[Insert "Short" pun here]

Daniel Finkelstein writes:

[Claire Short] assumes that a hung parliament will lead to proportional representation. This would only happen if a majority of MPs are willing to vote for it (or vote for a referendum on it). Yet many MPs are absolutely opposed to PR and would not support it in any circumstances.

A hung parliament means that a majority government would need support of the Lib Dems. The Lib Dems would (if remotely sane) give support to either party in exchange for PR. MPs "absolutely opposed" to PR might vote for it if it were a condition of being government rather than opposition.

It's not a certainty, but a hung parliament would have a decent chance of producing PR, and the opinions of individual MPs towards PR is almost beside the point.

In a simplified model, it looks like a hung parliament would not produce PR:

Two main parties are P1 and P2. Balance of power held by D (Lib Dems).

If neither P1 or P2 offer D PR, then D will make a choice P1

If P2 offers PR, P1 can choose either

Offer PR : outcome is P1 in government, with PR.
Don't offer PR : outcome is P2 in government, with PR.

P1 should therefore offer PR (since it will happen anyway) in order to get in government.

Therefore, for P2, their choice is:

Offer PR : outcome is P1 in government, with PR
Don't offer PR : outcome is P1 in government, without PR.

So effectively, P2 (whichever party is not preferred by the LDs) has no chance of getting into government, but does have the choice of whether PR will be introduced.

I would guess that the LDs would be more inclined to go into government with Labour than with the Tories. If so, it is the Tories (P2) who would have the choice over whether to force Labour into offering PR or not. Possibly they would. If they can't get a majority now, it is reasonable to ask whether they ever will. If not, then PR becomes less of a sacrifice.

Of course, my simplified model can be attacked. It makes the following questionable assumptions:

Perfect information
Major parties can commit to introducing PR with perfect credibility.
PR is a yes-or-no issue
LDs care more about PR than about whether Lab or Con get the government (that's the "if remotely sane") bit.

I have a non-rigorous feeling that in the real world the doubts and grey areas could drag both P1 and P2 towards offering PR to improve their chances.

That might be wishful thinking though. I am strongly in favour of PR, as it would split the main parties and allow voters the choice of a party that more closely represented their views.

Actually, there's another move in the game. I was assuming the LD strategy was "Support the P1, unless P2 offers PR and P1 doesn't, in which case support P2". If the LD strategy is "Support P1 if P1 offers PR, otherwise support P2", then, provided P1 would prefer to be in government than to keep out PR, P1's best strategy would be "offer PR", and that would be the outcome.

That's really counter-intuitive. It's saying that the LDs should say "We prefer Labour to Conservative, but we will only support them if they give us PR. Otherwise we will punish them by support the Tories, whether the Tories give us PR or not."

I thought this game was solveable, but my limited grasp of game theory might not be up to the task. I'll have to go away and think about it (and look up the proper notation).