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.

Common Questions about AMS:

“So Labour got the most regional votes in North Wales in 2011, but no regional seats?” In this case, that is correct. Although if there had been five regional seats per region, Labour would have won the fifth one in North Wales.

“How is that fair? Labour got the most regional votes in north Wales – so why didn’t they win any regional seats?” The AMS system is designed to achieve greater proportionality in the overall result than you get from just the outcome of the constituency elections. By proportionality, we mean a closer match between the percentage of the vote that a party gets and the percentage of the members of the National Assembly that they win.

We can show how this works by looking once again at our North Wales example. In North Wales in 2011, Labour won 38.0% of the constituency vote and 32.2% of the regional vote. But Labour won over 50% (5 of the 9) constituency seats in North Wales. After the four regional seats for North Wales were elected Labour had won 5 of all the 13 Assembly members from North Wales – or 38.4% of the total. So Labour’s share of the vote now matched much more closely its proportion of the elected representatives. In short, the system did exactly what it was designed to do.

“Who do the Assembly members represent?” Those elected in the constituencies represent that constituency. The regional members represent their party across the region as a whole.


  • Graham Hahaway

    A question Roger arising from your well worked example of the regional lists election procedure. As a purist, has including the Election for the Police Commissioner over complicated the voting: and given the handling of bulky pieces of paper for election for the Assembly are there on average a greater percentage of spoilt ballot papers.
    If so the adding of an extra ballot paper will place extra confusion into an already rich mix.
    I think this is all adventurous stuff but extra pieces of paper does little for better understanding.

    • Roger Scully

      I don’t think the PCC election has helped things. (To be frank, my own personal view is that PCC elections don’t help anything!). But given the poor understanding of how AMS works, throwing another ballot paper into the mix isn’t helpful.

  • robert orchard

    How much evidence is there of people using their two votes differently – for different parties – and, if they do, is it because they are backing an individual candidate they like, irrespective of party? Do they know, moreover, who is at the top of their regional list of candidates for each party? Presumably, those names are on the ballot paper in order, but I can’t recall if they are. So, overall, how sophisticated are the choices that voters are making here? I

    • Roger Scully

      Plenty of evidence ticket splitting, Robert – c.20-27% of those voting according to past Welsh Election Studies. But not so much evidence that this reflects political sophistication – in more cases it seems to be about confusion.

  • Welshguy

    It’s a terrible system, especially as implemented in Wales.

    1) As stated above, it seems that many, many voters are confused by it. These are disproportionately likely to be those who are less politically engaged, so it represents another barrier to voter participation in this respect. Whilst the ability to split your ticket allows for a certain degree of preferential voting, there is no way to distinguish this from confusion. The fact that tens of thousands continue to vote Labour on the lists in the three S-Wales regions – despite none of them ever having returned a Labour list AM – suggests that even many who don’t split their ticket still don’t understand the system.

    2) Candidates at the top of certain parties’ lists in certain regions are pretty much guaranteed to be elected, bar a catastrophic decline in support, even if they do no campaigning whatsoever.

    3) It encourages tactical voting in constituency seats: in the S Wales regions for example, it is in all non-Labour parties’ interests to vote for whichever non-Labour candidate is most likely to win the seat, regardless of who they are – for example, if the Tories or Lib Dems had won a constituency seat in South Wales Central in 2011, the net result would have been an extra seat for Plaid Cymru (!).

    4) With so few AMs elected on the lists, the overall result still isn’t proportional. Labour had slightly more than 50% more votes than the Conservatives in 2011 yet more than twice as many seats.

    5) The “jobs for life” element described in #2 above notwithstanding, in other regions candidates can lose their seats because of their own parties’ successes elsewhere in the region. I’m no fan of the Conservatives nor of Nic Bourne, but I don’t think anyone can claim that Bourne’s unseating in 2011 – simply because his party did “too well” on the constituencies – was in any way fair or appropriate.

    #3 and #4 could be mitigated by expanding the number of list seats relative to constituencies, but this would exacerbate #2. #5 could be mitigated somewhat by doing away with the actual list, and assigning regional seats to the failed constituency candidates who got the most votes in their seats. There’s not a lot you can do to about #1 though. Overall it’s a terrible system, barely better than having 60 FPTP constituencies would be.

  • Christian Schmidt

    The Welsh (and Scottish) system is actually quite similar to the one Germany uses since 1945, and you cannot argue that that hasn’t worked well.

    The main difference in Germany is that there are more list seats (50/50 with constituencies), so the result is more proportional. And in case some unproportionality remains, there are then special rules to make bring it in line (though these are sometimes complex and not thought through). And nowadays the actual allocation system has mostly been changed from d’Hondt to Saint-Lague, which uses odd-numbered dividers to increase proportionality further.

    To deal with #2 and #5 you would need an open list system like in Bremen or Zurich. But as this takes away constituencies it is disliked by politicians who want to continue feeling like being the king of their land.

  • Philippa Mahen

    I’ve been following your MOOC course and was confused by the explanation of the voting system as the total of votes you gave in the North Wales example were the constituency votes not the regional votes
    (comparing to http://www.assembly.wales/Research%20Documents/2011%20Assembly%20Election%20Results%20-%20Research%20paper-18052011-216014/11-023-English.pdf) (Table 9, page 14)

    Looking at this transcript, it is not the same as the video! The vote totals in this transcript are the regional totals not the constituency totals. (E.g. Labour votes in the video are 74,017, in this transcript they are 62,677). So could you please confirm that the numbers used in the D’Hondt formula are the regional votes not the constituency votes. (If so could you please put a note next to the MOOC video as it’s quite confusing).

    • Roger Scully

      Dear Philippa,

      Thanks very much for pointing this out.

      I really have no idea how this mistake came to be in the video. My original script, which I used for the filming, is as published on the blog – ie with the correct figures. It certainly wasn’t me who changed them. And I didn’t think to look at the figures when reviewing the video, as it would never have occurred to me that someone would have changed them.

      I’ll find out what went wrong and try to get it put right.

      Thanks again


  • Jo

    How does each party chose their regional list and what influence do their membership have in each case?

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