Following last night’s inconclusive votes in the House of Commons, MPs are heading for another round of voting on Brexit options next Monday. The hope is that new voting rules will help deliver a compromise solution. In this post, Alan Renwick argues that a bold approach to the voting system could achieve a great deal – though, ultimately, compromise will be attainable only if MPs want it.

MPs last night declined to give majority backing to any of the eight Brexit options put before them. The architects of the ‘indicative voting’ process expected this and have therefore reserved next Monday for a second round. They hope to find a route towards a compromise that will break the Brexit impasse, and they have repeatedly suggested that a different voting process could facilitate that.

There are at least three fundamental questions about that process. First, what options will be included? All of last night’s options – plus the deal as it stands – might go forward, or they could be whittled down to a shorter list, or some options could be packaged in a new way. Second, how should the choice be structured? Writing on this blog earlier in the week, Meg Russell suggested that the options put should be mutually exclusive and exhaustive, and that two dimensions – outcomes and processes – should be separated out. Some MPs have adopted similar arguments. Third, by what voting system should MPs make their choice? Last night’s ballot used a series of yes/no votes, but something less crude is envisaged for Monday.

All of these questions are crucial, but this post focuses largely on the third. Its message is that MPs could indeed greatly ease the path to compromise through their choice of voting system. The rules cannot, however, do all the work on their own. Compromise can be reached only if MPs want it.

A preferential ballot

The plan for Monday seems to be that MPs will abandon traditional yes/no voting in favour of a preferential system, allowing them to rank the options in order of preference. If outcome and process are to be separated, this would result in two ballots: one on the optimal form of Brexit (hard, soft or no Brexit at all) and the other on whether that should be immediately proceeded with, or made subject to a referendum.

In any such preferential ballot there are three main ways in which the votes might then be counted (for more exhaustive discussion of different systems, see a recent Hansard Society post):

Alternative Vote : This is the most familiar system to MPs, already being used to elect the chairs of select committees. First preferences are counted. If one option has an absolute majority (more than 50%), it is declared the winner. If not, the last-placed option is eliminated and the second preferences of its supporters are counted. This continues until an option passes the 50% threshold. A variant of this approach spreads the process across multiple rounds of voting, as in the election of the Commons Speaker. Borda Count : This system is familiar to any fan of either the Eurovision Song Contest or Formula 1 racing. Points are awarded to options in proportion to their place in MPs’ rankings. In the simplest version, and with, say, eight options, an MP’s first preference receives seven points, their second preference six points, and so on down, until the last option, which receives no points. Points are added up, and the option with most points wins. Exhaustive Pairwise Comparison : Under the third approach, the rankings are used to compare each option individually against every other option. If there is one option that defeats every other in these head-to-head contests, it is declared the winner. It is known as the ‘Condorcet winner’ after the 18 th -century French mathematician and voting theorist who worked out the underlying logic.

Choosing among these systems

All of these systems tend to enable compromise solutions to be found. Each asks MPs to consider what they would be willing to put up with if they do not get their first preference, not just what they really want. All favour options that attract large numbers of high and middling preferences, rather than options that score very high for some MPs, but very low for others.

No discussion of voting systems can avoid the basic truth that a perfect voting system cannot exist. Each of the preferential systems has its own strengths and weaknesses:

The Alternative Vote can deliver a clear majority for one option. But it could eliminate early on an option that many would accept as a reasonable compromise, even it has few ardent adherents. That might be the case if (hypothetically) most MPs wanted either the existing deal or a complete cancellation of Brexit, but a majority were willing to compromise on a softer form, such as continued customs union membership. The Borda Count is far less likely to miss a generally accepted compromise. Yet if that is a compromise of the ‘miserable’ variety – widely loathed, but loathed less on each side than the option on the other side – we might question whether it really deserves to win. At least in its simple form, the Borda Count is also particularly vulnerable to the problems of incomplete and insincere voting that I discuss below. Exhaustive Pairwise Comparison is guaranteed, unlike the other systems, to find a Condorcet winner. As with the Borda Count, that is fine if the compromise is considered noble, less so if it is thought miserable. More basically, there is no guarantee that a Condorcet winner actually exists. A back-up counting method is therefore needed for the eventuality that it does not.

In this particular case, the problem of settling on a compromise considered by MPs to be ‘miserable’ might be offset by the separate ballot on process. If the compromise is some version of a softer Brexit, many MPs might be prepared to accept that in principle if the public were given the final say.

Whichever of the above systems is adopted, however, two challenges will need to be confronted.

Incomplete voting

These three sytems work best if all voters – in this case, MPs – rank all of the options. Unless MPs register preferences beyond their favourite, potential compromise territory will not be found.

Given free rein, many MPs seem unlikely to do this: they will refuse to record support for any but their most favoured option or options. This would be partly to signal virtue to their parties and constituents, and partly because they think it is the right tactic. Some ardent Leavers (though a dwindling number) appear still to believe they can win a ‘no deal’ Brexit if they hold out for long enough. Ardent Remainers, meanwhile, think that, if no compromise can be reached, parliament will ultimately prefer to revoke the Article 50 notification than ‘crash out’ without a deal. It is notable that SNP, Liberal Democrat, and Independent Group MPs last night refused to back any element of a ‘soft Brexit’. If they had, Kenneth Clarke’s motion on customs union membership would have won majority support.

This problem could be removed, however, by requiring MPs to rank all options in order for their ballot paper to be ruled as valid. That would be a bold move, going against the tradition that MPs can express their preferences as they wish. But it is necessary to enable compromise – and adopting this rule would send a powerful signal that MPs are serious about seeking a consensual way forward. Many people would argue that MPs have been elected to make tough judgement calls, and compulsory complete ranking would hold them to this.

Insincere voting

Even if MPs have to rank all of the options, they might not do so sincerely. With any of these voting systems, it is possible to advance your own preferences through tactical voting, so that the overall result does not necessarily reflect the wishes of the House as a whole. Under Borda Count, for example, if you are confident that your favoured option is most vulnerable to defeat by a particular alternative, you have an incentive to rank that other alternative last, to minimise its chances of winning out.

Temptations towards such insincere voting cannot be eliminated, but they can be minimised. Borda Count is particularly vulnerable for the reason just given. Under the Alternative Vote, by contrast, your lower preferences are not counted if your favourite remains in the game, so cannot defeat that favourite. Tactical voting can make sense under the Alternative Vote too, but the circumstances are more particular and the necessary calculations more complex. In particular, tactical voting is harder the less information you have about others’ preference orderings. That means it is advisable to use a single preferential ballot as discussed here, rather than multiple rounds of voting.

In sum

Any of the three voting systems discussed here will facilitate compromise among voters who are willing to rank all their preferences sincerely. The choice among these systems is not straightforward. Using the Alternative Vote would maximise the chances of a clear, sincere result, but would also create the possibility that a viable compromise could be eliminated in the early stages of the count. One option would be to look first for a Condorcet winner through pairwise comparison, and then count by the Alternative Vote only if no such winner turns out to exist.

If compromise is sought, compulsory complete ranking, though unusual, would be enormously beneficial. Its adoption would be a clear signal that MPs really do want to find agreement on a path forward. If they don’t want compromise, the voting rules cannot do all the work for them.

About the author

Alan Renwick is Deputy Director of the Constitution Unit and has written or co-written three books on voting processes. He is also the co-author of Doing Democracy Better: How Can Information and Discourse in Election and Referendum Campaigns in the UK Be Improved?