On Wednesday evening we will know who wins the elections – for now. Because after all votes have been counted, a second, less visible battle begins: the one for the remaining seats. Esther Ouwehand of the Party for the Animals recently stated that these mainly go to the major parties. Is that correct?
To answer that question, we call the Belgian mathematician Filip Moons, didactician at the Freudenthal Institute of Utrecht University. He knows a lot about electoral systems and recently wrote the booklet From vote to seat – the mathematics behind the Dutch elections.
“Yes, Ouwehand is right,” Moons confirms. To understand why, you need to know how the seats are distributed. This is done with the ‘method of largest averages’, an algorithm from 1885 by the Belgian lawyer Victor D’Hondt, which is used worldwide to convert votes proportionally into seats.
Moons explains it using a simple example. Suppose that the House of Representatives consists of ten seats and that four parties participate in the elections: Maxi, Fors, Mini and Nano. Suppose further that 10,000 people have cast a valid vote: Maxi has 5,700, Fors 1,950, Mini 1,500 and Nano 850. If you divide 10,000, the number of votes, by ten, the number of seats, you have 1,000: that is the so-called electoral quota, the number of votes required for one seat. Maxi gets five ‘full’ seats, because 1,000 fits five times into 5,700. Fors barely gets two full seats and is stuck at one. Mini also gets one, while Nano doesn’t get a single seat.
Seven full seats have been distributed, leaving three remaining seats. Who do they go to? Nano is eliminated, because according to the Dutch Electoral Act, residual seats are only distributed among parties that already have at least one full seat. “That is the mini Dutch electoral threshold,” Moons explains. “In the real House of Representatives, with 150 seats, this amounts to 0.67 percent of the votes.”
Bidding in three rounds
Moons compares the distribution of the three remaining seats to a bid in three rounds. Maxi, Fors and Mini compete for those remaining seats. What price can they wager? “Maxi already has five seats and is competing for a sixth. You therefore calculate the average number of votes per seat if they actually got six,” Moons explains. So you divide their 5,700 votes by six, which is 950. This number is Maxi’s bid.
You do the same for the other two parties. Fors already has one seat and would like a second one, so we calculate 1,950 / 2 = 975. Analogous for Mini: 1,500 / 2 = 750. Conclusion: Fors has the highest bid with an average of 975 votes per seat and therefore gets the first remaining seat.
Then the second round. Fors now has two seats and offers 1,950 / 3 = 650 votes for a third. Maxi and Mini remain at 950 and 750 respectively. Maxi now offers the highest and therefore gets the second remaining seat.
In the third and final round, Maxi tries to get a seventh seat. The bid will be 5,700 / 7 = 814. Fors (650) and Mini (750) bid lower. Maxi wins again and ends up with seven seats.
So much for how the system of largest averages works. But why do large parties – such as Maxi in the fictional example – benefit more from this than small parties? In this system you divide the number of votes by the number of seats already obtained plus one. If a party has thirty full seats, divide by 31 for the first remaining seat. If the party wins that remaining seat, it will be divided by 32 in the next round. That doesn’t make much of a difference: the average only drops a little. But if a party only has three full seats, you first divide the number of votes by four, and for the next remaining seat by five: that makes a big difference. Moons: “Large parties see their bids drop less quickly than small parties.”
Method prevents fragmentation
Isn’t that unfair? Moons does not think so: “The D’Hondt method allocates seats in proportion to the number of votes. All parties receive at least their full seats. The fact that large parties can obtain more than one residual seat has the advantage that winners who together receive approximately half of the votes can more easily form a majority cabinet.”
Moons adds that the method of largest averages prevents more fragmentation. “The Dutch political landscape is already quite fragmented. This is partly because voting takes place in one national electoral area. Almost all other countries with proportional representation do so per electoral district. Much fewer seats can be allocated in such an electoral district, which also means fewer parties enter parliament.”
According to Moons, it is not worthwhile to stand up separately with a small split from a party, such as Peace for Animals. “The D’Hondt method rather encourages parties to approach voters together.” You can also see this in the fictional example: if Fors and Mini were to participate as a merger party, they would together get four seats instead of three.
The D’Hondt method is not one hundred percent fair, but that is not the case with any seat distribution system. “That follows the Balinski and Young theorem“, says Moons. “Everything you would want from a seat distribution system can never be fulfilled at the same time. A slight preference for winners is then an honorable compromise.”
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