Thursday, April 14, 2011

One nation under PR

A comment from Harryurz over at the Shuttle got me wondering about how PR would have affected the 2010 election. As I've mentioned before due to the spread nature of PR the only true system would be to take the entire UK vote and allocate seats by Party with each Party then determining who gets to fill each seat.

It all sounds fair, but how would this be done?

The total valid vote for 2010 was 29,650,211; with 650 seats available each Party needs at least 45,616 votes to gain a seat. Except they don't. They need 45,615.709... seats. Do I round up; do I round down? I'll do neither and leave it at that figure exactly. Now how do I allocated seats? I could start with the highest voted Party divide by the seat requirement take the lowest integer and then repeat for each Party. Except by doing so a Party with only 0.02% of the vote (5,379 votes) will gain a seat that's really an eighth of a seat; hardly fair.

Instead I'll drop any Party that has under the seat-vote requirement. However now I'm dividing 650 seats between their combined total votes; in this case that would mean the new seat-vote requirement is 45,185.638.... Do I divide by the original figure or the reduced figure?

Whichever figure I use do I then round those seats up or down; if I just take the integer will I reach 650? If I don't do I then put back in the previously dropped Parties or allocate the remainder? How do I allocate the remainder?

Is this still fair? Here the flaw is that by using the Original seat-vote a Party may gain a seat with the remainder of the vote which is less than the full vote to one of the Parties removed.

The process I use therefore is as follows:

  • Calculate the vote required per seat from the total.
  • For both the Original Seat Vote (O PR) and the Reduced Seat Vote (R PR) drop any Party below the figure and allocate the integer of seats to each Party. If any seats remain allocate them to each Party in order of their remainder, highest to lowest, until all seats are filled.
  • For the O PR+ allocate the seats to the Parties with votes above the Original Seat Vote; list the remainders then reattach this new vote tally to the dropped Party list and assign seats by this figure highest to lowest. (So the Conservatives have a remainder of 43,441 which is still the highest figure so they gain one of the unassigned seats. The Alliance Party have 42,726 votes in total, which is higher than the SNP's remainder of 35,218, so they get a seat. Then the SNP gain a seat and so forth).

In all cases ignoring the Speaker, who should be assigned a seat from one of the Parties, the result is as follows:

PartyCurrentO PRO PR+R PRVotes
Alliance Party of N.Ireland101042,762
Christian Party001018,332
Democratic Unionist Party8444168,216
English Democrats022164,826
Liberal Democrat571501501516,827,832
Plaid Cymru3444165,394
Scottish National Party6111111491,376
Sinn Fein5444171,942
Social Democratic and Labour Party3333110,970
Traditional Unionist Voice001026,300

Although more complicated to work out the O PR+ result is perhaps the truest reflection of the political make-up of the UK and I think it is safe to say we'd have probably ended up with a Lab/LibDem coalition.