The Colombia Referendum and the Magic 50% Threshold

This is a follow-up to the article I wrote with Neil Johnson on the Colombia peace referendum.

I learned a lot from the comments that were posted both for the original write-up and on the blog of Andrew Gelman.  This comment, in particular, seems important to me:


The problem here is naive dependence on simple majorities. Even if the referendum had passed by 100,000 votes, the correct response is to not conclude the treaty with FARC. Simple majorities are not stable under perturbations.

For another example, Brexit should have required (say) a 60/40 vote. For a third, entrance to the EU should have required 60/40, making Brexit moot. If there would still be an EU, it would have institutions that are more robust, although with a smaller scope.

The main point seems to be that there is an enormous and unwarranted discontinuity at 50%.  In the Colombia case it appears that a fraction of a percentage of the votes can make the difference betweeen war and peace, at least on the face of things (although now it seems that the choice is less stark than this – see below).

We don’t know for sure what would have happened if the treaty had prevailed by 50.2% to 49.8% but it seems likely that it would be full speed ahead for implementing the treaty.  This would be a pretty risky course of action in the face of so much opposition as Dzhaughn points out.  In other words, he/she thinks I was barking up the wrong tree with my article because implementation shouldn’t have gone forward anyway, even if “yes” had registered a narrow win in the count.

That said, Dzhuaghn and I do seem to converge on the view that the result was more like a draw than a win.  Of course, under the rules there is no such thing as a draw.  There is just a big discontinuity at 50%.

Still, the Colombian government does seem to be treating the referendum result kind of like a draw.  They aren’t saying “we lost so we’re going back to war.”  Rather, they seem to have concluded that they need to listen to the opposition, try to address their concerns and gain approval (somehow or other) for a new peace treaty.  The Nobel Peace Prize Committee seems to be thinking along similar lines.

Of course, whether or not this all works out in the end is an open question.

But a strange thought occurs to me.  It could be that the narrow loss yields a greater chance for a building a sustainable peace than a narrow win would have done.  Now at least the FARC knows that they have to renegotiate.  With a narrow win it would have been very hard to get FARC support for mollifying the opposition.   This reinforces the case for having an official category of “draw” in such referenda.

A couple final thoughts.

I’m not impressed with the way some people invoke low turnout ( < 40%) as further evidence that support for the treaty is really weak.  This argument cuts both ways.  You can say that only 20% of the population turned out to support the treaty so it has really weak support.  But you can just as well say that only 20% of the population bothered to vote against the treat so it also has really weak opposition.

Finally, I’m sure some people are wondering whether I still think that “yes” might have had more votes on voting day than “no” did.  As of now I wouldn’t totally rule out this possibility but I think it’s pretty unlikely.  One thing I learned from online comments and private emails is that the counting process was better managed than I thought at the time that I wrote the article, at least in the areas where my correspondents worked.

I’m still puzzled by the high number of blank and nullified ballots on such a simple yes-no vote.  Someone on Andrew Gelman’s blog suggested that maybe voters wanted to assert their rights to vote but without taking a stand.  I guess this is possible but somehow I  doubt that many people would behave this way.  So I don’t know for sure what happened although I do think that “no” probably did have more votes on the day.

Summing up, I hope that over time the referendum will come to be seen more as a draw than a loss and that the peace process will move in a positive direction.



Article on the Colombian Referendum

Please have a look at this new article on Colombia’s peace referendum that I’ve just written with my long-time co-author Neil Johnson.

The point is that there are many sources of statistical error in the counting process for the referendum to the point where it would be more reasonable to call it a draw than to call it a win for “no”.