Why elections are unfair

In 2017, elections to the Chamber of Deputies of the Czech Republic were held and the ANO movement won with 1,500,113 votes and 78 seats. The last ones who still made it into the Chamber of Deputies were the Mayors and Independents, who won 262,157 votes and 6 seats. The ANO movement needed 19,232 votes for one seat, while the Mayors needed 43,692 votes! The ANO movement won six times more votes than the Mayors, but they won thirteen times more seats in the Chamber of Deputies! What caused this disproportion?

🐈 vs 🐩

Let's explain it with a simpler example. Let us imagine that there are only two parties competing against each other: the party of cats 🐈 and the party of dogs 🐩 and that our imaginary House of Commons has only ten seats to fight for:

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In the election campaign, the dog party promises to ban fireworks, while the cat party promises fireworks every day to keep the dogs away. An election is held and out of 1,000 votes, 600 are for the cat party and only 400 for the dog party. The cats win with 60% of the vote, while the dogs have only 40%. How do we divide the seats between the two parties? The cat party gets 60% of the seats, i.e. six seats. The dog party gets 40% of the seats, i.e. 4 seats:

🐈 🐈 🐈 🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩

All is well, all is fair. But the next year the election is repeated. The dog party promises to make it mandatory for owners to walk their dog for an hour every day. The cat party counters with a mandatory two-hour walk. Out of 1,000 votes cast, the cat party gets 750, the dog party only 250. So the cat party gets 75% of the vote, the dog party 25%. How do we divide up the seats in our House of Commons? Of the ten seats, the cat party gets 75%, the dog party 25%. But 75% of ten is 7.5 and 25% of ten is 2.5. We can give seven seats to the cats and two seats to the dogs, but what about the last seat?

🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐩 🐩 ❓

Who has a better claim to the last seat? Is there any fair solution? There isn't. We can either say that we want to prefer the stronger side and give the last seat to the side of the cats

🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐩 🐩

or we will prefer the weaker side and give the last seat to the dogs

🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐩 🐩 🐩

Neither solution is better or worse. In both cases we are committing a rounding error. But if it was just this one seat, that would be nice. But it's much worse, because it comes down to electoral districts.

Constituencies

In the elections to the Czech Chamber of Deputies, 14 regions are up for election (Moravian-Silesian, Liberec, etc.). And the way it works is that in each region, its inhabitants elect their MPs. When all the elected MPs from all the regions are counted, we get 200 MPs. What is the problem? Let's simplify it and assume that our election between the party of dogs and the party of cats takes place in five different electoral counties. In each of them, ten seats are up for grabs, giving us a total of 50 seats:

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To make it count, the election was the same in every county. In each county, the dog party got 65% of the vote, while the cat party only got 35% of the vote. In the first region, the dog party has 65% of the seats, i.e. 6.5 seats, and the cat party has 35% of the seats, i.e. 3.5 seats. We then have the same results in each region:

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 ❓

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

We see that we have a total of five seats that belong to no one so far and we have to decide what strategy to take. We can say we prefer the stronger side and assign the undecided seat to the dog side:

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐈 🐈 🐈 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

The dog party wins 35 seats in the election, the cat party wins 15. Now let's try to imagine what would happen if we didn't have five constituencies of ten seats each, but if we had one constituency of fifty seats. How many seats would each party have if the dog party got the same 65% of the vote and the cat party got the same 35% of the vote? The dog party would get 65% of the seats, so 65% of 50, which is 32.5 seats, and the cat party 35% of 50, which is 17.5 seats. At the moment we have only one seat undecided:

🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈

🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐩 🐩 🐩

🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 ❓

We'll assign that one to the dog side because we prefer the stronger side:

🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐈

🐈 🐈 🐈 🐈 🐈 🐈 🐈 🐩 🐩 🐩

🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩 🐩

So in the end we have 17 seats for the cat side and 33 for the dog side. So even though the elections were the same, even though in both cases the cat party got 35% of the vote and the dog party got 65%, the election with five counties went better for the dog party and the election with one county went better for the cat party. What is the catch?

The more counties we have, the more rounding errors we have to make. With five counties, we had a total of five question marks on our scorecard - a total of five undecided seats. But with one constituency, we only have one undecided seat - so the results are closer to the real results.

Now imagine that there were elections in 14 constituencies in 2017. And the more counties, the more rounding errors you have to make. This is the main reason why the ANO movement got six times more votes than the Mayors, but won thirteen times more seats.

The second reason is the strategy of distributing seats between parties within an electoral region. The D'Hondt method was used to distribute seats in a setting that favoured the stronger parties.

Therefore, in 2021, the Constitutional Court ruled that the electoral law had to be changed, which it eventually did. Although the new electoral law still provides for 14 regions, the distribution of seats is done in a different way, no longer using the D'Hondt method. In principle, the new electoral law works by first calculating how many seats a party should get in total across all the regions, and then distributing the seats to each region. For a more accurate description, you can read a Facebook status by Dušan Janovský or a description of the electoral law on aktuálně.cz.