I’ve been thinking about a potential second Brexit referendum, where a three-option menu is given:

• 1: Exit the EU with no deal
• 2: Accept the negotiated deal
• 3: Remain in the EU

Three-way choices are alien to British experience of referendums, but don’t really pose great difficulties. First Past The Post (FPTP) is clearly undesirable, but instant runoff (IRV) and Condorcet voting are easy to implement and explain to the electorate. So I built a little simulation to help me understand the problem, particularly to look at the relative performance of IRV and Condorcet.

My conclusions in brief: Condorcet is much more likely to go for the compromise solution (the deal), IRV less so and FPTP the least. Condorcet also seems to correspond well with the average of the underlying utilities. When the population is skewed pro-leave or pro-remain, IRV and Condorcet give more similar results (because it becomes more of a two-horse race). Condorcet cycles are rare. Finally, FPTP is crap.