UK coalition government permutations 2010

So the UK elections were held 6 May 2010 and the outcome is as shown in the following table (headings under party names). The UK voting system is somewhat arcane, but basically for a party to win outright it needs a majority of seats in the house of parliament. (Seats in the house of parliament are allocated one to each constituency, a geographic voting area. Within each constituency, the prospective MP with the largest percentage of the votes wins). As there are currently 650 seats the minimum seats needed to form a majority is more than 650/2=325 seats ie 326 or more seats.

The UK is formed of 4 countries: England, Scotland, Wales and Northern Ireland. One of the parties in Northern Ireland, Sinn Fein, which has 5 seats as of the May 2010 election refuses to take their seats, because there is a ceremony where new MPs must swear an oath of allegiance the British Monarch (the Queen Elizabeth). As Sinn Fein would prefer that Northern Ireland be reunited with Ireland, and the country of Ireland separated from the UK after a civil war of sorts, Sinn Fein do not consider they have an allegiance to the Queen, so refuse to swear this oath, and consequently are excluded from parliament.

Anyway so that means there is an effective majority that can be thought of excluding the 5 Sinn Fein MPs, of more than (650-5)/2=322.5 ie 323 or more seats.

As I go on to describe below there is a coalition mechanism which can be used as a tie breaker with some peculiar rules. As news that I could find online (searching with google) and television commentators and politicians didnt seem to be talking much about what the permutations actually are, nor how many permutations there are etc, I figured I'd have to rectify that and do the calcuations myself! And here they are...


So bizarrely if the party with the highest number of votes doesnt have an overall majority, nor an effective majority, the current government gets the first right to see if it can form a government by forming a coalition with other parties that has collectively a majority (326 seats or more) (or perhaps more than the effective majority of 323 seats or more). It seems there is no particular rule about the maximum about of time the current government can take try to form a coalition. Nor how reasonable they have to be - leading to strange questions like could they hold out indefinitely? Seemingly so, only embarrassment would stop them. I think the tie breaking would be technically the Queen has the authority to step in and disolve the current government. So the main "threat" forcing sensible behaviour is going down in history as having embarrassed the queen by forcing her to disolve the current government.

The outcome of the May 2010 election unfortunately was that no party had a majority, nor an effective majority.

The current Labour (socialist) government's unpopular prime minister Gordon Brown, is a stubborn fellow who may just be the kind of person to see how far he can push it.

Now the opposition party (the party with actually the most votes now, the Conservatives (capitalists)) could try to form a coalition, with other parties also. However they only have second go at it. Only if the current government fails to form a majority can they go ahead.

And finally it is also possible for the Conservatives to form a minority government, and if the current Labour government resigned, the Conservatives would prefer to do that. However, if the Conservatives refuse to form a coalition with the 3rd largest party, the Liberal Democrats, then Labour could form a coalition with them. Intruigingly even the combination of Labour and Liberal democrats dont have enough votes to form a majority and they would have to include a minimum of one other party to form even an effective majority.

Also it is possible for the Conservatives to form a majority coalition, even with out either of the current Labour (the 2nd largest) party, nor the Liberal democrats (the 3rd largest) using a minimum of 3 other parties to form an effective majority (or 4 other parties to form a majority).

Defacto the Liberal Democrats have said they will give the Conservatives the first chance to form a coalition, but they will want concessions and some Liberal Democrat policies that the Conservaties think are stupid. The conservatives could chose to play hard ball and reject them. Then the Liberal Democrats would try to form a coalition with the Labour government. Or hypothetically Liberal Democrats could refuse to form a coalition with either party (being rejected by Conservatives, and themselves chosing to refuse Labour). But that doesnt seem too likely because the Liberal Democrats have not been in power for 80+ years so they are pretty keen to use this unique situation to their advantage.

However the conservatives dont get to form a coalition at all, until Labour (or Labour and Liberal democrats in search of other parties) gives up on trying to form a coalition. If Labour and Liberal democrats get together, while they need at least one other party, there are several to chose from. And some of those parties are Labour in leaning just of other countries in the UK (Scotland, or Northern Ireland), plus its relatively easy to bribe a smaller party with concessions that is not that closely politically aligned.

All of which goes to say that probably the conservatives have to do a deal with the Liberal Democrats, otherwise the Liberal Democrats and Labour will form a coalition with at least one other party and then the Labour pact will remain in power. This would obviously be very unpopular, particularly if the unpopular Labour prime minister Gordon Brown remained prime minister. It would not be viewed postively by the British public if two main losing parties got in power. Makes a kind of joke of voting. And many people were quite keen to have Labour and Gordon Brown removed from power.

Now also the liberal democrats are pretty keen to change the voting system - to one of proportional representation, so that in future they would have an influence in government proportional to their seats or votes, rather than with present system where they have no power, other than to vote against laws they dont like in parliament. Labour have offered a referendum on voting reform to try to interest the Liberal Democrats in a coalition deal. The limitation with the Liberal Democrats forming a government with Labour (and at least one other party) other than massive public unpopularity of such an act, is that it maybe unstable. Any party could pull out over a disagreement and force a fresh election. The process of changing voting reform would take at least 2 years. A Labour, Liberal Democrat (and other party) coalition would be relatively unstable because of the number of parties involved, and the unpopularity may not help the coalition stability either. And so depending on how they view the likely longevity of such coalition, the Liberal Democrats may not get to succeed in getting the voting system changed.

So the Conservatives could gamble on the weakness of the stability of the potential Labour, Liberal Democrat coalition to call the Liberal Democrats bluff. Ie to either reject them, or give very few concessions beyond already shared policies. Gambling that the Liberal Democrats dare not form a coalition with Labour due to the unpopularity of such a government, and the low stability of that government making it potentially unlikely they would achieve their main difference with the conservatives - proportional representation. In that way the Conservatives could get the policies they want and a Liberal Democrat coalition, or a minority government formed by the Conservatives only. (If the Liberal Democrats remained unwilling to risk a coalition with Labour and if they refuse to concede on proportional representation with the Conservatives). In fact the Conservatives have already offered an all party committee to discuss voting reform, but that is not a big promise. The UK has such things before and nothing came of it.

At least in the UK, proportional representation would probably not work out very well, because they are not used to dealing with it. Leads to a kind of stale-mate perpetual state of arguments, or compromise horse-trading, neither of which is very good. Especially in a period after 13 years of Labour government, when the economy is pretty much bankrupt - the UK is forecast to have a worse debt-ratio than Greece by the end of year. So the markets were looking for the Conservatives (capitalists) to sort out the economy, reduce taxes, reduce debt, reduce government waste etc. Right now the GBP exchange rate is falling vs other currencies as a result of this uncertain outcome.

All in there are 60 permutations of smallest potential coalitions. There are even more if you include coalitions with more than the minimum majority/effective majority. There may be some use to having more than the effective majority in case a minor party pulls out so the government still retains minimally an effective majority.

death Also note that there were 306 Conservative seats but it is assumed they will also go on to win in the Thirsk and Malton constituency which postponed for three weeks because of the death of a candidate, then having 307 seats.

And here are the table of permutations. one of those permutations is very unlikely: Conservative and Labour.

The permutations are below in the table.

Or you can download an openoffice format or excel format spreadsheet.

The permutations were formed by running this bc program through unix sort | uniq and importing into the spreadsheet.

conservative labour liberal

(northern ireland)

sinn fein
(northern ireland)

social democrat
& labour

(northern ireland)
green alliance
(northern ireland)
(northern ireland)
majority first
parties in
307(*) 258 57 8 6 5 3 3 1 1 1
minority 307338110000000000
majority 364281210100000000
majority 565 80211000000000
effective 324321410011010000
effective 324321410011001000
effective 323322510011000011
effective 323322510011000101
effective 323322510011000110
effective 325320510011010010
effective 325320510011010100
effective 325320510011010001
effective 325320510011001001
effective 325320510011001010
effective 325320510011001100
majority 327318510011011000
effective 323322610010011011
effective 323322610010011110
effective 323322610010011101
effective 324321610011000111
majority 326319610011001110
majority 326319610011001101
majority 326319610011001011
majority 326319610011010101
majority 326319610011010110
majority 326319610011010011
effective 324321710010011111
effective 323322301110000000
effective 324321401101001000
effective 324321401101010000
effective 324321401110000010
effective 324321401110000001
effective 324321401110000100
majority 326319401110001000
majority 326319401110010000
majority 329316401111000000
effective 323322501101000011
effective 323322501101000101
effective 323322501101000110
effective 325320501110000011
effective 325320501101001001
effective 325320501101001010
effective 325320501110000101
effective 325320501101010001
effective 325320501101010010
effective 325320501101010100
effective 325320501110000110
effective 325320501101001100
majority 327318501101011000
effective 323322601100011011
effective 323322601100011101
effective 323322601100011110
effective 324321601101000111
majority 326319601101001110
majority 326319601101001101
majority 326319601101001011
majority 326319601101010110
majority 326319601101010101
majority 326319601110000111
majority 326319601101010011
effective 324321701100011111

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