Can tactical voting work under the Euro elections' PR system? Some commentators have cast theoretical doubt on it, but the evidence shows that it could win lots of seats.
Electoral Calculus was commissioned by Remain United to forecast the results of the 2019 Euro Elections. Using MRP methodology, we calculated the expected vote share for each party in each electoral region. The aim of Remain United is to encourage tactical voting by supporters of the clearly pro-Remain parties (Lib Dems, Greens, Change UK, SNP and Plaid Cymru) to maximise the number of seats won by those parties.
The advice given (see Remain United's website) was for all pro-Remain voters in each area to switch their vote to the leading pro-Remain party in that area.
A few commentators have questioned that advice and suggested that "the best outcome for pro-Remain parties would actually be for the vote to be as evenly split between them as possible" (see, for example, Brandenburg).
But should advice appears to go against the evidence. And here is that evidence.
The first hard fact is about the D'Hondt electoral system for proportional representation. Among its features is a pro-coalition property which guarantees that parties which combine together will do better than those that don't. In precise terms, the seats won by two (or more) parties which combine their forces can never be less than they would get if they fought separately, and will usually be better.
Now the pro-Remain parties have not made a formal pact, but their voters can maximise the seats won by all supporting the same party within each region. No other strategy is as good, if all voters follow the advice.
But what if only some voters follow the advice. We did an experiment to test between two strategies:
The experiment assumed that the party support in each region has a little random sampling error, which was realistically modelled using a stochastic model involving random simulation. The expected number of seats won, which can have a fractional value, is calculated by averaging over all those various possibilities. Another realistic assumption was that not all voters will follow the tactical advice. Some voters will just stick with their first preference party. The experiment defined the Tactical Fraction, which is the fraction of pro-Remain voters who follow the tactical voting advice. This tactical fraction can be anywhere between 0pc (no voters at all are tactical) and 100pc (every pro-Remain voter is tactical).
We ran the simulation across all the English regions (since Scotland and Wales are a bit different) under both strategies, and using a variety of different values for the Tactical Fraction. The overall results are shown in the first graph:
The two strategies are equally bad if the tactical fraction is zero and no-one votes tactically. But they behave very differently as more voters go tactical. The Leading Party strategy significantly outperforms the Equal Split strategy. Indeed, the Equal Split strategy is worse than doing nothing. The Leading Party strategy could gain up to seven seats on average, the Equal Split strategy reduces the total seats won by about one seat.
However, proponents of the Equal Split strategy did not recommend it for the whole country, but for three particular regions: London, the South East and the North West. Let's see how the strategies compare for those regions. The second graph shows the two strategies for the seats won across those three regions. The blue line represents the Leading Party strategy and the yellow line is the Equal Split strategy.
In fairness, the two strategies are quite similar for tactical fractions less than 40pc. And the Equal Split strategy is very slightly better if the tactical fraction is around 20pc, with an advantage of one twentieth of a seat. So the theoretical distinction is just visible. But in practical terms the advantage is negligible, and it depends on a precise value of the tactical fraction which is unlikely to occur. The potential benefits of the Leading Party strategy are much more significant.
In summary, the Leading Party strategy, adopted by Remain United, is both the theoretical best strategy if all pro-Remain voters behave tactically, and also significantly outperforms the suggested alternative strategy over a wide range of realistic scenarios.