# PR counting – d’Hondt and STV systems

After perusing the results of the Euro Elections I just about feel confident enough to explain how the two different types of PR counting work. Northern Ireland, in common with the Republic, use the Single Transferable Vote system. The rest of the United Kingdom use the d’Hondt system, originally invented by Thomas Jefferson and given the name of an obscure Belgian Mathematician, Victor d’Hondt, who merely described what until then had been known as the Jefferson system. To quote Wikipedia

Empirical studies show that the D’Hondt method is one of the least proportional among the proportional representation methods.

Perfectly suited to that bastion of democracy, the European Union then. First is the description of the d’Hondt system, it is easier to understand. The voter chooses one and only one party. The total votes are then counted and arranged in order. The official explanation that the party with the highest number of votes wins one seat and then their count is divided by their number of seats plus 1 is best shown if we just divide all parties’ votes by 2 then 3 then 4 and so on. Here are the results for the London Region. The figures in red represent a seat.

 Party Votes Votes/2 Votes/3 Votes/4 Votes/5 LibDums 608,725 304,363 202,908 152,181 121,745 Labour 536,810 268,405 178,937 134,203 107,362 Brexit 400,257 200,129 133,419 100,064 80,051 Green 278,957 139,479 92,986 69,739 55,791 Tory 177,964 88,982 59,321 44,491 35,593 Chuckup 117,635 58,818 39,212 29,409 23,527 UKIP 46,497 23,249 15,499 11,624 9,299

The columns Votes/2, Votes/3 are the total votes divided by 2 then 3 then 4 and finally 5. It is then a matter of finding the eight highest numbers. The eighth seat went to the Brexit Party with a count of 200,129. This calculation is done for each Region, the number of seats is already known from the North East’s 3 to the South East’s 10. There that was reasonably easy to understand.

Now to the STV system used in Northern Ireland and oddly enough in the rest of the island of Ireland. Instead of choosing just one party with an X, the Northern Irish use numbers to indicate their preferences. They write 1 against their first choice, 2 against their second choice and so on. They only have to write 1 for their first choice , how far they go with choices is up to them.

Having looked at the published results it is now slightly easier to understand than it was though one part is still shrouded in mist. There were 572,447 valid votes cast. The first thing to do is calculate the Quota, this is the valid votes divided by 4 giving 143,112. It is divided by 4 because it is the number of seats, three, plus one. Any party getting more than the Quota gets a seat. This time, no party reached that total in round 1. The number of preferences cast were as follows

 Party Pref 1 Pref 2 Pref 3 Pref 4 Pref 5 DUP 124,991 2,300 28,131 Alliance 105,928 9,399 6,936 1,654 46,453 Sinn Fein 126,951 1,166 73 11 24,236 TUV 62,021 1,851 15,668 10,314 225 SDLP 78,589 2,360 1,152 313 UUP 53,052 1,684 Greenie 12,471 UKIP 5,115

What happens now is that they start adding preference 2 to preference 1 for each party and then preference 3 to that total and so on. As soon as a party hits 143,112 or more, they get a seat. Here is the calculated number of votes. A number in red means that party gets a seat.

 Party Count 1 Count 2 Count 3 Count 4 Count 5 DUP 124,991 127,291 155,422 Alliance 105,928 115,327 122,263 123,917.00 170,370.00 Sinn Fein 126,951 128,117 128,190 128,200.50 152,436.50 TUV 62,021 63,872 79,540 89,854.00 90,079.00 SDLP 78,589 80,949 82,101 82,413.50 UUP 53,052 54,736 Greenie 12,471 UKIP 5,115

On a first past the post it would have been, IRA, DUP, Alliance. With the STV system it was DUP, Alliance, IRA. The lardarse Alliance candidate profited from the immense number 5 preference vote of 46,453. Unlike the d’Hondt system where the numbers decrease from left to right, in the STV system they increase.

The way they count the votes explains why it takes so long to get a result in Northern Ireland and it seems they are still counting in the Republic. They count all the number ones, then they have to get all the ballot papers with a number two and count them and so on.

On the electoral reform website there is a wonderful PDF called What-is-STV and it is a trip into Alice in Wonderland. The mist part of my understanding is where they eliminate candidates from the count. This is somewhat explained in this PDF. It also explains that when a candidate reaches the required quota they apportion the preferred votes as follows. They calculate the difference between the votes and the quota (e.g. DUP 155,422 minus 143,112 = 12,310) and then allocate the DUP’s preference votes according to this ratio. This may go some way to explaining the IRA’s low numbers in Pref 4, DUPers are unlikely to choose the IRA as any kind of choice. No wonder one of the Republic’s counts ended up in court. Furthermore the electoral reform website make various claims about the advantages of STV, many of them look like lies or disadvantages to my jaded eye. Most PR systems lead to permanent coalition gummint and as bad as FPTP is, coalitions are worse.

Having looked around for this information it seems there are as many ways of calculating PR results as grains of sand on a beach. It is a bit of a shambles.