Last year we did an N=1 poll on the Democratic primary election for governor of New York. And the poll worked pretty well. To recap:
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 our respondent’s left-right ideology, relative to the general primary electorate.
– An informative measure of the respondent’s attitude. He didn’t just answer a yes/no question about his vote intention; he told me that he wasn’t even considering voting for the alternative candidate.
– 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 Democrats, but I’m implicitly considering him as representative of Democrats at his particular point in left-right ideology.
Substantive information + informative data + model + assumption. Put these together and you can learn a lot.
Today I ran into survey respondent and I thought I’d ask him, my representative center-left Democrat, who he supported in the presidential race. Not who he thought would win, but who he supported.
So I asked him, he paused for about a second, and then said, Beto.
P.S. According to Predictwise, Beto’s currently at 15%. I don’t really have a sense if this is too low or too high. And, in any case, there are several reasons why primaries are hard to predict. But, for now, given my N=1 poll, I’m going with Beto.
Predictwise also has odds for the Republican nomination. Their probabilities are Trump 86%, Kasich 20%, all else 4%. The Kasich number doesn’t seem right to me. Trump 86%, that seems reasonable enough, but conditional on Trump not being the nominee, is there really an 80% chance that it will be Kasich? That conditional probability seems too high. I guess that implies I should lay some money on Mike Pence, Paul Ryan, etc.
The Kasich number appears to be some kind of numerical error (or spurious signal from one Predictwise’s sources). If you look at the graph, he suddenly went from ~0% to 20% within the last day. Also evidence of the numerical error: the fact that Trump+Kasich = 106%, which seems a bit high.
I call him Beso. ;)
”
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 our respondent’s left-right ideology, relative to the general primary electorate.
– An informative measure of the respondent’s attitude. He didn’t just answer a yes/no question about his vote intention; he told me that he wasn’t even considering voting for the alternative candidate.
– 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 Democrats, but I’m implicitly considering him as representative of Democrats at his particular point in left-right ideology.
Substantive information + informative data + model + assumption. Put these together and you can learn a lot.
”
This is the same general response I give when people try and tell me something like ‘frequentism totally fails for n=1 cases’. Nope, you’d just make assumptions, get a model, auxiliary variables, etc. etc., and it can still ‘work’.
Justin
Re Kasich:
I don’t know that you can just drop Trump and get decent conditional probabilities, because that would change the situation so greatly.
Let’s march back to early 1968 and make up some numbers: LBJ 76% of getting the nomination, McCarthy 20%, all else 4%.
This would imply that after LBJ drops out, McCarthy would have an 83% chance of getting the nomination. But as we know, that isn’t what happened. After LBJ’s narrow win in New Hampshire, RFK (may he rest in peace) jumps in.
When LBJ withdraws, HHH decides to run, and ends up getting the nomination easily.
The Luce choice axiom doesn’t really work well in this arena. (In probability theory, Luce’s choice axiom, formulated by R. Duncan Luce (1959), states that the probability of selecting one item over another from a pool of many items is not affected by the presence or absence of other items in the pool. Selection of this kind is said to have “independence from irrelevant alternatives” (IIA).)
Let’s suppose Trump drops out, for whatever reason. If 1968 is a guide, then some Trumpette would likely jump in. Steve Bannon? Sean Hannity? Steve King? Who knows.