User blog:Laptop Zombie/2015 UK election with a regionalised form of Proportional Representation

The d'Hondt method, a form of Proportional Representation, had long been used across Europe and around the Globe.



In Britain, however, the political landscape varies wildly between the constituent countries. GB-based parties have rarely won a seat in Northern Ireland, leaving parties like DUP, UUP, Sinn Fein, SDLP and the Alliance in Northern Ireland. Meanwhile, there are nationalist parties in Scotland (SNP) and Wales (Plaid Cymru). The fact that many parties have particular regional bases mean they receive much more seats that those whose votes are spread out evenly. Furthermore, parties generally neglect voters and refuse to campaign in "safe seats". In the US presidential election of 2012, most of the campaign money went to states like Iowa, Florida, Pennsylvania, Ohio, North Carolina, Nevada etc.

When considering the use of the d'Hondt method, however, the localised nature of UK politics must be taken into consideration. Thus, this blog will use the d'Hondt method as if the elections in England, Scotland, Wales and Northern Ireland have taken place separately. The d'Hondt method will be used with votes of individual parties in individual constituent countries.

The data was fetched from BBC. Only parties with more than 10,000 votes in a constituent country will be included.

Link: http://www.bbc.com/news/election/2015/results

Abbreviations:

Con = Conservative, Lab = Labour, LibDem = Liberal Democrats, TUSC = Trad Unionist and Socialist Coalition, NHA = National Health Action, SNP = Scottish National Party, PC = Plaid Cymru, SF = Sinn Fein, SDLP = Social Democratic and Labour Party, DUP = Democratic Unionist Party, UUP = Ulster Unionist Party, TUV = Traditional Unionist Voice

Eng = England, Scot = Scotland, NI = Northern Ireland

Step 1: Fill in the Votes


Only parties with more than 10,000 seats were included.

Due to the fact that DUP and UUP have very similar policies, it would be natural these parties join an electoral alliance to receive more votes (because the d'Hondt method usually favours larger parties). This calculation follows that assumption. The d'Hondt method would again be used to distribute the seats won by the electoral alliance among the two members.

Step 2: Calculate the Seats


The link I used was http://icon.cat/util/elections

Since in any case TUSC, NHA, TUV and Sylvia Hermon did not won a single seat, they were omitted from the seat table. The seat distribution was independently performed in each constituent country, and the seats were then added up.

This, of course, is far off the real results. Tories get 90 seats fewer, Labour 31, SNP 26; but the LibDems get 42 more, the Greens 22 more, and most importantly UKIP 81 more than the real results. How pivotal the UKIP becomes will be discussed later.

Step 3 and 4: Confirm the fairness




I calculated the Vote/Seat ratio for each party that won at least 1 seat: This is generally fairer than the real results, which gave SNP a ratio of just 26k v/s, and UKIP a ratio of 3900k v/s.
 * The 6 largest parties (Con, Lab, UKIP, LibDem, SNP and Greens) have roughly the same V/S ratio, about 46k-50k votes/seat
 * Alliance Party in NI gets a markedly high V/S ratio, because the d'Hondt method favours larger parties in NI
 * Plaid Cymru and the remaining Northern Irish parties have roughly the same V/S ratio (30k-36 votes/seat)

Next, I computed the vote percentage of each party, ignoring the votes from small parties that did not amount to anything. The first sum (30393921) is calculated as the sum of votes for any seat-winning party that was included in the table (discounting NI Conservatives and NI Greens, which was a reality). The second sum (30336392) is calculated as the sum of votes for any seat-winning party in a particular constituent country (further discounting NI UKIP and Scottish Greens votes which did not yield a single seat).

Percentages received based on these two sums differ modestly, owing to the fact that these sum differ by only about 50k votes. The seat percentages also follow the vote percentages closely, confirming that this system is much fairer than FPTP.

However, there is something that needs to be noticed: while normally, the d'Hondt method benefit large parties; in this scenario the d'Hondt method actually reduce the share of the Conservatives (-0.25%), UKIP (-0.11%), LibDem (-0.27%), SNP (-0.17%) and the Greens (-0.25). You guessed it - it's because the seats were distributed unfairly between the constituent countries. The Northern Irish parties (and Plaid Cymru) have lower V/S ratio and get a larger seat share than British parties (excluding PC). This will be investigated below.

Step 5 (not really a step but anyway): Investigate Constituent Countries Seat Distribution


You see? England and Scotland get 47k-50k v/s. Wales and NI get 37k-39k v/s. It's an obvious problem, and, under some continental models, proportional representation is used to distribute seats among their (multi-seat) constituencies.

If the d'Hondt method is used to distribute seats among the Constituent Countries, England would get 543 seats (+10), Scotland would get 62 seats (+3), Wales would get 31 seats (-9) and NI 14 seats (-4). This problem was discovered too late, when the whole project was almost finished; thus the whole seat redistribution was never done. You can try it.

Step 6: What are the possible Coalitions?


Just the Conservatives and UKIP had 323 seats, enough to govern; the Irish Unionist Parties have 9 more seats. On the other hand, the left-wing parties (Labour, SDLP, SNP, PC, Greens) won just 262 seats between them.

Without UKIP, Parliament is left with 563 seats. The maximum number of seats the Conservatives can gather in such a Parliament would be Con+DUP+UUP+LibDem+Alliance, or 301 seats. Labour may gather a maximum coalition of Lab+LibDem+SNP+PC+Greens+Alliance+SDLP, or 313 seats. (of course, none of these is stable in a slightest sense; especially LibDem+Greens is disastrous). UKIP would play a pivotal role in such a parliament. Think of the Danish People's Party or the Sweden Democrats.

Maybe FPTP wasn't bad at all for Britain?