Why is WA Gov race important to the entire US? Thoughts from Soundpolitics today.....Horsing around with statistics
December 04, 2004
My good friend David Goldstein of the Horse Manure blog ("straight poop" from the Horse's Ass, in his own words) dumps a pile of horse product on his readers with his posting about error rates in vote counting machines:
With a hand recount looming in our historically close gubernatorial election, there has been much debate over the relative accuracy of hand counts versus machine counts, and the error rate of vote counting technologies in general… most of it uninformed.
And now thanks to David, we have even more uninformed debate.
He discusses a couple of research papers, which he apparently read, but didn't understand very well; e.g. "Using Recounts to Measure the Accuracy of Vote Tabulations: Evidence from New Hampshire Elections 1946-2002".
David then announces the following conclusions, none of which are correct in the context of the Washington gubernatorial vote:
1. The "Residual voting" rate (includes both blank and improperly marked ballots), which he calls "the primary statistical measure of the performance and accuracy of voting technologies" is 1 - 2%.
2. The error rate of machine counting ("tabulation error rate") is 0.56% for optical scanning machines.
3. He infers from (2) that
A .5 percent invalidation rate in a gubernatorial election with over 2.8 million votes cast amounts to 14,000 erroneous votes!
4. Finally, he claims that "Republicans scoff at Gregoire calling this election a tie, but statistically speaking, it is."
Again, all of David's statements 1 - 4 are incorrect.
I do agree with David that our current voting system is prone to inaccuracies, and that we're not going to emerge from the hand recount with confidence that we measured the will of the voters with ball-bearing precision. I hope after this whole mess we can actually work together for meaningful election reform. But the numbers he's throwing around for error rates and "erroneous ballots" are wildly off the mark, and we are not in a "statistical tie". Dino Rossi's TWO victories are exactly that. Victories.
Corrections and clarifications of David's erroneous claims:
1. The "Residual Rate" (blank and otherwise disqualified ballots) in Washington was far less than 1% this year. Furthermore, all indications are that the vast majority of blank ballots were really intended to be left blank. If you look at the Presidential race, you'll see that a total of 2,883,499 votes were cast and 2,859,084 votes were counted., so there were 24,415 residuals, or 0.85%. But the SoS page doesn't break out write-in votes and they're included with the other residuals. I don't have ready access to write-in numbers from all counties, but I do have those numbers for King County. The SoS page imputes 4,704 residuals for King, but the "e-Canvas" reports 1,194 write-ins, so the real residual rate in King is only 0.39%. That's more or less equal to the Libertarian vote and about half the Nader vote. That doesn't seem to be an unreasonable number of people who would simply chose not to vote for any of the presidential candidates. Some of those residuals may be unintentionally spoiled ballots. But in the King County gubernatorial recount, the canvassing board managed to convert exactly 717 initial residual ballots into non-residuals, out of 898,238 ballots tallied in the first count. That is only 0.08% of ballots that were plausibly miscast such that there is some reasonable claim that the voter filled out the ballot improperly, but well enough to leave marks from which discernable intent can be inferred.
2. The "Tabulation Error Rate" (the difference between the outcomes of the first count and the recount) in the governor's race was nowhere near 0.56%. It was 0.0040% when looking at the entire state, and even taking the weighted average of the (absolute values) of the counties' errors it is still only 0.0046%. [copy this table into Excel and do the math] This result is so far off the mark of the cited paper (7 standard deviations), that the paper's analysis doesn't seem to have any relevance to the systems and processes we use here in WA state.
3.There is absolutely no basis for screaming that there were "14,000 erroneous votes!" [David's exclamation mark]. First of all, the so-called tabulation error rate does not give the number of erroneous votes, it only gives the discrepancy between two counts. The true number of erroneously counted votes would, on average, be half of the discrepancy. Second, the number is based on a presumed tabulation error rate (0.5%) that is 125 times larger than what we actually experienced. Third, much of the actual discrepancy between the two counts was explained by the discovery of hundreds of new ballots around the state, and not by discrepancies between different methods of reading a controlled sample of ballots.
4. The election is not a tie, statistical or otherwise.. Governor-elect Rossi won the first count by 219 votes and he won the second count by 42 votes. It is close, but it is not a tie. David compared Rossi's two victories to "flipping a coin and having it land on heads two times in a row". Wrong. If we make the reasonable approximating assumption that the percentage of votes given to Rossi in a count is a normal random variable, we can use statistics to calculate the odds that Rossi truly won more than 50%. His share in the first count was 50.004722%. His share in the second count was 50.000729%. Let the null hypothesis be that Rossi's true share was < 50%. Use the t-distribution (Excel TDIST() function). Calculate the sample mean and standard error and you get a t-statistic of about 1.36. The one-tailed t-distribution with 1 degree of freedom gives the answer that we can reject the null hypothesis at the 20% level. In other words, the probability is 80% to 20% that Rossi beat Gregoire. That is much better than a tie. Those odds wouldn't be quite good enough for me to trust, say, elective surgery. But if I have to choose between two candidates in a close race, I'll go with the 80% winner over the 20% loser anyday.
Legally, the third count decides the race. But what will we learn statistically from the hand recount? Certainly if Rossi wins, then he's the undisputed winner. But what if Gregoire wins? Would she be the statistically legitimate winner, i.e. can we believe with confidence that she really won the majority of the votes? It depends on how large her margin is. All indications are that the hand recount will be far less accurate than the earlier counts, with opportunities for introducing new kinds of human errors. But let's be charitable and assume that these errors cancel out and add the 3rd count into the sample with the first two. The t-distribution tells us that it's still considered a Rossi victory unless Gregoire wins the 3rd count by more than 50.005450%, or by about 300 votes. Even she wins by, say, 250 votes, she might be the winner in the legal sense (assuming there wasn't fraud). But the statistics will still favor Rossi (albeit the more of a lead for Gregoire, the lower the confidence in Rossi's victory). Only if Gregpore wins by more than 300 legitimate votes should she be considered the statistical winner of the first three counts. If she does win the 3rd count by fewer than 300 votes, the statistics will still tell us to assume that Rossi won most of the votes. That scenario would be problematic. In our system, where leaders have to win the consent of the governed, political legitimacy goes to those who win the majority of the votes. Too slender a lead for Gregoire in the 3rd count would award political legitimacy to Rossi but a legalistic victory to Gregoire. That's not a recipe for a smooth transfer of power. It's a recipe for a widespread perception of a stolen election and a Ukraine-style crisis. Let's hope we don't see that. But if we do, we can only blame Gregoire and the Democrats for their arrogance in trying to overturn as certain an electoral victory as we'll see in this race.
And in any case, join me in reading David Goldstein's blog if you enjoy his occasionally entertaining posts. Just don't go there expecting to learn anything having to do with math.
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