Both the internet searches and the Regrexit movement are indications of the impact of political ignorance on the vote. But we should not make too much of this kind of evidence. Regarding the searches, we do not have good data on how many people are doing them, or even whether they voted for “leave” or “remain.” We also don’t yet have systematic survey data on how many pro-Brexit voters are now in a Regrexit mood because they feel they were duped or misinformed [but see update below on some very limited data pertaining to this].

Some (as yet undetermined) number of Leave supporters have indeed come to regret their decision. But there might also be some Remain voters who today prefer the Leave option. Data from past elections indicate that there is a often a significant “bandwagon effect” that leads people to shift their views in favor of whichever side seems to be winning. In post-election polls, it is common to see a higher percentage say they voted for the winning candidate than actually did. People like to identify with a winner and dislike being associated with losers. Although media coverage has not focused on it, it’s possible that the Leave camp is benefiting from a similar bandwagon effect. That, of course, does not mean that Brexit was a good decision. Bandwagon effects are themselves often the result of ignorance. But the possibility of bandwagon effects cautions against drawing any hasty conclusions to the effect that a majority of British voters have come to regret last week’s result. It could be that the majority in favor of Brexit is as large, or even slightly larger, today than it was on the day of the vote.

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Despite such caveats, we do in fact have more systematic evidence indicating that the result of the Brexit vote may have been significantly influenced by ignorance. Preelection survey data indicates that many voters were significantly misinformed about many of the issues at stake in the Brexit debate. And the direction of these errors largely favored the Leave option. On average, voters greatly overestimated the number of EU immigrants living in Britain and the amount of child welfare payments given to them by the British government, while greatly underestimating the extent of EU investment in the UK. Polls showed that both fear of immigration and economic concerns were among the top issues on voters’ minds. Widespread ignorance likely gave the Leave side a boost on both issues. Especially given the closeness of the vote (Leave prevailed by a narrow 52-48 margin), it is quite possible that the result would have gone the other way if the electorate had been better-informed.

That does not necessarily mean that the voters made the wrong choice. Although I personally believe that the British should have voted for Remain, I also recognize that there were strong arguments in favor of Leave and that the issue is a very difficult one. In my book on political ignorance, I describe a number of scenarios where political ignorance actually has beneficial effects. Perhaps the Brexit vote was another such case, though these sorts of situations are very much the exception rather than the rule.

Even so, it is troubling that there was widespread ignorance on a vote of such great importance. Sadly, British voters’ ignorance about Brexit-related issues is just one example of the broader phenomenon of rational political ignorance, under which voters make little effort to learn about politics and public policy because the chance of any one vote influencing the outcome is extremely small. Such ignorance is common in Britain, the United States, and around the world.

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Georgetown Professor Jason Brennan, one of the world’s leading academic experts on voting and political knowledge, argues that the Brexit case suggests that we should not allow such decisions to be made by popular referendum. Perhaps it would have been better if the Brexit question were decided by Parliament, whose members, on average, know more than the voters do, and who overwhelmingly oppose Brexit. They could still potentially veto the referendum result by refusing to follow through on it.

Brennan is right to argue that referenda are often influenced by ignorance. But it is not clear that leaving more decisions to elected officials will improve the situation. As Brennan recognizes, public ignorance also heavily influences our choices on who to vote for in regular elections. Candidates and parties are well aware of that, and their platforms are heavily influenced by the need to cater to poorly informed voters. In some respects, elections are even more susceptible to the influence of ignorance than referenda are. In a parliamentary election (or a presidential election in the United States), there is an extremely wide range of issues at stake, which makes it difficult or impossible for the voters to be well-informed about more than a small fraction of them. By contrast, a referendum can focus on a single, discrete issue, which may reduce the information burden on voters.

In some cases, referendum initiatives actually lead to better policy than legislative decisions. For example, in the aftermath of the Supreme Court’s flawed decision in Kelo v. City of New London, allowing state and local governments to condemn property for dubious reasons, reforms enacted by referendum initiatives generally provided stronger protection against abusive takings than those enacted by state legislators.

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This is not to say that referenda are systematically better than conventional elections. Sadly, the problem of political ignorance besets both. If we want to mitigate its effects, we should consider making more of our decisions outside the electoral process entirely. When people “vote with their feet,” they usually have better incentives to seek out information and use it wisely than when they vote at the ballot box.