Are you any good at those contests in which you guess the number of beans in the jar? If so, I sense an opportunity in the Minnesota recount. The first entry comes from FiveThirtyEight: Franken by 27 votes. Several commentators have linked to it with great credulity.
This seems like a classic setup for biased assimilation. If Franken wins by anywhere from 10 to 50 votes, fans will love it. If not, then people will remember the disclaimers. So – let’s all get into the game. Be a prognosticator for a day!
A statistically responsible move in any model is to calculate the uncertainty. What is it in the case of the 27-vote prediction? At least +/-200 votes.
Go start by reading the post. A summary: As the Minnesota recount progresses, some precincts have more challenged ballots than others. Counting the challenged ballots would favor Franken slightly, perhaps enough to tilt the election.
The analysis is predicated on the idea that there’s a systematic relationship between the number of challenges per precinct and the net effect on the Franken-Coleman margin:
…the fewer the number of challenged ballots, the better Franken is doing, and the higher the number of challenged ballots, the worse he is doing; the relationship is in fact quite strong.Precinct-Level Returns Analysis # Challenges n Franken Coleman Net 0 2233 +34 +6 Franken +28 1 419 -94 -125 Franken +31 2 154 -90 -122 Franken +32 3-4 133 -157 -171 Franken +14 5-9 59 -158 -116 Coleman +42 10+ 26 -156 -141 Coleman +15
Then the idea is to estimate the net change in support for Franken and Coleman:
We can address this phenomenon more systematically by means of a regression analysis.
The data (precinct-level, I hope) are fitted to an eight(!!!)-parameter model that takes into account all the challenges. After setting six of the parameters that relate to challenges to zero. this formula remains:
franken_net = t * 8.922 – 3.622
where franken_net is the net gain that comes from an uncontested recount, t is Franken’s initial vote fraction, and 8.922 and 3.622 are the two remaining fit parameters. When t is plugged in, the result comes out to a net projected gain of 242 votes for Franken. Since the initial lead was Coleman by 215 votes, this would lead to a 27-vote victory.
But there’s a problem. Fit parameters always have uncertainties. In this case, the uncertainties are not given. Let’s assume some modest uncertainties. For example, what if the values are 8.922 +/- 0.5 and 3.622 +/-0.5? Running through the calculation presented, this makes the net projected gain anywhere from 26 to 458 votes. The final result would then be anywhere from Coleman winning by 189 votes to Franken winning by 243 votes. Or, to put it another way, a more accurate prediction would have been “Franken by 27 +/- 216 votes.” So 27 is basically a random guess.
Well, let’s all play. I’ll guess as follows. Model 1: Assume that precincts where 0-2 ballots were challenged reflect the likeliest change after challenges are resolved. They represent a net of 91 votes for Franken (28+31+32)/(2233+419+154)=0.032 vote per precinct. If the remaining 133+59+26=218 precincts perform similarly after challenges are resolved, they will yield a total of 7 more for Franken, for a a net gain of 91+7=98 votes. Model 2: Assume that total net gains in high-challenge precincts are similar to low-challenge precincts, i.e. Franken +91, for a total of 91+91=182 votes. So the range of final margins is Coleman by 33 to 117 votes. If you want an exact guess, I’ll go with Coleman by 117.
Wow, that was fun! Speaking of biased assimilation, maybe now I’ll get some links from right-leaning sites.
Enter your own guess in comments. Give reasons if you have them.
P.S. In comments, the topic arises of the degree to which challenges represent an attempt to throw the credibility of the recount into question. Perhaps relevant, via electoral-vote.com, is Minnesota Public Radio’s images of challenged ballots. Aggressive challenges seem to have been made by both sides.