One of my favourite logical paradoxes (What, doesn’t everyone have a favourite logical paradox?) is the Unexpected Hanging. I first read about it from Martin Gardner, but you can read a summary here. A recent article in the Oxford Times, about the career plans of a local MP, raised a corresponding problem in the political realm:
Conservative Tony Baldry MP has announced he will stand down at the next General Election.
In a statement Sir Tony said: “One of the consequences of now having five year fixed term Parliaments is that if I succeed in being re-elected at the forthcoming general election, given my age, most people will assume that Parliament will be my last.
“I think this creates a danger that I may be unable to be as effective as I would wish to be; and that the constituency will be distracted from more important issues by the need to choose my successor.”
We might summarise his argument as beginning with three axioms:
- It is irresponsible for a politician to stand for parliament if the strong expectation is that this would be his or her last term.
- There is a strong expectation that someone will not stand for parliament past age 70.
- Terms are now fixed at five years.
Consider, now, the position of a responsible politician, whom we will call Tony65, who who will be, shall we say, 65 years old at the next election. He could stand for parliament now, but he will be 70 at the next election (axiom 3), and so the strong expectation is that he will not stand at the next election (axiom 2). Hence, by axiom 1, and the fact that he is responsible, he should not stand in this election.
But now consider Tony’s younger colleague; call him Tony60, who will be 60 years old at the next election. If Tony60 is elected, he will be 65 at the following election. As a responsible politician, like Tony65, he will stand down at that age. Thus this would be his last term, so by axiom 1 he will not stand at this election either.
By the same reasoning, Tony55 will not stand, since we know that he won’t stand again when he is 60. And so, we can keep backing it up to Tony20, who also can’t stand, because he won’t stand again when he is 25. (18 is the minimum age for election to the House of Commons.) Thus, we have proved:
Theorem: No responsible politician can stand for election to the House of Commons.
This theorem does not apply, for obvious reasons, to the House of Lords, so there will still be space for responsible (if unelected) government.