Proponents of voter ID laws say that they’re necessary to ensure electoral integrity. When we hold elections, we want the candidate who gets the most votes from eligible voters to win, and voter ID is proposed as a way of ensuring that the votes of ineligible voters can’t put a candidate who doesn’t have a majority of support from eligible voters over the top.

But what if voter ID laws created a scenario in which a candidate with less support from the eligible voting population winds up winning?

In a 2015 paper published in the Columbia Law Review, University of Virginia law professor Michael Gilbert makes this case, starting with the following thought experiment:

[S]uppose that without a voter ID law candidates A and B would receive 13 and 10 lawful votes, respectively, and B would receive 2 fraudulent votes. Candidate A wins, 13 to 12, and the outcome is nonfraudulent. Now suppose that with a voter ID law, candidates A and B would get 9 and 9 lawful votes, respectively (less than before because of depressed turnout), and B would get 1 fraudulent vote (less than before because of fraud deterrence). Candidate B wins fraudulently, 10 to 9. The voter ID law caused the problem it was meant to solve.

Implicit in the arguments made in favor of voter ID is the claim that they will block all fraudulent votes while leaving all eligible voters unaffected. If pushed, this is sometimes revised down to the claim that the laws will at least deter more fraudulent votes than they will prevent eligible voters without acceptable ID from casting ballots. But there is no reason to believe that either of these propositions are true, and there is little reason to believe that those who lack voter ID are the only people affected by voter ID laws. To the contrary, all available evidence suggests the opposite. The single biggest observable effect voter ID laws have been shown to have is that they confuse and discourage eligible voters with acceptable forms of ID, lowering turnout people who Gilbert defines as “lawful voters.”

From a real-life version of Gilbert’s thought experiment that played out in a 2014 congressional election:

Jones, Granato and Cross surveyed 400 of the 271,005 registered voters who did not participate in the 2014 election, asking them why they didn’t cast ballots. Voters were asked first to indicate all of their reasons for not voting, and were then asked to select which one was the principal reason for not voting. 12.8% of respondents indicated that a lack of necessary ID was a reason for not voting, while 5.8% of respondents said that it was their principal reason for not voting. Applying that percentage across the entire population of non-voters (insert necessary qualification about margins of error here), that’s nearly 16,000 registered voters in TX-23 who stayed home primarily due to a perceived lack of acceptable ID. However, most of those perceptions were incorrect. When respondents were then given the list of which forms of ID were accepted at the polls, only 2.7% of respondents didn’t have any of them. … While Latinos constituted roughly 66% of the district’s non-voting population, they constituted 77% of non-voters who cited a lack of proper ID as their primary reason for staying home. Those voters also favored Gallego over Hurd by a whopping 54-9 margin — a margin large enough to have proven decisive if even roughly half of them had turned out to vote. Some quick back-of-the-envelope math based on the numbers in the study (again, margins of error excluded) finds that confusion over Texas’s voter ID law was the principal reason why 7089 would-be Gallego supporters and 1430 would-be Hurd supporters stayed home. Had they all turned out to vote, Gallego’s 2422-vote loss would have flipped to a 4667-vote win. For those of you keeping score at home, that’s a swing of just under six percentage points. And again, that’s only including people who cited confusion over the law as the primary reason why they didn’t cast a ballot.

Voter ID proponents can’t point to a recent election in which voter impersonation fraud — the kind of fraud that such laws are meant to prevent — swung the outcome in favor of the candidate who did not in fact have the most support from lawful voters. But in both theory and practice, the case can be made that voter ID laws can and do swing electoral outcomes in favor of the candidate that does not have the most support from lawful voters.

Held to their own standard, these laws sometimes cause the problem they’re meant to solve.