Brexit as hypothesis testing

last run on Clifton and Durdham Downs, Bristol, Jan. 27, 2012While I have no idea of how the results of the Brexit referendum of last Thursday will be interpreted, I am definitely worried by the possibility (and consequences) of an exit and wonder why those results should inevitably lead to Britain leaving the EU. Indeed, referenda are not legally binding in the UK and Parliament could choose to ignore the majority opinion expressed by this vote. For instance, because of the negative consequences of a withdrawal. Or because the differential is too little to justify such a dramatic change. In this, it relates to hypothesis testing in that only an overwhelming score can lead to the rejection of a natural null hypothesis corresponding to the status quo, rather than the posterior probability being above a mere ½. Which is the decision associated with a 0-1 loss function.  Of course, the analogy can be attacked from many sides, from a denial of democracy (simple majority being determined by a single extra vote) to a lack of randomness in the outcome of the referendum (since everyone in the population is supposed to have voted). But I still see some value in requiring major societal changes to be backed by more than a simple majority. All this musing is presumably wishful thinking since every side seems eager to move further (away from one another), but it would great if it could take place.

4 Responses to “Brexit as hypothesis testing”

  1. David Draper Says:

    hi christian

    thanks for this thoughtful post

    it seems more natural to me to formulate the problem decision-theoretically rather than with hypothesis testing

    in that regard, the brexit situation reminds me strongly of the decision about whether to launch the challenger space shuttle back in 1986

    consequences of problem ‘positive’ decision ‘negative’ decision false positive false negative

    challenger launch don’t launch catastrophe wait and launch later

    brexit leave europe status quo economic slow- status quo moving train-wreck, many other bad things, …

    when you look at this table, you don’t even need to estimate probabilities — the decision in both cases is clear across an extremely wide range of probabilities

    comments?

    all best wishes, david

    • Thanks, David: indeed, this problem is a decision-theoretic problem and not a test! At least for the (few) rationally minded voters. What I saw in the comparison with testing is completely decision-theoretic as well, in that the probabilities per se are meaningless when not incorporating the consequences. And dire those will be! Best, X

  2. Like the point but for this to be done, one should have defined the prior in advance, while Cameron always promised he would have just followed the consultation results. Unfortunately I think it’s too late now…alea iacta est

    • True fact. But since Cameron seems to leave the burden to his successor, why would anyone else feel committed?! Funny enough, I was under the impression in the past days that France had rejected Maastricht by a referendum that was then ignored, but I was confused with the 2005 French referendum (another “great” initiative of Jacques Chirac) which rejected the European Constitution and had no visible effect.

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