There have been 9 recall petitions in Wisconsin filed this year - 6 Republicans (Dan Kapanke, Randy Hopper, Luther Olsen, Sheila Harsford, Robert Cowles, Alberta Darling) and 3 Democrats (Jim Holperin, Robert Wirch, Dave Hansen.) Julie Lassa might possibly face a petition as well (hers is due in about 10 days.)
All 9 petitions have had challenges filed to them already. This diary is an attempt to analyze them in-depth.
First, the Republican challenges. All 6 Republican challenges appear to attempt to rely on a technicality: That specific petitioners were the ones who signed a statement of intent and filed the thousands of petitions, but the registration statement was filed to the Government Accountability Board by the recall committees instead of specifically by the petitioners in question. This laughable statement was described by organizers as such:
If there were a glimmer of substance to the argument, it might charitably be deemed to be at the furthest flung edges of hypertechnical, insubstantial potshots.
(Also, sample rebuttal)
My interpretation is that the Republican challenges took the form they did because Democratic petitions were volunteer-fueled and received far more than the required number of signatures. Most of the challenges also cited a trivial number (in the hundreds) of invalid signatures, while the Cowles challenge did not even do that. (Sample challenge)
Still, the Republicans had to challenge with some reason (to gain the press's attention, if nothing else), so they chose this.
The Republican petitions against the Democratic senators are more interesting. Many of the signatures were falsified or sloppily taken because they used out-of-state petitioners paid on a per-signatures basis. This included a Colorado felon who allegedly stole several belongings while petitioning. The Milwaukee J-S examined 200 pages of recall signatures and found that more than 75% of them were taken by out-of-state petitioners.
The result was to be expected. Democrats called hundreds of signatories and found that6-9% of them testified that they had never signed, or were misled into doing so. According to affidavits they gathered, many petitioners had claimed that the petition were on different subjects, including schools, tribal rights, parks, and recall of Republican officials. In addition, according to the GAO website, excluding the phone challenges, thousands of signatures were challenged in each district for various reasons ranging from forgeries, signers being outside the district, duplicate signatures, and improperly filed forms (among others.)
In response, the Hansen recall leader released a very confusing and spelling/grammatical-error rife statement.
"Recall Dave Hansen's" response to The Democratic Party of Wisconsin trying to disquality[sic] the hard work of grassroots petitioners is simply, "Hog Wash."[sic] The GAB will not through[sic] out over 5000 extra signatures. We understand the amount of work it has taken to get over 18,800 signatures to force a recall. It would be impossible for the democratic party to obtain over 5000 fictious[sic], fraudulent, afidavits[sic] in 10 business day, to throw out this petition. Its a shame the democratic party would go to such a low level to disallow the voice and will of the people.
The main point of this diary, at which we have finally arrived, is to perform a statistical analysis to try and determine the validity of each petition. Such an analysis is required because for obvious reasons, Democrats could not call all the signatories in each district (some would not answer, some would not be interested in responding, and there is simply not enough manpower to call everyone.) As such, I first consider the non-phone challenges, and then statistically extrapolate the results of the phone challenges to determine the likelihood in each case that the petitions should be invalid. This is not a legal analysis! I am not certain whether such an argument would be allowed in court at all.
My assumptions will be as such:
Assumption #1: 95% of the non-phone challenges will be found valid. No real statistical reason for this; I tried to find challenge success rates for past petitions, but no luck on that front. I assume that Democrats were pretty thorough in the challenges. Additionally, it does not seem like there was a motivation to challenge enough signatures to be past the cutoff, as the non-phone challenges did not reach that level in two of the three districts. I am excluding challenges from phone sampling, as I cover those separately, and my numbers are obtained from the GAB website.
Additionally, the GAB estimates are a maximum based off the number of filed sheets (each sheet has 10 possible signature entries.) So if you submit 3000 sheets, the GAB estimates it as 30,000 signatures: But the sheets might not be completely full. For instance, the GAB estimated the Kapanke recall signatures as 30,000, while organizers listed it as 22,561. The 95% also attempts to fold the 'nonexistent signatures' into the challenges. So for instance if only 90% of the challenges succeed, but a few hundred more didn't exist, that would also reach around the 95% value. As such, it would also be possible for the actual 'rate' to be greater than 100%.
Assumption #2: Less than 10% of the signatures were obtained misleadingly (the numbers were 6-9.2% in the three districts.) This is needed for statistical purposes to calculate the margin of error. One can think of it intuitively that for instance, if 0% of the population is 3-headed, a survey of people to determine how many are 3-headed will always return 0%. The general assumption is to set the percentage at 50% to maximize it, but I think this is a valid assumption for this case. In any case, the mathematical standard deviation is given by sqrt(p(1-p) / N), where p is the probability for the result (0.1 in this case), and N is the sample size.
- The margin of error is 1.5x that of what we would normally expect (due to perhaps not being a completely representative statistical sample, and other sampling issues), and is normally distributed (the normal approximation makes sense where there are tens of thousands of signatories, and the results are no more than a few standard deviations from the mean as here.)
And anyways, to the challenges:
Holperin recall
The Holperin recallers obtained roughly 23,300 signatures, with 15,960 needed to force an election. Thus, the number of necessary challenges is 7340.
Excluding phone challenges, Democrats challenged 6362 signatures to the Holperin recall petitions, and they sampled 534 people, of which 9.2% indicated that their signatures should be invalid (by reason of falsely obtained, or never given in the first place.)
We assume that 95% (6044) of the challenges will be successful. This leaves 17256 purportedly valid signatures.
Arriving at the phone challenges, the standard deviation of such a sample is 1.3%, which we multiply by 1.5 to receive 1.947%. Thus, the invalidly obtained signatures are normally distributed around the value of 1588 + / - 336. For the petition to be valid, less than 1296 of the remaining signatures must be invalidly obtained. We may now use the normal distribution to determine the result.
Given our assumptions there is a 78.2% chance the Holperin recall petition should be invalid.
Other possible results from different assumptions:
- If we assume 90% of the challenges are successful, with other assumptions the same, the probability is 48%
- If we ignore assumption #3 (with all other factors kept constant), the probability is 90.4%.
Wirch recall
The Wirch recallers submitted 18,300 signatures, with 13,537 required. Democrats challenged 3882, and claimed that 6.6% of 225 surveyed said that their signatures were invalid.
After non-phone challenges, there will be 14,612 signatures remaining (assuming 95% success rate.) Extrapolating from the surveys, 964 + / - 438 of the remaining signatures are invalid.
Hence, given our assumptions, there is a 40.13% probability that the Wirch recall petition is invalid.
Hansen recall
The Hansen recallers submitted roughly 18,900 signatures, with 13,852 required. Democrats challenged 4992, and stated that 8.6% of 372 surveyed said that their signatures were invalid.
After non-phone challenges (assuming 95% success rate), there remain 14,157 signatures. Extrapolating from the surveys, 1217 + / - 330 are invalid.
Thus, given our assumptions, there is a 99.7% probability that the Hansen recall petitions are invalid.
Other possible results from different assumptions:
- If 90% of challenges are valid (vs 95%), with all other assumptions the same, the probability is 97.9%.
My conclusions: Given the Democratic challenges and survey results, the Hansen recall is almost certainly invalid (which makes sense, as it featured the highest number of out-of-state paid petitioners and other shenanigans), while the Holperin recall is probably invalid (call it 75/25), and the Wirch recall is iffy (call it 50/50, as my estimates are by no means precise.)
However, it's uncertain whether the board will allow such evidence. Specifically, it's probably unlikely that they would allow statistical extrapolation as I performed (after all, it relies on Democratic reports of their surveys), so it's much less conclusive how they will rule.
My two cents, at any rate.
(Note: Parts of this diary may resemble parts of the Wikipedia article in question, but that's because I wrote the relevant sections of the article. Really.)
Update 1:
Through examination of the #s, it appears that there was a typo in the Democratic press release.
* Senate District 12: Of the 534 people contacted who had signed the petition, 9.2% indicated they were misled into signing the petition or asserted they had never signed.
* Senate District 22: Of the 225 people contacted who had signed the petition, 6.6% indicated they were misled into signing the petition or asserted they had never signed.
* Senate District 30: Of the 372 people contacted who had signed the petition, 8.6% indicated they were misled into signing the petition or asserted they had never signed.
Based on examination of the challenges with the GAB, it appears that the number of people listed as contacted (534, 255, 372) are actually the number who reported their signatures as invalid. If we assume that to be the case, the number of surveyed people are much larger (respectively, 5804, 3409, and 4325.) Consequentially, the standard deviations decrease considerably to 0.394%, 0.514%, and 0.456% (or after the 1.5x factor, to 0.591%, 0.771%, and 0.684%.)
Thus, retaining our previous assumptions, the percentages are:
Holperin recall: The expected number of invalid signatures (from phone challenges) are now 1588 + / - 102. Thus, we require a 2.863-sigma result, so the probability the petition is invalid is now 99.7%
Wirch recall: The expected # of invalid signatures are now 964 + / - 113, so the petition is invalid with probability 16.3%
Hansen recall: The expected # of invalid signatures are now 1217 + / - 97, so this is a 9.4-sigma result. Hence, we can't use the normal distribution approximation. Instead, I use Hoeffding's Inequality to estimate the maximum probability. Here, n=14,157, p=0.086, and k=305.
The probability is thus at least 1-e^(-117.6)
Or rather, the probability that the petition is valid is at most 10^(-51). This is of course a ridiculously precise result; in such a scenario, we have to consider other sources of error as well (in the # of valid challenges, for instance.)