Friday, 11 February 2011

Games and the Acts of the Apostles

One of the standard textbooks in operational research a generation ago was "Fights, Games and Debates" by Anatol Rapoport. Rapoport distinguished between Fights, where you want to overpower your opponent, Games, where you want to outwit your opponent, and Debates, where you want to convince your opponent. Last week our home group Bible study was looking at chapter 25 and I commented that the story there illustrated those three situations.

The fight: in 25v7, When Paul came in, the men who had come down from Jerusalem stood around him. They brought many serious charges against him, but they could not prove them.

The game: in 25v3, They requested Festus, as a favour to them, to have Paul transferred to Jerusalem, for they were preparing an ambush to kill him along the way.

The debate: in 25v8, Then Paul made his defence: “I have done nothing wrong against the Jewish law or against the temple or against Caesar.”

As is clear from the whole chapter, the various parties present were not working to the same agenda, and hence they never communicated with one another.

Tuesday, 8 February 2011

Optimal search

A contribution to the February 2011 INFORMS blog theme, "OR and Love"

Way back in 1997, there was a news story about a psychologist who had published work about optimal strategies for finding a marriage partner. Seeing the report, I wrote a tongue-in-cheek letter to the national newspaper (The Independent) which pointed out that the mathematics behind this was familiar. I also wrote that it had created opportunities for light-hearted examination questions. The newspaper published my letter ... and a few days later I received an email from a mathematician at the University of Cambridge who wanted me to expand on the letter. It is a small world; that mathematician had tutored me as an undergraduate, but hadn't made the association of the signatory of the letter with one of his ex-students. He wanted to use my piece as part of a series of interesting mathematics for schoolchildren.

So I wrote a piece, still light-hearted, and it appears as "Marriage, mathematics and finding somewhere to eat" concerned with optimal stopping (the secretary problem). Cambridge provided the illustrations and a simple interactive game of "Googol".

Since then, that piece has been widely read, and I have had feedback from all over the world. (How I wish that my more serious written work was so widely read!) One friend told me that the item had been posted on her staff-room notice board, and she had acquired considerable kudos when she revealed that the author was a friend of hers.

I followed the article up with correspondence with the psychologist, which never led to a publication, but we learnt a lot from each other. Over the next year, I collected a stack of publications about this problem of optimal search, including several concerned with the mating habits of birds and animals, and the search habits of birds looking for nest sites.

Falling in love is not something to be modelled by O.R. techniques, but finding a partner can be simply modelled as a secretary problem. "A succession of potential candidates present themselves, and you can accept them or reject them. If rejected, you cannot go back and change your mind. What is your strategy to find 'the best'?" There are various variations on the problem.

But there were two bizarre twists to the story, as I heard from adults who had read this article for schoolchildren.

First came an email from an American lady. She asked, I assume seriously, if I could advise her whether her current partner was the right one for her. She asked for a mathematical formula which she could apply to him, to see if he was the best.

Second, another lady wrote (I forget where she came from) asking for my advice about increasing the pool of potential partners. Again, I think it was serious, but again I had to reply that there was no mathematics or other O.R. techniques which could be used in such circumstances.

One thing that the secretary problem does not address is how to approach the problem when both partners are using the search strategy! But dating agencies which encourage sequential search start with an assignment problem ... another O.R. and love technique.