One of the truly gratifying aspects of this blog is the expertise offered by readers, both in the comment threads, and through private email. For example, my analysis of the legal issues surrounding the election contest lawsuit would not be nearly so coherent (or accurate) without the invaluable help of Lawyer X. Likewise, I have been greatly aided in understanding the intricacies of the GOP’s proposed “proportional deduction” by a reader whom I would call Statistician X… if not for the fact that you all know him as DJ, a frequent contributor to the comment threads.
In recent days, the Rossi camp’s spin has veered away from the felon vote, and back towards the “total mess” thesis… an unsurprising tactic considering the number of offsetting illegal votes the Democrats have alleged. But this shift is also likely due in part to the report recently issued by the Democrats’ expert witness, Christopher Adolf, who effectively exposes the Republicans’ data as “unrepresentative”, their methodology as “flawed”, and their entire case as “hopeless”.
DJ has graciously summarized Prof. Adolf’s report for me, and not surprisingly, found that his arguments largely echo the same arguments DJ has made in the comment threads here and elsewhere. As DJ modestly explains, any statistician doing an objective analysis should reach the same conclusions. But I’ll just let DJ explain it in his own words… think of it as a kind of guest blog.
Professor Adolph states the first flaw this way: “Use of a non-random, non-representative, and incomplete sample of invalid votes … is useless for answering questions about the net effect of all invalid votes on the state-wide election outcome.”
The take home message is that the Republican’s invalid voter data are not suitable for any type of statistically or scientifically valid analysis.
Essentially, there were systematic biases in collecting the invalid ballots. The invalid votes are not drawn randomly or representatively across the state. Adolph did a very simple analysis to demonstrate this fact using the Republican and Democrat invalid voter lists. The Republican list was certainly cherry-picked. The Democrat list was cherry-pocked, too, but that is partially an artifact of the Democrats going to the precincts that the Republicans ignored.
Adolph points out that “[o]nly a complete statewide census, or a random or representative sample, has any hope of offering an unbiased estimate of the effect of invalid votes.” What should the Republicans have done? “Only if the Rossi campaign put as much effort into searching for invalid votes in precincts they won . . . as in precincts they lost can we begin to trust the experts’ reports.” (This is identical to the “equal scrutiny” argument I was making.)
Professor Adolph goes into much detail on the ecological fallacy in both Professors Katz’s and Gill’s analysis. He points out that “Modern, accepted [statistical] methods would provide strong warnings to the researcher that ecological inference in this case is impossible.” In other words, Katz’s and Gill’s arguments constitute an ecological fallacy. Both of the Republican expert witnesses make a single critical assumption that vote choices within any sub-population in a precinct are the same as the average vote choice in the precinct as a whole. “This assumption is strong, implausible, and unwarranted. Moreover, it flies in the face of decades of warnings from social scientists and statisticians. . . .” (Adolph).
To demonstrate this, Adolph first provides some technical background on Gary King’s solution to the ecological inference problem (which is state-of-the-art social science). I will skip the technical details, except to say that ecological inference can work under some conditions. One condition is that the groups about which we wish to make inference are represented in high enough numbers to provide mathematical limits (or bounds) on their characteristics.
For the 2004 election, it would be necessary that a reasonable fraction of the votes within precincts were invalid votes in order to infer the limits of their voting behavior from the aggregate voter data. Such is not the case. In all 1,344 precincts in which invalid votes have been identified, none of them have a high enough fractions of invalid votes to set these “bounds” and infer felon voting patterns out of the aggregate patterns. This is mathematical fact, not opinion. “The bounds [test] show[s] it is possible that every invalid vote in every precinct was cast for Rossi. Alternatively, every vote may have been cast for Gregoire