Liberal observers are astonished and thrilled that Judge Richard Posner, the most influential judge sitting on the federal bench, has written a scathing condemnation of Wisconsin voter ID laws. Posner was appointed by Ronald Reagan, and his law-and-economics approach with its libertarian overtones can in a certain sense be described as conservative. Notably, Posner wrote a 2007 opinion upholding Indiana’s strict voter ID law — an opinion subsequently upheld by the Supreme Court. Now, it would seem from the headlines, Posner has reversed himself. Newsworthy, right?

Well, sort of. A close reading of Posner’s opinion indicates that the judge hasn’t so much reversed his earlier view as he has taken seriously data that were unavailable in 2007. The numbers, as Posner now interprets them, do strongly suggest that the purpose of voter ID laws is to make it more difficult for poor people, especially blacks and Latinos, to cast votes. According to Posner, he wasn’t wrong in 2007. It’s just that then, there was no basis to assume that Indiana was trying to exclude minority voters. Now, there’s evidence in favor of that view.

A careful look at Posner’s opinion is an object lesson in how a rational person should reconsider initial presumptions in light of new evidence — an approach pioneered by the British statistician Thomas Bayes in the 18th century and now dubbed Bayesianism. When Posner had to analyze the Indiana statute, he made much of the fact that, as he now puts it, “there was no evidence that the Indiana law was likely to disenfranchise more than a handful of voters.”

One of Posner’s then-colleagues, Bill Clinton-appointee Terence T. Evans, depicted the Indiana voter ID law as “a not too thinly veiled attempt to discourage election day turnout by certain folks believed to skew Democratic.” But, as Posner pointed out in his most recent opinion, Evans “cited no evidence to support his conjecture.” In Posner’s current view, Evans was “prescient” — but prescience is a form of prophecy, not a form of reasoning based on evidence. Posner believes that he was correct not to take account of his colleague’s speculations in 2007.

Since then, the nature of the evidence has changed. According to Posner, in the 2007 case, 1 percent of Indiana’s population lacked the relevant ID. Yet 9 percent of registered voters in Wisconsin lacked the documents required by its state law. Posner went on to describe the extraordinary “litany of practical obstacles” a person would have to overcome in order to vote without a driver’s license in Wisconsin. He added that although Indiana’s voter rolls were inflated by as many as 1.3 million people, “there is compelling evidence that voter-impersonation fraud is essentially nonexistent in Wisconsin.” Posner was apparently impressed by an expert witness who had “studied Wisconsin elections that took place in 2004, 2008, 2010, and 2012 [and] found zero instances of in-person voter-impersonation fraud.”

Then Posner moved on to the macro-level data. He noted that “all the strict photo ID states are politically conservative, at least at the state level.” The pattern might have been intuited in 2007, but it was not yet systematically established. Posner was dismissive of what he used scare quotes to call the “evidence” of voter impersonation fraud. In terms rarely used by appellate judges, he called the fake evidence, “downright goofy, if not paranoid.”

Finally, Posner, who is noted as a theorist not an empiricist, offered his own take on why voter-impersonation fraud should be very unlikely. His reasoning was characteristically blunt: Individual voters get almost nothing out of casting their votes. He wrote: “Voting is a low-reward activity for any given individual, for he or she knows that elections are not decided by one vote.”

Why waste the time and take the risk of getting in trouble if you’re only getting one vote at a time for your preferred candidate? What’s more, Posner added, it would be too risky for most politicians to orchestrate “a massive campaign of voter-impersonation fraud.” They would probably get caught, and the punishment would be severe. Strictly speaking, this theorizing went beyond the evidence, and Posner could have relied on it in 2007. But nobody’s perfect. Most likely, Posner just couldn’t resist overlaying some theory on the evidence he gathered.

The main takeaway is that Posner has now allowed evidence of discriminatory effects to overcome his initial belief that the state of Indiana should not be assumed to discriminate. Does this logical progression merit praise?

By Posner’s own lights, it shouldn’t. He is, and has always been, a staunch advocate of following the facts where they lead. By temperament and philosophy, the judge has always been a kind of pure embodiment of abstract reason, seemingly untouched by ordinary humans’ sympathies or passions. His most egregious views — to be fair, mostly expressed in lectures and books rather than judicial opinions — have always shocked precisely because of their apparent unfamiliarity with human emotion. (Think of his notorious, and morally outrageous, economic analysis of rape.)

So if we asked Posner whether he deserved special approbation for relying on newly available evidence, he would certainly say no. A Bayesian judge updates information constantly, Posner would say. Don’t give him a medal for it.

Yet in this time of partisanship, perhaps we can be excused for praising a man who lets the data do the talking. But let’s be careful not to do so only when we like his judgments.

[Cross-posted at Bloomberg View]

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Noah Feldman

Noah Feldman , a professor of constitutional and international law at Harvard, is a Bloomberg View columnist.