u/TenebrisAurum

In the 2026 election a new electoral system was introduced for the Senedd, whereby seats were distributed in six-member constituencies using the D'Hondt method.

The alternate electoral system I used here was inspired by the electoral systems used in Denmark, Iceland, Norway and Sweden (and by Ballot Box Scotland, who does similar projections for Scottish and UK elections). I've described the methodology in more detail below, but put succinctly the idea is that the seats in each constituency are allocated proportionally, but the final seat in each constituency is reserved as a levelling seat to ensure national proportionality. The levelling seats are back-allocated to the constituency where the party was closest to winning a(nother) seat, so the national result is proportional and the constituency results are close to proportional. Usually in systems of proportional representation there is a trade-off between constituency size and proportionality, whereas this system produces an almost perfectly proportional legislature with smaller constituencies.

There are numerous ways of implementing this system (indeed, Denmark, Iceland, Norway and Sweden all use slightly different methods) but this is the methodology I used (again inspired by Ballot Box Scotland):

Methodology:

1. A 3% electoral threshold was applied to the national election results. These are the parties which were eligible for levelling seats, and I'll refer to them as eligible parties.

2. In each constituency, five of the six seats were allocated to parties or candidates using the Sainte-Lague method (a more proportional version of D'Hondt). If a below-threshold party or independent candidate would've been entitled to the sixth seat they would've won it, but this was not the case in any constituency.

3. After the first five seats had been allocated, a quota was calculated in each constituency for each eligible party. First the proportion of votes each party had won was multiplied by the total number of seats available (six), and then the seats already won by that party was subtracted from this number.

For example, in Afan Ogwr Rhondda Plaid Cymru won 36.9% of the vote and had been allocated 2 seats, so its quota was 0.214.

4. The seats won so far were totalled at the national level, and the Sainte-Lague method was used to calculate which eligible party was next entitled to a seat. The party then won the seat where it had the highest quota of support (i.e., where it was closest to winning a(nother) seat).

For example, the first party entitled to a seat was the Liberal Democrats. The constituency with the strongest quota of support for the Liberal Democrats was Caerdydd Ffynnon Taf at 0.574, so the final seat in Caerdydd Ffynnon Taf went to the Lib Dems. The next party entitled to a seat was the Green Party, whose strongest quota of support was 0.492 in Sir Fynwy Torfaen. This process continued until each constituency had received its sixth seat.

The Gallagher Index is a measure of proportionality - essentially what proportion of seats in the legislature have been misallocated compared to a perfectly proportional result. Lower scores are more proportional. This system would produce a Gallagher Index score of 1.6, while the real-life results scored 9.4. The 2024 UK Parliament results in Wales (using the non-proportional first-past-the-post system) scored 38.1.

One thing to note is that the Labour Party's votes were distributed in such a way that by a mathematic quirk they managed to win 12 seats across the constituencies before any of the sixth seats had been allocated, despite having an overall proportional entitlement of 11 seats. This deprived Plaid Cymru of a 35th seat. Other than that, the result is as proportional as it can be among parties winning 3% or more of the vote.

In the 2026 elections a new electoral system was introduced, whereby seats were distributed in six-member constituencies using the D'Hondt method.

The alternate electoral system I used here was inspired by the electoral systems used in Denmark, Iceland, Norway and Sweden (and by Ballot Box Scotland, who does similar projections for Scottish and UK elections). I've described the methodology in more detail below, but put succinctly the idea is that the seats in each constituency are allocated proportionally, but the final seat in each constituency is reserved as a levelling seat to ensure national proportionality. The levelling seats are back-allocated to the constituency where the party was closest to winning a(nother) seat, so the national result is proportional and the constituency results are close to proportional. Usually in systems of proportional representation there is a trade-off between constituency size and proportionality, whereas this system produces an almost perfectly proportional legislature with smaller constituencies.

There are numerous ways of implementing this system (indeed, Denmark, Iceland, Norway and Sweden all use slightly different methods) but this is the methodology I used (again inspired by Ballot Box Scotland):

Methodology:

1. A 3% electoral threshold was applied to the national election results. These are the parties which were eligible for levelling seats, and I'll refer to them as eligible parties.

2. In each constituency, five of the six seats were allocated to parties or candidates using the Sainte-Lague method (a more proportional version of D'Hondt). If a below-threshold party or independent candidate would've been entitled to the sixth seat they would've won it, but this was not the case in any constituency.

3. After the first five seats had been allocated, a quota was calculated in each constituency for each eligible party. First the proportion of votes each party had won was multiplied by the total number of seats available (six), and then the seats already won by that party was subtracted from this number.
   For example, in Afan Ogwr Rhondda Plaid Cymru won 36.9% of the vote and had been allocated 2 seats, so its quota was 0.214.

4. The seats won so far were totalled at the national level, and the Sainte-Lague method was used to calculate which eligible party was next entitled to a seat. The party then won the seat where it had the highest quota of support (i.e., where it was closest to winning a(nother) seat).
   For example, the first party entitled to a seat was the Liberal Democrats. The constituency with the strongest quota of support for the Liberal Democrats was Caerdydd Ffynnon Taf at 0.574, so the final seat in Caerdydd Ffynnon Taf went to the Lib Dems. The next party entitled to a seat was the Green Party, whose strongest quota of support was 0.492 in Sir Fynwy Torfaen. This process continued until each constituency had received its sixth seat.

The Gallagher Index is a measure of proportionality - essentially what proportion of seats in the legislature have been misallocated compared to a perfectly proportional result. Lower scores are more proportional. This system would produce a Gallagher Index score of 1.6, while the real-life results scored 9.4. The 2024 UK Parliament results in Wales (using the non-proportional first-past-the-post system) scored 38.1.

One thing to note is that the Labour Party's votes were distributed in such a way that by a mathematic quirk they managed to win 12 seats across the constituencies before any of the sixth seats had been allocated, despite having an overall proportional entitlement of 11 seats. This deprived Plaid Cymru of a 35th seat. Other than that, the result is as proportional as it can be among parties winning 3% or more of the vote.

The Senedd is the legislature of Wales. In the 2026 elections a new electoral system was introduced, whereby seats were distributed in six-member constituencies using the D'Hondt method.

The alternate electoral system I used here was inspired by the electoral systems used in Denmark, Iceland, Norway and Sweden (and by Ballot Box Scotland, who does similar projections for Scottish and UK elections). I've described the methodology in more detail below, but put succinctly the idea is that the seats in each constituency are allocated proportionally, but the final seat in each constituency is reserved as a levelling seat to ensure national proportionality. The levelling seats are back-allocated to the constituency where the party was closest to winning a(nother) seat, so the national result is proportional and the constituency results are close to proportional. Usually in systems of proportional representation there is a trade-off between constituency size and proportionality, whereas this system produces an almost perfectly proportional legislature with smaller constituencies.

There are numerous ways of implementing this system (indeed, Denmark, Iceland, Norway and Sweden all use slightly different methods) but this is the methodology I used (again inspired by Ballot Box Scotland):

Methodology:

1. A 3% electoral threshold was applied to the national election results. These are the parties which were eligible for levelling seats, and I'll refer to them as eligible parties.

2. In each constituency, five of the six seats were allocated to parties or candidates using the Sainte-Lague method (a more proportional version of D'Hondt). If a below-threshold party or independent candidate would've been entitled to the sixth seat they would've won it, but this was not the case in any constituency.

3. After the first five seats had been allocated, a quota was calculated in each constituency for each eligible party. First the proportion of votes each party had won was multiplied by the total number of seats available (six), and then the seats already won by that party was subtracted from this number.

For example, in Afan Ogwr Rhondda Plaid Cymru won 36.9% of the vote and had been allocated 2 seats, so its quota was 0.214.

4. The seats won so far were totalled at the national level, and the Sainte-Lague method was used to calculate which eligible party was next entitled to a seat. The party then won the seat where it had the highest quota of support (i.e., where it was closest to winning a(nother) seat).

For example, the first party entitled to a seat was the Liberal Democrats. The constituency with the strongest quota of support for the Liberal Democrats was Caerdydd Ffynnon Taf at 0.574, so the final seat in Caerdydd Ffynnon Taf went to the Lib Dems. The next party entitled to a seat was the Green Party, whose strongest quota of support was 0.492 in Sir Fynwy Torfaen. This process continued until each constituency had received its sixth seat.

The Gallagher Index is a measure of proportionality - essentially what proportion of seats in the legislature have been misallocated compared to a perfectly proportional result. Lower scores are more proportional. This system would produce a Gallagher Index score of 1.6, while the real-life results scored 9.4. The 2024 UK Parliament results in Wales (using the non-proportional first-past-the-post system) scored 38.1.

One thing to note is that the Labour Party's votes were distributed in such a way that by a mathematic quirk they managed to win 12 seats across the constituencies before any of the sixth seats had been allocated, despite having an overall proportional entitlement of 11 seats. This deprived Plaid Cymru of a 35th seat. Other than that, the result is as proportional as it can be among parties winning 3% or more of the vote.