# The Brexit cycle

EDIT: the pollster has corrected an error. May’s deal is a Condorcet winner after all (i.e., it would beat either of the other options in one-on-one competition.) The Delta Poll blog post about the poll has been corrected, without any indication of the previous error, although its author did note the error on Twitter. The first pie diagram in the image has the numbers reversed.

_______original post below

Sometimes it just really is awesome to be a political scientist. You see, we have a large literature on the theoretical problem of preference cycles. But they don’t ever happen in real life, right?

Or we could depict it the following way, which makes clearer why it is called a “cycle”:

## 10 thoughts on “The Brexit cycle”

1. Tom Round says:
• Tom Round says:

That poll asked for second preferences as well?!! — So some lucky Britons get two votes on Brexit, while everyone else only gets one?!! Niall Ferguson, throw yourself under Prince Harry’s racehorse at once to protest this gross departure from the UK’s nine-centuries-old unbroken tradition of political equality! https://en.wikipedia.org/wiki/Women%27s_suffrage#cite_note-ag-5
/ Sarcasm off

• Yes, the post has been updated accordingly.

2. MIke says:

Ah well, it was fun while it lasted.

3. Bob Richard says:

For reasons I can’t articulate, it seems to me that cycles are more likely when there are more than three choices, and very unlikely when there are exactly three choices. Does anyone know of research, analysis or speculation (better informed than my own) on this point?

• Dave Hutcheon says:

The Wikipedia article “Condorcet Paradox” says there is 8.77% probability of a cycle in the case of 3 choices. I don’t understand the mathematics that leads to that number.

Reference 10 seems to say that the cycle probability increases as the number of choices increases. I can’t follow the math in ref.10 either, but it does have a nice historical intro.

• Bob Richard says:

Thanks, Dave. I think the Gehrlein paper (Reference 10) does support my hunch that the probability of cycles increases as the number of candidates increases. But I think that all specific numerical results (e.g. 8.77%) are derived from abstract models that don’t think have much to do with real voters in real elections.

4. Of course, it’s even not a simple three-way question (remain-deal-no deal) because the survival of May is at stake too: e.g. I prefer deal over no deal but is it more important to me to see May fail? With what kind of strategy can I trigger an early election or a second referendum if that’s more important to me than the question pro/contra May’s deal?

I think a grand coalition would have been better, because it’s an exceptional phase the UK is going through, Brexit is the most important fork in their road since … and once decided, the deal will be very difficult to reverse, so a one time near-consensus is better suited for this kind of decision than shifting bare majorities

5. John says:

Still, there could be a lesson to learn from this on Condorcet vs. IRV. In this poll May’s deal is only ahead of no deal by slim margin in first-preference votes. It is conceivable that May’s deal could be the Condorcet winner in a referendum with these three options, yet an IRV loser because it would gather so few first-preference votes that it is knocked out in the first round of counting. Something to consider if Britain does decide to hold another referendum to settle this matter.

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