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Skip to 0 minutes and 4 secondsNational Assembly for Wales election is now only a few weeks away. But do most people know how the voting system for the Assembly works? Well, probably not. Here, we'll try to make it more clear. We use a different voting system for National Assembly elections than in general elections for 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's known as the Additional Member System, or AMS. Under AMS everyone has two votes-- one for an individual candidate in their local constituency, the other for a party in a border region. The regional vote is not a second preference vote.

Skip to 0 minutes and 49 secondsAnd people can vote for the same party in the region and the constituency. National Assembly for Wales has 60 members. 40 are elected in the constituencies, the same constituencies we use in general elections. The 40 constituency members of the Assembly are elected in just the same way as we choose our MPs. So the winner in each constituency is the individual candidate who gets the most votes. Now that's fairly simple. The more complicated bit of AMS concerns how we use the regional, or party vote, to elect the other 20 members of the Assembly. These people are chosen in five broad regions-- North Wales, Mid and West Wales, South Wales West, South Wales Central, South Wales East.

Skip to 1 minute and 37 secondsAnd 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 divided by S plus 1, where V equals the number of votes a party has won and S equals the number of seats that is 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 that is won in previous rounds.

Skip to 2 minutes and 28 secondsNow, 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. 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 plus 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 for round one.

Skip to 3 minutes and 12 secondsAfter 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 Conservative list of regional candidates for North Wales, in this instance, Marcus Wood. 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. So it equals three, based on their two constituency seat wins, plus their regional seat from round one. This produces the following calculations in round two. In this round, Plaid Cymru has the largest total.

Skip to 4 minutes and 0 secondsSo they win the second North Wales regional seat. This seat went to the top candidate on the Plaid North Wales list, LLyr Hughes Griffiths. We again repeat this 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 in round two. So here's round three. This time around, the Conservatives again have the largest total and so win the third North Wales regional seat. This was awarded to the second highest candidate on the Conservative list for North Wales, Antoinette Sandbach.

Skip to 4 minutes and 46 secondsFinally, the last North Wales regional seat is 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. So here is round four. 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, simple, eh? Well, 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.

Skip to 5 minutes and 33 secondsAnyway, like it or not, it's the system we have at the moment, so people ought to understand how it works.

Skip to 5 minutes and 43 secondsIn this case, that is correct. Although if there had been a five regional seats per region, Labour would have won the fifth one in North Wales.

Skip to 5 minutes and 57 secondsThe AMS system is designed to achieve greater proportionality in the overall results than you get from just the outcome of the constituency elections. By proportionality, we mean a closer match between the percentage of the votes that the 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 votes and 32.2% of the regional votes. But Labour won over 50%, five of the nine constituency seats in North Wales.

Skip to 6 minutes and 37 secondsNow after the four regional seats of North Wales were elected, Labour had won five of the 13 assembly members for North Wales, or 38.4% of the total. So Labour's share of the votes now match much more closely this proportion of the elected representatives. In short, the system did exactly what it was designed to do.

Skip to 7 minutes and 0 secondsThose elected in the constituencies represent that constituency. The regional members represent their party across the region as a whole.

How Does the Electoral System Work?

The Welsh Assembly uses a different electoral system from the UK Parliament. Roger Scully explains how the Welsh system works and examines previous election results.

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This video is from the free online course:

Scotland and Wales Vote 2016: Understanding the Devolved Elections

The University of Edinburgh