Why don't I want Pompey to go bust?

I am a Saints fan. Our local rivals are Pompey. It would be fair to say that their is a fair amount of historical animosity between Southampton and Portsmouth and the rivalry can be pretty bitter between the two sets of fans.

(The photo is of the three known hard-core Saints fans in Lesotho - I am in the Basotho hat, taken during Saints' 4-1 defeat to Pompey in the cup last week - a nice game despite the defeat. An American we watched the game with thought we were the Premier League side and Portsmouth the lower division side.)

Portsmouth (Pompey) are in dire risk of going out of business, but I really hope that doesn't happen. Why would I not want to see our bitter rivals disappear from the face of the earth?

I think for two reasons: firstly, I value the rivalry, and don't want to lose it. The rivalry increases my own pleasure. Secondly, despite that rivalry, I don't think any true football fan should want to see another club go out of business.

Despite the way we treat each other sometimes, football fans all belong to one big community - yes, including even our bitter rivals. Having nearly gone bankrupt ourselves a few months ago (it has been a bad year for south coast clubs), I know the pain supporters can go through. I don't think that any football fan deserves that.

I think that that might give me an altruistic streak somewhere!

Since it's always nice to have a model, my utility, u (call it 'happiness' if you will), is a positive function of the continued rivalry between Saints and Pompey, but also of the utility, v, of other football fans, including, in this case, Pompey fans:

u = u(rivalry, X, v(Pompey fans))

(X is all other things that contribute to my happiness)

I say a positive function but in fact, it is not linear. I like the rivalry, but if it becomes too much and descends into violence, I don't like that - so, we can probably say the function is concave (first derivative positive, second negative) and non-monotonic - too much rivalry brings negative utility (it is an inverted U-shape in fact).

How would Pompey fans' utility affect me? Also, not linearly. I don't like to see Pompey doing too well (few Pompey fans like to see the Saints do brilliantly either, so we're even), but I hate the idea of them going bankrupt. Thus, when they do *very* badly, my happiness (utility) is negatively affected. When they start to do a little better, I become indifferent. But when they start to do well over a certain point, my happiness declines again. Pompey fans' utility function (v) above, enters my own utility function in an inverted-U but in the negative domain and reaches its peak at zero (having no effect on my utility)*.

Below is a picture to illustrate:

I am sure that there are a few Saints fans who feel differently, but I hope not too many.

Good luck Pompey.

* And you thought it was all glamour being an economist :)