Game Theory of UK Coalition

There has been a lot of hand wringing in the UK press about a Conservative (US: Republican) party with 47% of the seats getting together with a Liberal Democratic party (US: Democrat-ish) with 9%, but as the above chart shows the game theory of the situation shows there is only one situation which has a good outcome.

In essence this coalition means that c 60% of the seats and c 60% of the voters are in its camp. A Liberal/Labour coalition would have been 52% of the vote and 48% of teh seats, which means a minority government. A Tory-on--its own (largest single party) minority government would have c 1/3rd of the voters and c 48% of seats - again an unsustainable minority.

There is a question about the Liberal Democrats being better off going it alone, but its hard to see how they could have carried on in that position as the press would have hounded them to form an alliance, as they have done over the last few days