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UK Election Arcana, Explained By Software
An anonymous reader writes "For the first time in 35 years the UK government is looking to be at risk of getting a hung or coalition government. (The most recent previous hung parliaments were in 1974 and 1929.) The voting rules are somewhat arcane and the votes this time are such that there are many strange possible outcomes and a surprisingly large number of permutations of coalitions that could be formed and political strategies that may go into their forming. There are at least 60 permutations, some more politically plausible than others. Adam Back wrote some software to work out the permutations, and lists some of the arcane factors affecting the outcome. If Labour Prime Minister Gordon Brown chose to, it would appear even that he could simply refuse to resign, ostensibly trying to form a coalition indefinitely, maybe even forcing the Queen to dismiss the current government, which last happened in 1834 under King William IV."
Silly Brits.
This is why they need a reasonable, commonsense system like our electoral college.
Why is coalition government called "risk"? It's quite common in continental Europe and in European Parliament too. What is the problem here?
What will Slashdot do without the steady stream of news about how the UK is becoming more of a surveillance state? There will hardly be anything here anymore.
I'll be going back to hang out with the overzealous teenage ubuntu fanboys and militant atheists on Digg
I would be perfectly happy letting a piece of software choose the goverment. As it is now we aren;t represented by the best person for the job, rather the person most able to gather votes.
How is this arcane? The article plainly describes how a British-style parliamentary system works, as practiced in many countries throughout the world (including Canada), and with a special emphasis on the outcome of the most recent election. This is only confusing to foreigners and people unfamiliar with basic civics.
This shit happens when you have more than 2 parties, but the genuine options are:
Tory+lib dem coalition
Tory minority gov
Rainbow coalition (Labour+Lib+SDLP+DUP+Green+plyd cumri+possibly SNP) [the murdoch media like to call this the coalition of the defeated but aslong as i get my electoral reform i don't give a shit]
"The voting rules are somewhat arcane"
If no party has >50% of seats, there is no majority and parliament is hung.
Must be tricky for you ex-colonies to understand, I know
1/ The conservatives go it alone, and try to run a minority government with occasional help from the Northern Ireland parties they are allied with, and possiby the liberal democrats on some issues. This is unlikely to last long to be honest
2/ The conservatives and Liberal democrats do a deal, and make a joint platform. This is the only one that has got any possiblity of lasting. The tricky part is as the 3rd Party the Liberal Democrats want some form of proportial representation (which would double their seats in parlament). The conservatives don't want that at all. They like the current system. I don't know what is going to happen here. I guess the Lib Dems will blink "for the good of the coutry", and a deal will be done.
3/ Labour and the liberal democrats do a deal, this does not give them a majority though, so they will need the help of again ulster parties (different NI parties are alligned to each of the mainland parties). and the welsh/scottish natioanlist parties. This will probably fragment after a while too. This grouping is possible as they limp along for a while, and would bring in some form of proportional representation or other electoral reform and eventually we have an early new election.
Some of the more outlandish things like Gordon brown not resigning if there was a viable alternative is just silly. He *could* do it and it would be a mess if he did, but it would destroy most of the support for his party for years to come. You have to be gracious in defeat in these things if you want to bounce back.
I suppose there is
4/ They just call a new election, as well, but that is not going to be popular with the public and noone really has the cash to fight it (particularly the liberal democrats, who have the most to lose from a new election).
TFA is wrong - the most recent hung parliament was 1997 (before the election that year). Second most recent was 1977.
Full details in http://www.parliament.uk/documents/commons/lib/research/briefings/snpc-04951.pdf
This is why they need a reasonable, commonsense system like our electoral college.
Your electoral college was probably based on the UK parliament. We vote for MPs who then effectively determine the prime minister. The only difference is that the 'electoral college' then hangs around to pass laws in place of a separate house of representatives. In this way we have fewer elections and avoid the deadlock that would result from having a prime minister without legislative support.
;-)
I should also point out that the original article is wrong in that the UK is not 'at risk' of a hung parliament (not government): it already has a hung parliament. No need to get excited though: there is a word of difference between a hung and hanged!
1. Brown can't refuse to resign indefinitely -- there is always a confidence motion after the Throne Speech at the beginning of parliament, which is scheduled for the 25th. If he can't put together a majority vote in parliament then he will be gone then. So it'll be over in at most two more weeks, although it's unlikely to take that long. We'll probably know what's going on in the next couple days.
2. There are a bunch of tiny regional parties, but some of them are closely bound to one of the big players (SDLP is effectively Labour, Alliance is LibDem, DUP is Conservative), so there's really fewer options. In particular, if you consider a Labour/LibDem/Green/DSLP/Alliance combo they STILL wouldn't have a majority. Neither would Conservative/DUP.
In that scenario, the balance of power on every vote would come down to the nationalist parties: SNP (Scotland), Plaid Cymru (Wales), and Sinn Fein (Northern Ireland). [Note: Sinn Fein MPs make a point of *NOT* attending Parliament as a political statement, but if they thought they could control the balance of power they could always change that!] This would be completely unworkable and everybody knows it.
There's really only three options on the table right now:
AV+ * Maintain single-member constituencies.
* Would lead to a more proportional result than first-past-the-post system , but would still give a built-in advantage to the largest party and allow one-party rule during landslide years.
* Would be more likely to prevent extremist parties or fringe parties from winning seats than entirely proportional systems. [No BNP!]
* Would lessen the necessity of tactical voting.
The Roy Jenkins Commission settled on this option.
A government which can't use its whip to push its Party's MPs into voting a particular way such that a majority vote is inevitable is the best sort of government.
After all, an MP is voted in by his constituents to represent his constituents, not his Party.
Actually, a government cannot hold on indefinitely. Or at least, they can't pass legislation as a government. The reason being that when Parliament opens, the first item is a debate on the Queen's speech (which is parliamentary shorthand for a debate on the legislation that will be introduced by the government). If the speech is not approved, the government has lost a vote of confidence and is forced to resign, or hold another general election.
That is best dealt with via educational, not electoral reform. e.g. the ability to solve complex maths problems like: 'if there are 2,143 people on the electoral roll for my polling station what is the minimum number of ballot papers I need?'.
Electoral reform is to solve problems like why does it take approximately 4 times more votes to get one lib dem politician vs. labour/conservative ones?
For those not trained in the intricacies of the Westminster system, while it is true that Gordon Brown could refuse to resign, that's not quite the way it would happen. Gordon Brown, as the incumbent PM, has first dibs under the Westminster system to form a new ministry. Because, in the Westminster system, a country is never without a government, Brown's Labour party is still technically the government and still advises the Queen. Thus he could go to the Palace and advise the Queen that he is still capable of heading a government. Now, theoretically, the Queen could use her Reserve Powers to dismiss the PM, but such a thing has not been done in a very long. The normal constitutional procedure would be for the Queen to accept the advice of Her Prime Minister and Labour again would form the government, despite having less seats than the Conservatives, and no configuration of coalitions (there aren't enough Liberal Democrats, SNP and other groups who tend towards left-of-centre to add up to a majority in the House of Commons).
Now what happens at that point is entirely up to the Opposition. Immediately upon forming a new government, there is the Queen's Speech (or, as it's referred to in the Commonwealth the Speech from the Throne), which is a confidence motion. The Conservatives and whoever else they allied with would have the votes to topple the government. A vote of no confidence in the Westminster is instant death for a government. At that point, Brown would cease to hold the constitutional monopoly on advising the Queen, and she would have the choice of either calling a new election or asking someone else to form government.
However, political realities being what they are, if the Conservatives and the LibDems form a coalition, it's almost certain that Brown will resign.
The world's burning. Moped Jesus spotted on I50. Details at 11.
The problem both Labor and the Conservatives have with PR, is that it would lead to coalition governments. This is easy to see. The Liberals had 23% of the last vote, the Conservatives 36%, and Labor 29%. This is more or less the share of the popular vote that the three parties have had for the last 30+ years.
You can see that if each party has the same number of seats as they have percentage of the votes, then no party is generally going to have a total majority over the other two. You will just about always have a situation, like in Holland, where the third party is in every government, sometimes in coalition with Labor and sometimes with Conservatives.
The reason why both of the two larger parties do not want this, is that they represent essentially minority interests. The Conservative Party historically represents inherited wealth and also the rural areas. Which are dominated by large landowners. The Labor party represents big cities, the industrial workforce and the public sector trade unions. And of course the large welfare population of dependents. Both are ready and eager to impose heavy costs on the country as a whole, as long as they get some, often fairly small, percentage of those costs for their own interest groups. This tendency, which is a form of looting, gets more extreme with the second and especially the third term of any government. In the first term of any government, it tends to behave responsibly. The first Blair term, for instance, was marked by restraint in public spending and no deals with the public sector unions.
The second and third terms have seen enormous public spending, mostly on public sector union wages, which has been marketed as 'investing in our great public services'. This has imposed costs on the country which dwarf the benefits to the recipients of the benefits, but no-one cares what it costs the country, as long as they are doing better.
The Conservatives are no better. We can expect something similar in the second and third terms of any Conservative government. The interesting difference about this Labor government has been its approach to the finance sector, which is referred to in the UK as 'the City'. This Labor government has been much closer to the City than any previous one.
You can see that this pattern of behavior will be eliminated by coalition governments. The problem is, in your first term you generally govern for the country, the better to get a second term. When in the second or third term you move to payoff time, and start the outrageous rewarding of your interest group, if its a coalition government, the other partner will just say no, force an election, and then move into coalition with the other large party. It will be game over.
The sheer rage that the idea of proportional representation arouses in the hearts of Conservative Party stalwarts is due to this. They are seeing the prospect of the second and third term troughs being smashed before their eyes. No more feasting. The whole rationale of the parties goes.
What happens with coalition government, on say the Dutch lines, is that it replaces the focus on who is in power, with a focus on what the program is going to be, what the policies are. In the UK at the moment all anyone cares about is who is in power, because whoever it is, can hand out the spoils. Once you cannot do this any more, you have to focus on governing for the country. Now that is not what either of the two large parties want to do, at least, no more than they absolutely have to.
And this is why far more of the UK wants PR than anyone in either of the two big parties will admit. It is not just the 25% that vote Liberal. It is also those who routinely switch from one party to the other, to give the other guys a chance.
If you think about it, in the situation I have described, what does the rational voter do? He/she is confronted with a two party system in which the second and third terms of any government are going to feature irresponsible looting of a sort mos
> If Labour Prime Minister Gordon Brown chose to, it would appear even that he could simply refuse to resign, ostensibly trying to form a coalition indefinitely,
No. At any time a motion of no confidence can be raised; if a majority agree, the PM is out.
Just let the Queen rule. She can do no worse than any of these buggers!
But, she has to change the rules of succession so that that bat-eared freak Charles doesn't become King.
Britain's last hung parliament was in 1996-97, under John Major, not 1974. 1974 was the last time a hung parliament was elected; Major was elected with a slim majority, and the government became hung due to attrition during the course of the parliament.
Quidnam Latine loqui modo coepi?
"If Labour Prime Minister Gordon Brown chose to, it would appear even that he could simply refuse to resign, ostensibly trying to form a coalition indefinitely, maybe even forcing the Queen to dismiss the current Government"
It would be in VERY poor taste given the vote results. While technically possible it ain't going to happen that way. And should he refuse he would soon face a vote of non-confidence in the parliament. Fail that and BOOM, he's out, and the Queen asks someone else to form a government. The fundamental principle of parliament is that you only govern by the will of parliament. If you don't have that, you're gone. Even a government with a majority could technically fall if enough people in the governing party voted non-confidence. Piss off enough people and it could happen (say, if the cabinet and prime minister started doing something terribly unpopular, refused to resign, and the rest of the party split and turned on them).
Maybe Canada could give them some advice. We've got a very similar parliamentary system and we've had 3 "hung parliaments" (we call them "minority governments") over the last 6 years. The sky has not fallen. In fact, if you compare the fallout of the economic crisis in the UK or the US to Canada, a minority government obviously doesn't matter much to the equation. Furthermore, minority government is the main reason we haven't yet had DMCA-style laws passed (it's why the two previous bills with DMCA-style provisions died -- an election was called). Minority government is a *good* thing, as far as I'm concerned. It means the government in power doesn't have the ability to ram things through parliament without getting the support of the opposition. While that makes governing more challenging in some ways, it also means the government has to listen to the opposition and the people that voted those MPs there too. They all have to negotiate rather than rule by majority alone. Even the opposition parties sometimes manage to introduce and pass bills.
[Shrug] The UK knows what they're doing. The one thing you have to make sure of is that the politicians get the message from the people that you don't want another election and any party that doesn't try to get along will take a beating at the polls. That keeps the politicians talking with each other.
Don't you find funny that the image displaying the slashdot show an american flag on a UK election article ?
"It has been said that democracy is the worst form of government except all the others that have been tried," Sir Winston Churchill. The Brits don't have to keep proving his point.
The genius of Hare-Clark would be of great help in both the US and the UK. Pity only Tasmania and the Australian Capital Territory have grasped its simplicity, fairness and genius.
A dream is good. A plan is better.
Runaway recursion near line 2. Bailing out...
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Where does it say they're successful?
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Take half the seats and make them geographic constituencies directly elected by Single Transferable Vote. Allocate the remaining seats proportionally.
As an American living in the U.K., I can't for the life of me figure out why having no clear majority, necessitating that opposing viewpoints actually talk to each-other and compromise, could possibly even begin to be anything other than a very good thing. All I've heard are vague notions of "strong government", but when I ask what that actually means, and why it would be a good thing, I haven't heard an answer at all.
And parliament still looks a thousand times more sane than congress.
-- 'The' Lord and Master Bitman On High, Master Of All
Here you can see the dutch system in a "game". The site is in dutch but it should be simple enough, even for people from the colonies. Coalition game
You can select a poll to base the results on, and then select the parties you want to form a coalition with, you got to fill half of the seats to have a majority.
I will briefly list the parties to explain them to people with different political systems.
CDA: Christian Democrats, the leaders of the last government. Bakellende (sorry Balkenede) is about as popular as Blair/Bush but with the honesty or razor sharp wit. In european terms they are moderate right-wing but did take part in governments that legalized cannabis, prostitution and abortion. By American standards: Communists.
PvDA: Partij van de Allochtonen, sorry Party of labor (Allochtonen = Immigrants), a once socialist party that has become increasingly liberal. Armchair socialists. The party is split between its socialists background and its more modern liberal elite. There are clashes, because being liberal about immigrants hurts the "workers first" of the socialist backing. By American standards: Communists.
SP: Socialist Party, the protest party originally, it is now more and more the home of ex-PvDA who are "power-to-the-people" rather then tree-huggers. The party used to be lead by a charismatic guy who made the party from a tiny protest group into one of the bigger parties, but he gave up and since then the party has been in trouble. It suffers a lot from strategic voting. People who agree with them instead vote on PvDA so their vote is not "wasted". By American standards: Redder then red.
VVD: Liberals, probably closest to the lib dems. People here consider them capitalist, closest to the democrates in the US. This shows how little people here understand the US. By American standards: Communists.
PVV: Party of Liberty, Geert Wilders. The spiritual succesor to Pim Fortyun but a lot less nice, not gay and a lot more scary. The answer to everyone who is dissatisfied with the last few decades. SP if you have a heart, PVV if you don't. The party goes up and down a lot, but the signal the party is giving is that first we had Pim, he first dared to address that there might be issues with muslim immigrants. He was killed. This guy goes far further and openly blames Islam for pretty much everything. If this time the system still doesn't listen, then I fear who comes next. I don't fear Wilders, I fear the guy that comes after him. Hitler did not create the National Socialist party. There were others before him, not the same but indicators of a upcoming problem that was ignored. By American standards: Communists.
GL: Green left, prove the political spectrum goes far further then just left and right. This one is like the SP to the left of the PvDA, but also completly different from the SP, these are the tree-huggers. By American standards: Communists.
CU: Christain Union, a party impossible to really classify. Part of it is left-wing, others are right wing. Think caring conservatives, how difficult a concept that might be. Part of the last government, one of the smallest parties being given a huge role because the PvDA was to scared to form a left-wing coalition. Not the smartest move they made. By American standards: Communists.
D66: Democrats, no, not like the American ones. Yes, you know it is coming. By American standards: Communists. Liberals mostly but with a strong elitst element. In Holland the biggest struggle right now isn't so much right vs left but elitst vs man of the people. A lot of voters feel politicians don't listen to them, that they rule from an ivory tower. D66 is so far up the ivory tower they sit on gods lap. Party was decimated sometime ago, but has come back with the support of the elite who can ignore the discussion about immigration because no muslims can afford to live where they do. By American Standards: The dreamier side of the democrats
MMO Quests are like orgasms:
You may solo them, I prefer them in a group.
No it isn't, it means you get twice as many shit laws. Horsetrading. We want to put property taxes up! But *we* want to put income tax up! Compromise: all taxes go up.
The exception is where a compromise would actually make sense; in that case nothing gets done.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
If parties A, B and C get a declining share of the vote and require a coalition to get a majority then negotiation is required. However, the outcome of the negotiation is random. Any party may or may not form part of a government, regardless of popularity.
Indeed, if the largest two parties differ the most then the third most popular party is likely to govern continuously to the exclusion of more significant interests. That's too random and my vote doesn't make a difference.
Let each party have an MP for each constituency, but then multiply their voting power by the percentage of the vote in that constituency they got.
Of course it means you have more money grabbing MPs, and we'd need a bigger wall to put them against in the future! :)
No parties have a coherent idea about EU tax etc, so the Pirate Party is at least honest about not having much of an opinion on it.
Perhaps his next program could find a better color combination than cyan text on a black background?
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
The whole posts reads like someone who is unaccustomed to anything else than two-party democratic systems, which have a big problem representing minority interests. Coalition governments work well, and I think are the standard in most of Northern/Western Europe - the most stable and wealthy countries in the world.
Lib Dems support STV with several regions, so you still get a local link - larger than what we currently have, but with 650 constituencies, the UK is already pretty huge. And you have several MPs in each region. This has a side-benefit that you have more than one MP to go to. The problem at the moment is that if your local MP is a Party puppet (always votes with his party line), directly opposed to the issue you're concerned with, or just plain useless, you have no one to turn to.
A commission set up by Labour proposed a system called Alternative Vote Plus, which maintains local constituences pretty much as we have them now, but makes it proportional using a top up system.
the parties decide who the MPs are
No, this is also false. In both systems under consideration, people vote for candidates. What you claim is only an issue in closed party systems (which I agree are bad).
So please look at what's being proposed, before you dismiss all systems of PR based on some flawed version you heard about.
There's almost no situation where a proportional representation system would beat out a FPTP system
Let's see:
* Large problems of tactical voting and "wasted" votes. This would be reduced under STV and AV+.
* Problems of vote splitting, again reduced under STV and AV+.
* Problems where parties are vastly under-represented, needing many more votes to elect a single MPs (Lib Dems need about 4 times as many votes per MP compared with Labour and Tory).
* FPTP doesn't even maintain ordering - even if Lib Dems came second or even first in the popular vote, they'd still be third in terms of number of seats. It's possible for Labour to get the most seats, whilst still coming second or third in the popular vote.
Pretty much anything beats FPTP. Even if you don't want proportional, let's still have something like Alternative Vote, Condorcet. Anything but FPTP please!
Well, I suppose we should do like in Australia, where they tend to have a well-hung parlament, or so I am given to understand.
Instead of some fucking joke?
The Pirate Party is a fucking novelty. If you're working on the pirate party you're not making things better, you're making things worse.
If you were a Green, Libertarian, Free Soil, Whig, Tory, or anything but the current political system, sure, but Pirate Party? C'mon.
Non impediti ratione cogitationus.
The ability to dissolve government is very powerful POLITICAL power. and exists as a check on the power of the Government to decide that it no longer wants to be a democracy. The deal, that you so badly mis-characterised is that the Queen can use that power any time she deems too, but if she did so without good cause then the country would be mightily pissed off with her. It's a fear-fear thing, the Government is in fear that the Queen will dissolve it if it overreaches and the Queen is in fear that the country will kick her out if she overreaches. Believe me - if a majority coalition was agreed upon that did not involve labour, and Gordon Brown refused to resign then the people would expect her to dissolve Government.
Whilst Oprah might want to be a queen, she most definitely is not. The Queen earns the UK a ton of money each year in tourism revenue. Oprah does not. The Queen is famously neutral (publicly) on politics as long as everyone follows the rules. Oprah wasn't able to achieve this (she let her guard down by campaigning for Obama).
No system is perfect, but the UK's is pretty good. I think it would be better if it introduced single transferable vote instead of first past the post, as that would eliminate the concept of a wasted vote (at the local level). It would result in more hung governments as more parties would gain seats, and some would say that's a problem. Personally I believe that all good government is a form of negotiated compromise anyway. It's the whack-jobs of the World with unlimited mandates that you've got to beware of. But I digress. My point is that your choice of words, "ugly hack, patch, workaround" suggest two things. Firstly that you're a coder, and secondly that you'd like to see the whole UK governmental system thrown away and redesigned from scratch in a waterfall manner. Various countries have tried that in the past (Russia, China etc) and they ended up with communism. I'll stick to the agile principles thanks.
BTW, don't call my Queen a bitch you wanker, I bet your code sucks worse than your arguments.
What most people don't understand is while most countries have only two blocs, Israel has seven blocs, maybe four if you squint real hard. The system is unstable because the country is divided, not the other way around! And even this instability is exaggerated. Israel had 15 elections from 1945 to 2001. In comparison, the UK, Norway and France had.. 15 elections (figure 11 - yes, I know it doesn't count parliamentary replacement of PM which is why Italy looks too good, but that happened only once in Israel's history and at the end the ruling coalition kept its position).
PR guarantees that everyone is represented and that the government is legitimate and has majority support. Given the history of the Middle East and Israel, this is more than enough.
Americans may not fully appreciate the differences between the US and the UK systems. The most important is that the US system was deliberately set up to have lots of checks and balances. If you like, think of them as safety catches and damping mechanisms. The UK system has just about none of these.
If you look at a UK election, you see that one of three things has occurred to bring it about. One, the government of the day decides to call one. It can do that any time, and this is a very powerful weapon, as it can time elections to coincide with upsurges in the polls, caused by, among other things, short term financial booms. Two, it loses a vote in the legislature on some important issue. Three, it comes to the end of its term, which is a maximum set in statute. There is no minimum term. The UK does not have fixed length terms.
Once elected with a majority of seats in the legislature, the party winning now owns both the legislature and the executive. The leader of the party becomes Prime Minister, with something like presidential powers. There is no doubt of his/her ability to get legislation through - he has a majority in the legislature, and it was that which got him to be Prime Minister.
There is no written constitution. Parliament, by a majority vote and consent of the monarch, can pass any legislation at all. If it wanted to (for example) repeal Habeas Corpus, it could. If it wanted to implement rule by decree, it could. If it wanted to leave the EU, it could. There is no safeguard of any sort of civil liberties or human rights from an Act of Parliament. It could, to take a ridiculous and extreme example, legalize slavery. There is no constitution to be modified by a complex process of two thirds majority voting, it just needs a majority vote in the legislature, and its done.
The US of course is completely different. Various bits of the governmental apparatus are elected from time to time - there is no equivalent of a general election of the kind the UK has just had. Only part of Congress or the Senate is elected in any given year. And when the legislature is elected, it does not get to specify who is the President, that is a completely separate election process. The legislature and the executive were deliberately separated by the Founding Fathers. The result is that the process of getting legislation through the legislature is quite complex and difficult, and subject to delay and prevention. In effect, the US is most of the time in a sort of coalition government, in UK terms - one in which negotiation with other parties is necessary, for the party in charge to get legislation through. This situation is one that happens very rarely in the UK, the party in power can almost always get its legislation through at once.
So, in this system, the debate about proportional representation has a very different force from what it would have in the US. Winning an outright majority in the UK gives a party a degree of power in both executive and legislature that can only be dreamed of by a US President. This is what neither Labor nor the Conservatives are prepared to relinquish, and why only desperation to get into or stay in power would lead them to make the necessary concession on PR to get into bed with the Liberal Democrats.
Right now the Liberals have some 23% of the vote and 57 seats in the legislature. If the UK system were truly proportional, and seats were in proportion to share of the vote, the Liberals would have around 150 seats and the other parties less. Conservatives now have 206, they would have under 200. Labour would be, on their current share of the vote, in the low 200s.
The end result would be, as in Holland, that the Liberals would be in every government, with one of the other two parties as partners. In Holland, this role is played by the CDA. The effect of this is that by very different means you have a sort of check and balance which is similar to that which the US system imposes. It becomes very hard to loot the country and di
All this talk about the subtleties of British politics ignores the most important aspect of this problem: forming a coalition is an instance of the 0-1 Knapsack problem: given a set of heavy objects (here the objects are the parties, their weights their number of seats), find the subset of the objects whose weight comes closest to a given knapsack's capacity (here the capacity is 50%+1 of the seats in parliament). As TFA shows, there are many many combinations to consider, which is not surprising since the problem is NP-complete.
I doubt that Gordon Brown can complete negotiations before the 25th, if only because the problem is algorithmically intractable.
Alejo