The House of Commons cannot resolve its division over Brexit with repeated divisions

The current approach to determining the will of the House of Commons is not up to the task. Parliament must acknowledge this and find a new way.

Parliament can appear to be a strange beast. Back in January, the Prime Minister’s Withdrawal Agreement was defeated by 432 votes to 202, an historic majority of 230 against the Government, and on its key executive agenda item.

And yet the Withdrawal Agreement lives on. For a while May said she was listening and reaching out while reinforcing her previous red lines. Plan B was presented with no discernible difference from Plan A. Then she took the extraordinary approach of instructing her own MPs to take a hatchet to the agreement she made in the first place, with the intention of showing the EU27 what they would need to offer to negotiate an exit with a deal.

On the other hand, the People’s Vote campaign for a second referendum has suffered (in many People’s Eyes) a terminal set-back, after it was not voted upon. Yes, it is clear that it would have been defeated, but it is not clear it would have been more heavily defeated than May’s plan, which is still the only show in town.

The House of Commons is struggling with the challenge of reaching a majority in favour of anything (rather than majorities against things, which are much more manageable). It is clear there is no option which is the first preference of a majority of MPs, and those MPs are reluctant to lend their support to other options while their first preferences remain in the game.

So the issue of sequencing is critical.

May wants to knock down all options until the only two options remaining are her Withdrawal Agreement and a No-Deal Brexit.

Other groups have the same aims (to be among the last options standing), and the No-Deal Brexit option is immovable without the support of the Prime Minister, and she has no interest in moving it.

There is procedural precedent in Parliament for narrowing down options until there is one winner. Elections of the Speaker (and of the Conservative party leader) are conducted by runoff ballots. Each elector indicates their most preferred candidate, and in each stage, if no candidate has a simple majority (50% plus 1), candidates are dropped with the lowest support. The electors vote again (possibly for a different candidate) and the procedure continues until a candidate has a simple majority.

This procedure allows for widespread tactical voting, where MPs knowingly vote for something which isn’t their most preferred option in a round, in the interest of improving the chances of their most preferred option eventually winning.

Consider, for example, if there are four options being considered, and their support in the first round if everyone voted honestly would (hypothetically) be:

Option1st Preference Votes
Withdrawal Agreement236
Second Referendum162
EEA/EFTA126
No-Deal Brexit115

In this hypothetical example No-Deal Brexit would be eliminated first, with the vast majority of the MPs then switching their support to EEA/EFTA. This would cause EEA/EFTA to leapfrog Second Referendum, and then ultimately leapfrog the Withdrawal Agreement to win.

However, if proponents of the Withdrawal Agreement or Second Referendum vote tactically to put No-Deal Brexit ahead of EEA/EFTA, then it is likely the final round will be a straight fight between those two options.

Even if MPs are required (as would be the case in an instant runoff vote) to indicate all their preferences in one go, there is still the potential for tactical voting if sufficient information is known by MPs about the nature of other MPs’ preferences.

Worse still, this method can fail to identify when one option would actually trump all others in head-to-head votes. It might do so by constructing different coalitions each time, but it must surely be considered the most appropriate decision. This is the Condorcet winner (if it exists).

A number of voting systems will select the Condorcet winner if it exists, but they can produce different results if there is no Condorcet winner, and they are still subject to tactical voting.

The only way forward, in my mind, is for a process in which:

  • MPs list their preferences – MPs need to set out a logically consistent position that they are held to
  • It is a free and secret ballot – MPs must be free to say what they truly think is best for the country
  • The anonymised results are made available in full – Parliament needs to be accountable for the decisions it makes given the information

If there is a Condorcet winner it is highlighted and MPs are asked to support this in a simple up-down vote to acknowledge that whatever options they may prefer, they would lose in a head-to-head vote against the Condorcet winner.

If there is no Condorcet winner then MPs are shown how various different voting systems would lead to particular outcomes (assuming no MPs changed their preference lists tactically). The systems should include:

  • One or more recognised Condorcet methods
  • Presentation of the Smith set (the smallest non-empty set of options which can beat all options outside the set) – MPs could be asked to reject all options outside the Smith set
  • Instant runoff voting (a.k.a. Alternative Vote)
  • Coombs’ method (like instant runoff voting, but instead of eliminating the candidate with the least top preference support, the candidate with the most bottom preference support is eliminated; each round is a simulated rejection of the most unpopular remaining candidate on a plurality basis)
  • Borda method (first choice gets 1 point, second choice gets 2 points, etc. and the option with the lowest total points is the winner)

Debate would then be needed to determine the next step, according to whether different methods produced different winners. We would be in uncharted territory, but we would at least have a very good idea of the true will of the house, and how many people’s minds needed to change to reach an agreement.

For interest, the underlying hypothetical dataset is as follows:

1st2nd3rd4th5thN
WAEEAPVNDRemain200
PVEEAWARemainND162
EEAWAPVNDRemain120
NDEEAWAPVRemain105
WAEEANDPVRemain36
NDEEARemainPVWA10
EEANDWAPVRemain6

WA, Withdrawal agreement; PV, second referendum (People’s Vote); ND, no-deal exit; EEA, EEA/EFTA; Remain, Stop Brexit

In this example EEA/EFTA is the Condorcet winner, as well as the winner under IRV, Borda and Coombs’ method, but it is only hypothetical!