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Friday, 7 February, 2003, 13:18 GMT
The maths of Lords reform
House of Lords
Deadlock emerged in Tuesday's votes

Efforts at Lords reform probably ran into gridlock because MPs wrongly second guessed how their colleagues would vote, according to an expert in game theory.

A majority might have been secured for a mostly elected house had a crucial handful of MPs not thought their first choice would be preferred to no change at all, says Andrew Lilico, a game theorist at Europe Economics.

In Tuesday's votes, the House of Lords backed an all-appointed second chamber but MPs failed to give a majority for any of the seven options on offer.

Game theory is a mathematical method of decision-making, the key solution concept of which was the brainchild of John Forbes Nash, the man made famous in Oscar-winning film A Beautiful Mind.

Using those methods, Mr Lilico examined how the Commons votes failed to produce a majority for any of the seven options.

Split decision

MPs were allowed to vote for as many options as they liked.

The votes started with the extremes of an all-appointed and all-elected second chamber - and ended with the choice of a 50-50 split of elected and appointed peers.

Seven options
100% elected
80% appointed, 20% elected
20% appointed, 80% elected
60% appointed, 40% elected
40% appointed, 60% elected
50% appointed, 50% elected
100% appointed
The idea of having 80% of peers elected and 20% appointed came within just three votes of getting a majority.

But the other mostly elected option, having 60% of peers elected, was defeated by 253 votes in favour, 316 against.

Mr Lilico told BBC News Online: "The most likely cause of the problem here was that there were fairly even numbers of supporters of both the majority-elected-but-not-100% options.

"Each of them thought their option would be preferred to no change.

"In fact it turned out that the 60% vote came second and probably only the 80% elected option was really preferred to no change - a recipe for gridlock."

Voting order crucial?

Mr Lilico pointed to the example of an MP who wanted 60% of peers elected, but whose second choice would be 80% elected.

If such an MP decided the most likely choices were their first and second preferences, that could cause problems.

That MP could decide not to back the 80% elected option when that vote arrived (which was before the 60% elected vote), thinking that if the 80% elected option were defeated, their favourite option (60% elected) would be accepted later.

Mr Lilico explained: "If there were even two MPs in that position, then the order of votes was crucial to the outcome.

"If the 80% elected option had been voted for after the 60% option, such people might have voted the other way," he said.

 VOTE RESULTS
House of Lords reform

Elected
 53.81% 

Appointed
 17.01% 

A mixture of both
 29.19% 

4598 Votes Cast

Results are indicative and may not reflect public opinion


Talking PointTALKING POINT
House of Lords
How should it be reformed?
See also:

06 Feb 03 | Politics
04 Feb 03 | Politics
04 Feb 03 | Politics
04 Feb 03 | Politics
29 Jan 03 | Politics
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