On July 4th, the general elections took place in the United Kingdom. After the overwhelming victory of the Labour Party, with 411 seats out of a total of 650, the debates on the majoritarian electoral system and its effects in terms of proportionality reappeared (did they ever disappear?). While Labour won 63.2% of the seats with 33.7% of the vote, the Conservative Party won 18.6% of the seats with 23.7% of the vote. For its part, the Green Party won four seats with 6.4% of the vote and Nigel Farage’s party (Reform UK, ex-Brexit Party) five with 14.3% of the vote.
These figures have shown, once again, that the conversion of votes into seats, in a majority system, depends not only on the level of support but, above all, on how it is distributed in the different constituencies. The most striking case is that of the Liberal Democrat Party, historically the third party in the United Kingdom: with an increase in its vote share of 0.6 percentage points (pp), it went from 11 seats in 2019 to 72. For the Labour Party, an increase of 1.7 percentage points of the vote translated into 211 more seats than in 2019.
Behind these changes in seats, not accompanied by changes of the same magnitude in the percentage of votes, there are various causes. One of the most obvious was the division of votes in the right-wing camp: the result of Reform UK was accompanied by a drop of almost 20 percentage points in the vote for the Conservatives; this, in a majority election, is an obvious disadvantage. On the other hand, Labour and, in particular, the Liberal Democrats, have made their votes much more effective: in a majority system, further increasing your percentage of support in a constituency that is already yours does not give you additional MPs, while a small increase in the number of marginal seats can be decisive. In this sense, the Liberal Democrats focused their campaign on a few dozen constituencies in which they were well placed to snatch MPs, mainly from the Conservatives.
This is where so-called strategic voting (meaningful voting) has played a crucial role. In a majority system, those who sympathise with a third party with no chance of winning a seat may decide to support a party that, being less favoured, has a real chance of winning (or, if necessary, to do so to prevent another, even less favoured, party from celebrating victory). The “pincer” between Labour and Liberal Democrats against the government Tory This has been more or less obvious: from “anti-Tory” apps or websites that let you know which party was best placed to challenge the Conservatives for the seat, to explicit strategies of not campaigning in unviable constituencies. In fact, Ed Davey, the leader of the Liberal Democrats, has defined this election as “ABC” (anyone but conservatives).
In this context, the question arises: what determines whether a voter, faced with the decision of which party to vote for to prevent a Conservative victory, chooses to support Labour or the Liberal Democrats? In constituencies where the distance between the two opposition parties is very large, it is clear which is the “winning horse”. Therefore, comparing results in which Labour had a large advantage over the Liberal Democrats with those where the opposite situation occurred is uninformative and would distort our conclusions. But what happens in seats where the distance between the two other parties was very small? Is it enough to be “second”, even by a few votes, to be perceived as “more viable”?
In a different, but also electoral, context, Thomas Fujiwara and Carlos Sanz analyzed the effect of being the “most voted list” on winning the mayoralty. The authors study whether, given two parties with the same level of support (in terms of seats), the one that obtained (slightly) more votes (i.e. the most voted list) was ultimately the one that formed the government. The strategy I follow here is similar: by comparing the increase in the Liberal Democrats’ vote share between 2019 and 2024 in constituencies where Labour and the Liberal Democrats were almost tied in 2019, I can estimate the effect of “coming second” on the increase in support in 2024.
In fact, the magnitude of the effect (measured in percentage points of greater support for being above) is the least important. What I consider relevant (and want to analyse) is whether this effect exists, because that would indicate that voters take into account the relative standing of the parties when deciding who to support. Analysing this type of election has one advantage: it avoids the problem of attributing the rise in support for one party (Labour or Liberal Democrats) to the fact that it was already much more supported than the other in 2019.
However, applying this method to the 2019 and 2024 elections poses an additional problem. In 2023, the constituency map was revised, meaning that they are not directly comparable to each other. In fact, while some constituencies have not changed, others have changed significantly, and some have even disappeared. Fortunately, estimates (called “notional results”) of the 2019 result in the new constituencies are available (the methodology can be found here ). This information, far from being an electoral or demographic curiosity, is relevant for guiding the vote, particularly in the campaign, by serving as a basis for encouraging strategic voting in the different constituencies.
From the 2019 notional results and the 2024 results, discontinuous regression models are estimated using as the dependent variable the increase in the percentage of votes for the Liberal Democrats, taking as running variable the difference between their vote share with Labour in 2019.
The estimate of the impact, for the full sample, is 2.2 percentage points of additional support for the Liberal Democrats when they are above Labour, but the effect is not significant. The model is then re-estimated, but considering only constituencies in which the Conservative Party was actually first in 2019. The effect rises to 2.9 percentage points, but is still not significant.
A relevant fact to consider in these calculations is that, as mentioned, the constituency map has changed between 2019 and 2024. You may be choosing a seat in a larger, smaller, or simply different territory than the one in which the vote took place in 2019. Assuming that we use the (fictitious) 2019 results as the “base” for estimating a party’s viability, one might expect this to be simpler and more representative in cases where the constituency boundaries have changed little than in cases where they have changed a lot.
Since the database has a “change index” for the constituency (ranging from 0 if it has not changed to values above 100 if there is “little resemblance to a previous constituency”), the sample is split between constituencies with a change index below the median and those with a higher index. Reestimating the models yields a 5 percentage point effect for constituencies with little change (significant at 10%) and a zero effect (not significant) for those with a lot of change. The results, if we consider only those in which the Conservatives were the leading force, are 6.6 percentage points (p
These results suggest that in situations where the difference between two parties is very small, the fact that one is perceived as more viable is relevant when voters support it, but only if the constituency remains reasonably similar within its boundaries. This, in addition to being relevant from the perspective of learning how the electoral system works and assigning viability in strategic voting contexts, may be extremely important for the 2029 elections. For example, the number of seats won by the Liberal Democrats who came in second is very small, which may limit their opportunities to appeal to the useful vote (anti-Conservative or anti-Labour, as the case may be). On the other hand, Reform UK came second in several dozen constituencies in which Labour came first, which could lead to a campaign that strengthens its role as an alternative to the Conservatives.
*The model is estimated with a polynomial of degree one (linear) and optimal bandwidths above and below the threshold using the package rdrobust. The following figure graphically shows the increase in voting percentage compared to the running variablehighlighting the discontinuity at the threshold.
