Would a second Referendum on Brexit change the result?

A number of the Brexit (Leave) supporters are now unhappy with the actual outcome of the 23 June Referendum.

Is it because they were made aware of some new information? Apparently not all the promises that were made by the Leave campaign will be honored.

It is, however, possible that a second Referendum could change the result even if there were no new information about the consequences of a possible British EU exit. This possibility is to do with strategic thinking.

The typical voting model of a zero one decision (stay or leave the EU, in the present case) is such that all voters simply have a preference over the two outcomes. Some prefer to stay, some prefer to leave. If this is the case, voters do not have to engage in deep strategic thinking to simply vote their preference. In game theory jargon “voting for one’s preferred outcome is a (weakly) dominant strategy”.  The referendum will then simply demonstrate which of the two outcomes is favored by more people. Another referendum without any new information cannot change the result.

In the present case, however, many voters started googling “What is the EU?” only after the result of the Referendum became clear. Could it be that at least some of the leave voters did not really want to leave but simply wanted to make a statement of dissatisfaction? If this is the case, then some voters’ preferences could be as follows. Yes, they would prefer to stay in the EU, but they would like the result to be close. If you have such preferences and think that the result will be clearly in favor of staying in the EU – the bookies always saw Stay as the much more likely outcome – then you might cast your vote for the Leave campaign.

If enough people think so, then the ultimate outcome could be paradoxical. A majority of people vote to leave even though a majority of people actually prefer to stay. If this is the case a second referendum might correct this and reveal the true sentiment of British voters on the EU.


6 thoughts on “Would a second Referendum on Brexit change the result?

  1. Very interesting thoughts! However, the “google” as well as the “regret” argument may be rather myths than truths. Although the quoted google search statistics went viral few days after the referendum in social media networks, the mentioned effect is large only in relative terms. Whereas approximately 300 individuals in Great Britain googled “what is the eu” before the referendum, the number increased after the referendum to roughly 1,000, i.e., an increase by more than 300%. Given the population of Great Britain the absolute number is however still negligibly small.
    Media reports give the impression that the entire island is upset about the vote in favor of Brexit. According to a poll by ComRes it is rather the remain camp that is unhappy: 88% of them do not like the result. However, 92% of the leave voters are happy with the results. The important question remains whether the roughly 30% non-voters might care more in a second referendum.

    The links in this post were taken from a FAZ article about “referendum myths”.

    • Thanks, Sofie, for sharing this link which indeed uncovers some wildly held myths about this referendum (e.g. immigration was not the most important factor for Brexit voters).
      Related to that, the linked article above claiming that “not all the promises that were made by the Leave campaign will be honored” seems to be largely based on statements by Remain supporters. I would like to see some serious fact checking (who promised what? which promises won’t be honored?) before I believe the charge.

  2. Very interesting hypothesis which I’d like to see tested empirically soon. One comment on the betting odds.

    Yes, the betting odds did imply a low probability of Brexit and I relied on those odds to calm myself and others that Brexit would probably not happen. But it’s not difficult to see – and I’m still tearing my hair out for not seeing it in advance – why those betting odds were severely biased in favor of the Remain side. It’s a safe guess that it’s mainly the rich and educated who participate in betting markets – exactly those groups which predominantly voted for Remain. Therefore the market-based Brexit probability probably relied on a highly non-representative sample.


  3. Interesting hypothesis indeed! I would add that people depended to some extent on the trustworthiness of the respective politicians when forming their preferences (Will this cause rising unemployment? Will the UK fall apart?). Since the aftermath of Brexit has already brought some changes there, also the result might change. I would also like to remark on Max´s idea that mainly the rich and educated bet which biased the odds towards remain. According to http://deutsche-wirtschafts-nachrichten.de/2016/06/23/buchmacher-brexit-wenige-hohe-wetten-treiben-spekulation/ (which I agree is not the most reliable source but nevertheless) it was precisely the other way round. The majority of bets were on Brexit while the bias resulted from a few large bets on remain. The interesting story is that these few bets actually enabled Brexit. Many newspapers and reporters took the odds as the most reliable source for forecasting the result. With the odds pointing in a different direction the Pound Sterling would most likely have come under pressure the days before and at the day of Brexit. I seriously doubt if the extremely close result wouldn´t have turned round if the voters had seen stock markets crashing and the Pound dropping by 20% before voting.

    • Well doesn’t that support my claim? The biggest bets, which presumably come from the rich, were on the Remain side thus skewing the odds in favor of Remain. Of course it’s the relative amount of money wagered on each outcome that determines the odds, not the relative number of wagers.

      “I seriously doubt if the extremely close result wouldn´t have turned round if the voters had seen stock markets crashing and the Pound dropping by 20% before voting.” That depends on how much weight the marginal voter gives to economic factors. According to Sofie’s source the most frequently mentioned deciding factors for Brexit voters had little to do with the economy, but more with “gaining back sovereignty” (53%) and “controlling immigration” (34%). Also, the fact that only a small fraction of Brexit voters report to regret the result is evidence that they are quite unimpressed by falling stocks and exchange rates.

  4. Well, I had understood your point that primarily rich people participate in betting which drove the odds towards remain not the fact that rich people will most certainly tend to bet higher sums. But no matter. The fact that sovereignty and immigration have been the dominant issues for Brexit voters do not really counteract my argument since this does not tell us under which assumptions about the economy the Brexiteers decided. I just can´t imagine many people voting for Brexit if they had expected a high probability of losing their job afterwards. True, the fact that only few seem to regret their decision counteracts me to some extent, but on the other hand such polls have a considerable amount of uncertainty and it would not have needed many people changing their decision to overturn the result.

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