In many multi-party systems, it is common to talk about politics in terms of ‘blocs’: groups of parties that are not formal allies, but have similar stances on a primary, fundamental dimension of political competition.

Though parties within a bloc may differ on second-order issues and compete against each other in elections, they generally recognise each other as ‘natural’ partners after the ballot boxes are sealed.

Political scientists have found that much of the instability and ‘churn’ that we see in volatile multi-party systems such as those of Latin America and Eastern Europe in fact hides a fundamental stability in the relative strength of party blocs.

In other words, voters may not be as ‘loyal’ to a party as they tend to be in two-party systems, but – when they switch party between one election and the next – they often do so between parties of the same bloc.

Can we think of the Brexit camps as a similar two-bloc system? ‘Leave’ and ‘Remain’ have become political identities that voters relate to more strongly they do with political parties.

In turn, parties have clearly – though, in some cases, reluctantly – taken a stance on the central issue of the possibility of a ‘People’s Vote’, sorting themselves in one or the other camp: the Conservatives and the Brexit Party in the Leave bloc; Labour, the Liberal Democrats and the Greens in the Remain bloc.

Moreover, much of the turmoil in the polls earlier this year seems to map quite straightforwardly onto patterns of ‘within-bloc’ volatility, with 2017 Conservative voters flirting with the Brexit Party and Labour voters being tempted by the Liberal Democrats, while the total size of the two blocs remains constant over time: bloc stability below party chaos.

Granted, this is obviously an over-simplification of messy electoral realities.

Not only are there residual ‘Labour Leave’ and ‘Tory Remain’ voters, but there are key issues other than Brexit voters care about, which may lead them to switch ‘across’ blocs rather than ‘within’.

Nonetheless, it’s a simplification worth making, because it can give us a sense of how the dynamics of multi-party competition can interact with Britain’s electoral system.

In particular, the combination of ‘bloc politics’ and first-past-the-post yields two crucial biases.

The first is the ‘bloc split’ effect, which tends to favour the bloc wherein parties have the most unbalanced share: In this case, the bias favours the Leave bloc, where the Conservatives are clearly larger than the Brexit Party. Conversely, the Remain bloc, where Labour and the Liberal Democrats are almost level, stands to lose from it.

There is however also a second bias, which favours the bloc whose parties have the most spatially distinct electorates – that is, the bloc that has one party that is stronger where the other is weaker, and vice versa.

My argument is that this bias, which we may call ‘bloc specialisation’ effect, may counterbalance the negative effect of an even split between Labour and the Liberal Democrats – and I believe the Remain camp stands to benefit from it.

In this model, Remain and Leave add up to 50% of the vote each: all Remain voters vote either Labour or Liberal Democrats, and all Leave voters vote either for the Conservatives or for the Brexit Party.

With a crucial difference, which reflects polling realities: while the Conservatives rack up 2/3 of the Leave vote, Labour and the Liberal Democrats share the Remain vote among each other almost equally.

To avoid complications due to ties, in the graph below I gave 52% of the Remain vote to Labour and 48% to the Liberal Democrats.

Taking now into account first-past-the-post, we can compute how this scenario translates into seats by looking at the highest party line in each point: the Conservatives obtain a sizeable majority, as they win all ‘Leave’ seats, plus those ‘Remain’ seats where 2/3 of the Leave vote is bigger than half of the ‘Remain’ vote.

Specifically, here we get 63 seats for the Conservatives (blue shaded area) and 37 for Labour (red shaded area).

This model, however, assumes that the strengths of each party within a bloc are positively correlated: that is, both Liberal Democrats and Labour are stronger where Remain is stronger, hence by transitive property Labour is stronger where the Liberal Democrats are also stronger.

Let’s see what happens if we relax this assumption, and assume instead that the two parties in the ‘Remain’ bloc concentrate their relative strengths in different constituencies, whilst keeping their total and relative shares of the vote constant.

What happens is that the ‘Remain’ bloc, by apportioning their vote more efficiently, denies the Conservatives a majority, with the Liberal Democrats winning 20 seats, Labour 32 and the Conservatives 48.

This is a nice illustration of how a specialisation bias in favour of the Remain bloc may counterbalance the split bias’ that works against them – but is it a realistic scenario?

Do we need to assume that Remain voters are ‘better’ at tactical voters than Leave voters?

Not necessarily – this advantage can be in-built in the party system.

This is the case if the electorates of Labour and the Liberal Democrats are spatially and demographically more different from each other than those of the Conservatives and the Brexit Party.

This is not a heroic assumption: of the top 100 Liberal Democrat target seats, only 12 are Labour-held, while 82 are Conservative held; of the top 100 Labour target seats, none are Liberal Democrat-held.

Conversely, according to Professor Chris Hanretty’s estimates of constituency results of the 2019 European Parliament election, of the 100 seats where the Brexit Party did best, 76 are held by the Conservatives, and only 23 by Labour.

Luckily there is a way to test this. Let’s plot Labour and the Liberal Democrats’ results in each local authority in England and Wales in the 2019 European Parliament election, and do the same for the Conservatives and the Brexit Party.

The results should be encouraging for the ‘Remain’ bloc: the Liberal Democrats are stronger where Labour is weaker, and vice versa; while the Conservatives and the Brexit Party are stronger in the same places and weaker in the same places.

This is not even taking into account the nationalist parties in the ‘Remain’ camp: as the SNP and – to a lesser extent – Plaid Cymru are very strong in a few seats and don’t run in the rest of the country, they are effectively an extreme example of bloc specialisation.

The in-built advantage for the Remain bloc is not a quirk of the European Parliament election.

The two most recent general elections reveal a similar pattern: UKIP and the Conservatives competed for similar seats, while the Liberal Democrats and Labour divided up the task more efficiently.

If this pattern holds in the next election, there may not actually be a great deal of places where a ‘split’ in the Remain camp lets the Conservatives squeak into first place.

Viewing first-past-the-post elections through the lenses of bloc politics, it’s thus worth keeping in mind that two elements are key to the success of a bloc: the size difference between parties belonging to a bloc and their relative territorial strengths.

While the Leave camp is set to benefit from the first bias, the Liberal Democrats and Labour are better placed to exploit the latter.

This is not to say that ‘Remainers’ wouldn’t benefit from either Labour or the Liberal Democrats pulling ahead – but if the ‘Remain’ bloc is clearly hurt by its split down the middle, they may make up for it through their efficient spatial distribution of the vote.

Thus, ‘Leavers’ cannot be complacent: as things stand, the Conservatives’ comfortable poll leads may not translate into the large majority Boris Johnson is hoping for.

By Leonardo Carella, a Doctoral Candidate in Politics at the University of Oxford