If you think far enough, you can come up with a situation where any electoral system does not work

If you think far enough, you can come up with a situation where any electoral system does not work

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Boris Johnson announced his departure after scandals accumulated. The Conservatives will name their successor next week as Prime Minister until elections scheduled for January 2025. This appears to have made snap elections a thing of the past, although it wouldn’t hurt to take a look at the British electoral system.

UK election results are determined differently from ours. In our elections to the House of Representatives, it doesn’t matter whether you live in Aadorp or Zwolle: every vote counts equally. The distribution of seats is roughly the same as the vote share. For example, the VVD party won 22.7 percent of the seats last time with 21.9 percent of the vote. The difference between the two percentages was less than one percentage point for the other parties.

If not in the UK. In the previous election in 2019, the Conservatives won 43.5% of the vote and 56.2% of the seats – a big difference. (While the Conservatives kept repeating after the Brexit referendum that 48 percent of the opposition vote could best be ignored.) Even more surprising, small parties sometimes have more seats than large parties: the Liberal Democrats, for example, got three times as many. She voted for the SNP, but the SNP won more than four times the number of seats.

This is due to the constituency system. The country is divided into 650 electoral districts: each district has only one winner. So you have a majority of 326 districts. Not every neighborhood is the same size. The smallest district, Na Na h-Eileanan an Iar in Scotland, had only about 21 thousand voters in 2019, while the Isle of Man has 113 thousand. The 326 smallest districts account for 46 percent of the population, which is significantly lower than the 324 largest.

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In the Netherlands, something similar happens in elections to the upper house by members of the county council: the ratio between the number of members of parliament and residents is not the same everywhere. This solves the election code by working with voting numbers. This solution works well, but not perfectly: 1006 Zeelanders have the same voting rights as 1000 Flevolanders. What a pity for the zeelander, but the differences are minimal. With a natural variation in eligible voters, the opposite may be true in the next election.

With such skewed proportions in the British system, it is possible on paper to achieve a majority based on a large minority of the vote, as you can popular vote He loses to several others. It’s a long way off, but it is theoretically possible to get an absolute majority with a total of only 326 votes, while the other parties get 25 million votes: by getting one vote in the narrowest majority of the constituencies (and none for the other parties) and in the other provinces you don’t get on one vote.

Something similar can be imagined in the Netherlands. Suppose 150 parties participate in the elections. Of these, 149 parties received the exact same number of votes while 150 got slightly more. Because the 150th party is the only party that has reached the electoral threshold, it can take all the seats (except that parties are not allowed to have more than 80 candidates). The essential difference with the British system is that the most popular party also becomes the largest.

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If you think carefully enough, you can find a situation for any electoral system in which the system does not work. It is up to Johnson’s successor and her political opponents to ensure that voters still have enough confidence to go to the polls in a few years. Only then will the far-fetched scenarios remain highly improbable.

Kasper Albers is Professor of Statistics at the University of Groningen

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