On Thanksgiving, Bluestem posted Holiday post: just how thankful should Representative Mary Franson be for her luck?, which Gustavus math and computer science prof Max Hailperin calculated the odds of the shift to an eleven-vote margin for Representative Mary Franson (R-Douglas County) following a random pull of thirty-five ballots cast in three precincts in Douglas County.
Hailperin was concerned about the quality of his data because of frequent statistical differences between absentee and non-absentee ballots. As it turns out, the difference matters. Here's his update:
I got the data from Douglas County regarding the non-absentee ballots that were involved in the court-ordered ballot reduction process. As is quite typical, the non-absentee ballots were statistically rather different from the absentee ballots. Also, the total pool of ballots subject the the random selection was smaller than I had assumed in my preliminary numbers, because the absentee ballots weren't included. Putting those together, the net result is that Rep. Franson wasn't quite so lucky as I had initially given her credit for being, but still was lucky.
Where I had previously said 17%, the correct number is 24%.
Where I previously said 4.2, the correct number is 5.5.
Where I previously said 74%, the correct number is 81%.
Each of the two places I previously said 5%, the correct number is 4%.
Where I previously said 21%, the correct number is 15%.
Finally, where I said 16%, the correct number is 11%.
All of these numbers are cross-checked using both my original simulation approach (one million trials) and the more exact sum-of-hypergeometrics approach.
Whatever the odds, Bluestem is certain that Franson is thankful for the widened margin. It's unlikely that the recount will reverse the winner in the race, though not impossible.
The original post:Bluestem hopes all readers are enjoying the holiday rituals of their choice. We're grateful readers, especially ones like Max Hailperin, who has calculated the odds for the new margin in yesterday's Franson-Cunniff ballot pull.
He concludes: " In my simulations, a change at least this favorable to her occurred 17% of the time. That's a small enough percentage that she should definitely be thankful for good luck, but not so small as to cast any doubt on the proceedings."
That's about 1 in 6 odds that the change in the margin would have been at least this favorable to Representative Franson.
Programming a computer simulation of the random ballot withdrawal is a comparatively simple matte.
For each of the three precincts in question, I made a list of simulated ballots with the appropriate mixture of them marked for Cunniff, Franson, and neither. I then had my computer repeat one million times the same procedure the Douglas County Canvassing Board used. That is, it randomly selected 26 ballots from W1P1, 3 from W3, and 6 from W5P2.
In each of these million simulated cases, I had the computer total up what the positive or negative change to Franson's vote margin was, which was the number of withdrawn Cunniff ballots minus the number of withdrawn Franson ballots. (Withdrawn ballots marked for neither of the two candidates didn't affect the answer.)
My simulation assumed that all the ballots recorded for a particular precinct were eligible for random selection, independent of whether they were cast at the polling place or by absentee ballot. In reality, I would assume the canvassing board would have just drawn the 26, 3, or 6 ballots from those cast at the polling place. I don't currently have any way to rectify this error in my simulation because I don't have access to the vote counts for just the non-absentee ballots. These are a matter of public record -- in fact, a copy of the machine tapes showing these numbers is taped to the outside door of each polling place at the completion of the poll-closing activities. However, they are not so easily available. The Secretary of State's web site shows the votes after the separately-counted absentee ballots are added in.
As you know, the actual change in Franson's favor was 10 votes. In my simulations, a change at least this favorable to her occurred 17% of the time. That's a small enough percentage that she should definitely be thankful for good luck, but not so small as to cast any doubt on the proceedings.
For additional context, the average change over the million simulations was about 4.2 votes in her favor. She increased her margin by at least 1 vote in 74% of the simulations and broke even in 5%. Thus, there was about a 21% chance that Cunniff might have been the net winner of this ballot reduction process.
However, had this happened, his gain would almost surely not have been so large -- less than 1% of the time did he gain by 10 or more votes.
In fact, if he were to come out ahead at all, the most likely case would be to just counteract Franson's original 1 vote margin; that happened in about 5% of the simulations. That leaves only about a 16% chance that Cunniff would have headed into the recount in the lead.
The ballots now head to an automatic recount.
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Photo: Representative Mary Franson.