# AMS in Wales Explained

A number of people have been kind enough to say nice things about the video I recorded for our new online course (click here for more details) about how the electoral system works for the Welsh Assembly election. I’ve even had a couple of requests for the full script. So, here it is, below.

How We Elect Our Members of the National Assembly

The National Assembly for Wales election is now only a few weeks away. But do most people know how the voting system for the Assembly works? Probably not. This blog post tries to make things clear.

We use a different voting system for National Assembly elections than in general elections to the House of Commons. For the Assembly we have something very similar to the electoral system used for national elections in several countries, including Germany and New Zealand; it is known as the Additional Member System (AMS).

Under AMS, everyone has two votes: one for an individual candidate in their local constituency, the other for a party in a broader region. The regional vote is not a ‘second preference’ vote, and people can vote for the same party in the region and the constituency.

The National Assembly for Wales has sixty members. Forty are elected in constituencies – the same constituencies we use in general elections. The forty constituency members of the Assembly are elected in just the same way as we choose our MPs: the winner in each constituency is the individual candidate who gets the most votes.

That’s fairly simple. The more complicated bit of AMS concerns how we use the regional or party vote to elect the other twenty members of the Assembly. These people are chosen in five broad regions: North Wales, Mid and West West Wales, South Wales West, South Wales Central, and South Wales East. Each region chooses four regional representatives.

The regional seats are allocated proportionally between the parties, according to an equation known as the d’Hondt formula (after its inventor, the 19th century Belgian mathematician, Victor d’Hondt). This formula is:

V ÷ (S+1)

where V equals the number of votes a party has won, and S equals the number of seats it has won so far.

The four regional seats in each region are then allocated in four ‘rounds’, in each of which the winner of a seat is decided via the d’Hondt formula. In every round of calculations, S includes the number of constituency seats a party has won in that region plus any regional seats it has won in previous rounds.

How this works can best be illustrated by an example. So let’s look at North Wales in the 2011 National Assembly election.

This was the total number of regional votes won in North Wales by each of the five largest parties in 2011:

Labour: 62,677
Conservative: 52,201
Plaid Cymru: 41,701
Liberal Democrats: 11,507
UKIP: 9,608

In the first round of calculations, for each party we take V (the number of regional votes they won in the region) and divide it by S+1. In this first round, S is equal to the number of constituency seats in North Wales that each party won – which, as it happens, was five for Labour and two each for the Conservatives and Plaid Cymru. The d’Hondt formula thus produces the following calculations:

Round One
Labour: 62,677 ÷ (5+1) = 10,446.2
Conservative: 52,201 ÷ (2+1) = 17,400.3
Plaid Cymru: 41,701 ÷ (2+1) = 13,900.3
Liberal Democrats: 11,507 ÷ (0+1) = 11,507
UKIP: 9,608 ÷ (0+1) = 9,608

After we have applied the formula, the winner of the seat in round one is the party with the largest total. That is clearly the Conservatives. The individual elected is the person at the top of the Conservatives’ list of regional candidates for North Wales – in this instance, Mark Isherwood.

To elect the second regional member for North Wales, we repeat the process. However, as the Conservatives won a seat in round one, in the second round of calculations the value of S for them increases by one (it equals three, based on their two constituency seat wins plus their regional seat). This produces the following calculations:

Round Two
Labour: 62,677 ÷ (5+1) = 10,446.2
Conservative: 52,201 ÷ (3+1) = 13,050.3
Plaid Cymru: 41,701 ÷ (2+1) = 13,900.3
Liberal Democrats: 11,507 ÷ (0+1) = 11,507
UKIP: 9,608 ÷ (0+1) = 9,608

In this round Plaid Cymru has the largest total, so they win the second North Wales regional seat. This seat went to the top candidate on the Plaid North Wales list, Llyr Huws Gruffydd.

We again repeat the process to calculate the winner of the third regional seat. But after their success in round two, we adjust the value of S for Plaid Cymru – it now equals three, reflecting their two constituency wins and their regional seat win.

Round Three
Labour: 62,677 ÷ (5+1) = 10,446.2
Conservative: 52,201 ÷ (3+1) = 13,050.3
Plaid Cymru: 41,701 ÷ (3+1) = 10,425.3
Liberal Democrats: 11,507 ÷ (0+1) = 11,507
UKIP: 9,608 ÷ (0+1) = 9,608

This time around the Conservatives again have the largest total, and so win the third regional seat. This was awarded to the second highest candidate on the Conservative list for North Wales, Antoinette Sandbach.

Finally, the last North Wales regional seat was allocated in a fourth round of calculations; here, the value of S for the Tories was again increased by one to reflect their seat win in the previous round.

Round Four
Labour: 62,677 ÷ (5+1) = 10,446.2
Conservative: 52,201 ÷ (4+1) = 10,440.2
Plaid Cymru: 41,701 ÷ (3+1) = 10,425.3
Liberal Democrats: 11,507 ÷ (0+1) = 11,507
UKIP: 9,608 ÷ (0+1) = 9,608

This final regional seat is won by the Liberal Democrats, and was awarded to the leading candidate on their North Wales regional list, Aled Roberts.

And that’s it. Simples, eh? In truth, AMS is not the world’s simplest way of electing an assembly or parliament. But it has become increasingly popular around the world, because it combines local constituency representation with broader proportionality overall.

Anyway, like it or not, it is the system we have at the moment. So people ought to understand how it works.