British PM Theresa May is racing to secure passage of a Brexit deal by the March 30, 2019 deadline. There are important questions about the wisdom of her current proposal, but I am in no position to evaluate them. I wish instead to question the premise of the plebiscite that began this spiral. The Brexit referendum passed in 2016 with less than 52% support. Current polls show it would not pass a second time, having just 49% support.
A plurality vote is a meaningful threshold for elections (although with many candidates, instant runoff voting may be smarter). For a choice must be made, and any mistakes can be undone at the next regularly scheduled election. But ad hoc referenda are entirely different, and a 50% hurdle makes no sense. For since these need not be held, they essentially commit voters in the distant future to the current vote outcome. Economists call these irreversible decisions, as they may entail extraordinary transition costs (like Brexit surely will) and/or costs to undo. As such, a purely myopic hurdle, such as a bare plurality, is not optimal. Societal choices should reflect the will of the people, and as this evolves over time, irreversible votes should not be taken lightly. For instance, most nations impose a higher bar for constitutional change than for passing a law. The more irreversible the decision, the higher the bar should be.
A second consideration is that referenda can be strategically timed, and often arise at times of great popular enthusiasm, like Brexit did amidst the backlash to a refugee crisis. For instance, Quebec twice held referenda to separate from Canada — in 1980 and 1995 — when it deemed the separatist fruit ripest. Polling volatility is as real as stock market volatility, and a peak of 52% support inevitably arises, even if the average support is, e.g., 40%. Referendum outcomes ideally should reflect the preferences of voters for their anticipated duration, and this demands a higher support threshold for irreversible referenda. For the support at the time of vote statistically will overstate the time average support, given mean reversion.
How valuable is the option to optimally time votes? In a paper I co-wrote in 2008,“Optimal Electoral Timing: Exercise Wisely and You May Live Longer”, we solved for the optimal election timing decision of British Prime Ministers, before fixed terms were introduced in 2011. We used the time series of Gallup polling data (seen above) to estimate an intuitive model of the polling support for the two major parties. We solved for when a government should call elections, if it was solely motivated by a desire to maximize its expected time in office. This cynical assumption turned out to be remarkably accurate — it explained 45% of the variation in election timing from 1945–2005! We then computed that this flexibility to time elections within a five year window approximately doubled the expected time in power for any British government!
The 50% threshold was taken as self-evident by Quebec in its two quests for independence; it only very narrowly missed this threshold the second time in 1995, losing with 49.4% support. Catalonian separatists likewise assumed a 50% threshold sufficient to call for independence in 2017. And by design, the Brexit vote required a bare plurality. But while the Brexit process has been a failure in many ways, mostly it has been a failure to profit from political economy insights. If we wish an ad hoc referendum to reflect the will of the people, it is not inaccurate to think of the 50% threshold as anti- (economic) science.