Yes, you can learn a lot from N=1, as long as you have some auxiliary information.

The other day I was talking with a friend who’s planning to vote for Andrew Cuomo in the primary. What about Cynthia Nixon? My friend wasn’t even *considering* voting for her. Now, my friend is, I think, in the left half of registered Democrats in the state. Not far left, but I’d guess left of the median. If Nixon didn’t even have a chance with this voter, there’s no way she can come close in the primary election. She’s gonna get slaughtered.

A survey with N=1! And not even a random sample. How could we possibly learn anything useful from that? We have a few things in our favor:

– Auxiliary information on the survey respondent. We have some sense of his left-right ideology, relative to the general primary electorate.

– A model of opinions and voting: Uniform partisan swing. We assume that, from election to election, voters move only a small random amount on the left-right scale, relative to the other voters.

– Assumption of random sampling, conditional on auxiliary information: My friend is not a random sample of New York Democrats, but I’m implicitly considering him as representative of New York Democrats at his particular point in left-right ideology.

Substantive information + model + assumption. Put these together and you can learn a lot.

I could be wrong, of course, and I haven’t tried to attach an uncertainty to my prediction. But this is what I’m going with, from my N=1 survey.

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