support gay rights. It is possible, but I have no particular reason to believe it—if anything, given the nature of the issue, I’d be inclined to believe the opposite, that supporters of gay rights feel more strongly about the issue than do opponents. And you’d need a huge huge difference in intensity to overcome the huge disparities in support that we see from the polls. Finally, consider the estimates reported by Jeff Lax and Justin Phillips:
Estimated support for ENDA in [New Hampshire] is a whopping 77% and strong opposition only about 5%.
If anti-gay-rights voters really cared so much about the issue, I’d think we’d see much more than 5 percent in the “strong opposition” category.