# An analysis of different electoral systems applied to Belgium's 2024 elections

As every administrative matter in Belgium, its electoral system is complex.
Still, these electoral procedures were designed by people, and hence, we can alter them.
At this page, we have a look at the electoral system for the Belgian federal Chamber of Representatives.
We analyze it in terms of its **democratic deficit**: *the percentage of people that cast a valid non-blanco vote, but do not have any representation in the legislative body*.
Other fairness metrics of electoral systems exist, but because it is both simple and immediately clear that we want to keep the democratic deficit low, we focus on this measure.
We analyze the democratic deficit of the 2024 Belgian elections, estimate the worst case democratic deficit for the current Belgian electoral system, and compare this with the electoral systems of The Netherlands and the United Kingdom.

## Current democratic deficit in Belgium

Firstly, we calculate the democratic deficit of the 2024 Belgian federal elections.
It simply is the number of people that voted for a party that ended up with zero seats in the federal parliament, divided by the the total number of votes for all parties (so we ignore invalid and blanco votes, as well as people that did not vote).
This yields 299 027 / 6 984 906, for a final percentage of **4.3%**. More than 1 in 25 people that cast a valid, non-blanco vote do not have any representation amongst the 150 members of parliament.
If these unrepresented three hundred thousand people would get a proportional representation, they would fill at least **six seats** in parliament.

## Worst case democratic deficit in Belgium

Is a democratic deficit of 4.3% a high or low amount? Is it possible that in future elections we have an even bigger democratic deficit? How bad can this democratic deficit ever get? This all depends on the rules the Belgians decided to use in their elections.

Belgium is divided into eleven electoral districts, one for each province plus the Brussels capital region. Each district sends a number of representatives to the Chamber of Representatives, the country's national legislative body. These representatives are distributed to political parties based on the number of votes they get in a national election. Firstly, parties that do not reach an electoral threshold of 5% in an electoral district do not get to send representatives for that district. For those parties that do reach the threshold, representatives are distributed according to the D'Hondt method. Many parties identify as Flemish or Walloon, and hence do not participate in all electoral districts.

To perform our analysis, we make some extra assumptions based on the 2024 Belgian federal elections. We assume there are twelve parties, which is the number of parties with elected representatives in 2024. These twelve parties map to the largest existing Belgian parties, and we model their participation in the electoral districts as their participation for the 2024 election. Similarly, the number of representatives for each district is identical to the 2024 election, as is the number of valid non-blanco votes cast for each district. Finally, to reduce the computational burden, we divide all vote and population counts by a thousand. While this reduces numerical precision a little, it does not affect the overall conclusion.

We modeled these rules and assumptions as a ManyWorlds program and ran it on a powerful computer to find an extreme case of democratic deficit.
We find a a worst case democratic deficit of **31.9%**, or 2 231 000 votes, way more than 2024's blanco/invalid votes (416 577) and non-voters (966 546) combined.
So in the current electoral system, under assumptions based on the current elections, we can end up with amost one in three valid non-blanco votes completely ignored.

This democratic deficit arises when one party grabs all the seats, and all other parties end up either below the electoral threshold, or just short of enough votes for the D'Hondt system to assign them a seat. Of course, this is an extreme case that will not occur in practice. But it does provide another data point to compare with. Let's have a look how the Belgian elections would have turned under the Dutch electoral system.

## The Dutch electoral system applied to Belgium

In typical Low Countries fashion, the Dutch electoral system is much simpler. There is one electoral district encompassing the whole country. For every 0.67% of the vote a party gets, they get one of the 150 seats in the national parliament. If a party scores below 0.67%, they get no seats, making this the electoral threshold. Remaining seats are allocated one by one to the party with the highest average number of voters per seat. And that's it!

Before applying the Dutch electoral system to the 2024 Belgian vote results, we have to correct for the fact that Walloon electoral districts have more blanco/invalid votes and a higher non-voter percentage than Flemish ones. So instead of just using the raw 2024 national vote counts, we normalize these votes along the number of total eligible voters for each electoral district. After doing this, we model the Dutch electoral system in ManyWorlds and calculate the allocation of representatives:

N-VA | 25 | (+1) |

Vlaams Belang | 21 | (+1) |

MR | 17 | (-3) |

PTB-PVDA | 15 | (0) |

PS | 13 | (-3) |

Vooruit | 12 | (-1) |

cd&v | 12 | (+1) |

Les Engagés | 11 | (-3) |

Open Vld | 8 | (+1) |

Groen | 7 | (+1) |

Ecolo | 5 | (+2) |

Défi | 2 | (+1) |

Chez Nous | 1 | (+1) |

Blanco | 1 | (+1) |

There is a clear trend: large Walloon parties (MR, PS, Les Engagés) lose a lot of seats, which go to small parties as well as large Flemish parties. This happens even after the above correction for invalid/blanco votes and non-voters. The reason is three-fold. First, the Dutch system is less advantageous to large parties than the Belgian one, due to a low electoral threshold and a more proportional distribution of seats. This explains why small parties gained seats and large parties lost seats. Second, there exist quite a lot of small Walloon parties that do not reach the electoral threshold, but do take away votes from the other Walloon parties. Third, the Brussels electoral region has a higher ratio of representatives to eligible voters, because it has fewer eligible voters per inhabitant. Since almost all seats in Brussels go to Walloon parties, these last two reasons explain why only Walloon parties lose seats.

## Democratic deficit in the Dutch electoral system applied to Belgium

The democratic deficit in the Dutch electoral system applied to Belgium's 2024 elections yields **2.4%**.
This is a little more than half of the 4.3% democratic deficit in the Belgian electoral system.
In absolute vote numbers, this is an improvement of more than 130 000 valid votes that now have representation in a Dutch-style seat allocation.

To calculate the worst case democratic deficit for the Dutch system applied to Belgium, we make the same assumptions as before, ending up with a new ManyWorlds specification.
Running this yields a democratic deficit of **7.2%**, arising again when one party grabs all the seats, and all other parties end up slightly below the electoral threshold.
The important thing to notice here is that **by sensibly adapting our electoral system we could improve the fairness of our elections**, both in extreme worst cases and in sensible circumstances.
And the effects would not be minor: we are talking about hundreds of thousand of unrepresented voters!

## The United Kingdom's electoral system applied to Belgium

Where the Dutch electoral system has one big electoral district where all representatives are elected, the United Kingdom (UK) uses the opposite approach where each individual representative is elected in a tiny electoral district called a constituency.
The candidate with the most votes in a constituency gets that constituency's seat.
Such a *winner-takes-all* system does not require that the candidate has 50% of the votes of the constituency.
Indeed, if there are a handful of parties competing in one consituency, often only 30% or even 25% of the vote share is enough to claim the seat.

Again, we apply Belgium's 2024 vote results to the UK electoral system.
For this, we use the Belgian *cantons*: small districts where vote counts are collected before they are aggregated on the provincial electoral district level.
We assign to each canton a fractional seat proportional to the number of inhabitants in the canton, and each party gets the sum of the fractional seats of the cantons where they get the most votes.
The result looks like this:

N-VA | 56.5 | (+32.5) |

VLAAMS BELANG | 28.9 | (+8.9) |

MR | 28.1 | (+8.1) |

PS | 22.2 | (+6.2) |

Les Engagés | 8.4 | (-5.6) |

Groen | 4.1 | (-1.9) |

PTB-PVDA | 1.7 | (-13.3) |

Open Vld | 0.1 | (-6.9) |

Vooruit | 0 | (-13) |

cd&v | 0 | (-11) |

Ecolo | 0 | (-3) |

DéFI | 0 | (-1) |

These results wildly differ from the actual election result! E.g., Vooruit, cd&v and Open Vld, the classic Flemish broad center parties, together have 0.1 seats. The reason is simple: in (almost) no single canton do they win, and winner-takes-all implies loser-gets-none. To visualize this: the colors of this map represent the biggest party in each canton. And indeed, in Flanders (the north of Belgium), the colors red (Vooruit), dark orange (cd&v) and blue (Open Vld) are firmly lacking. Only the small Zwalm and Horebeeke cantons color blue but their combined population merits about 1/7th of a seat. Surprisingly, the small Groen party (green) does conquer a couple of seats as they are the winner in the Ghent canton, the third largest city of Belgium.

## Democratic deficit in the UK electoral system applied to Belgium

As even mid-size parties get no seats, it is to be expected that the democratic deficit of a winner-takes-all simulation will exceed the previous ones.
Indeed, assuming Open Vld's 0.1 seat counts as no representation, we get a current democratic deficit of **29.9%**, or almost 2 100 000 valid non-blanco votes that would not get any representation.
Though not uncommon for multi-party winner-takes-all, it is comparable to the simulated *worst case* democratic deficit of Belgium's current electoral system, and is more than four times as high as the *worst case* democratic deficit using the Dutch approach.

To estimate the worst case democratic deficit for the UK system applied to Belgium, we assume there are 150 constituencies in Belgium which all have 47 000 eligible voters.
We partition these in Walloon, Flemish and Brussels constituencies, and let only those parties participate in a constituency if they participated in any of the corresponding electoral districts.
Running the resulting ManyWorlds program yields a worst case democratic deficit of **83.2%**.
This democratic deficit again happens when one party wins all constituencies, and all other parties are close to this winner.
This worst case again is not realistic in practice, but it is a symptom of the unexpected electoral dynamics in a winner-takes-all electoral system.
Notably, in such a system, there is pressure on smaller parties to join the larger ones, thereby diminishing the diversity presented to voters and the diversity amongs the parliamentary representatives.
A clear example of this evolution towards a two-party state is the United States, where two center parties control almost all representatives, and non-center voices only have a chance of being heard as subordinate members of one of the two center collectives.

Given this comparatively high democratic deficit of winner-takes-all, surely nobody in Belgium is thinking of switching the current setup to a UK-style system. Right?

From N-VA's 2024 manifesto:

We [envision] introducing a new electoral system in which the majority of the Flemish parliamentary seats are divided on the basis of smaller local electoral districts in which one candidate ('winner takes all') is elected each time.

It definitely makes sense for N-VA to propose this: as the largest party in the country, they stand to gain a huge amount of seats, as already shown in the above table. But our analysis is a dire warning to small and even mid-size parties: in a winner-takes-all electoral system, they are doomed to obscurity.