h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

http://www.bbc.co.uk/h2g2/guide/A520372

I'd be interested in anyone's comments on this entry before I submit it to peer review. I'd quite like to add some more discussion at the end, so if anyone has any ideas... Also, comments on whether it is too technical would be good.

By the way, to pique people's interest, the entry is about "Arrow's Possibility Theorem", which says that there is no perfect voting system.

well, it's a quite complicated topic, dealt with in a concisely written entry. I skipped the math section for now (it's a little late in the evening), but I hope to come to that later.

A point for discussion: the theory seems to be based on the fact that the political choices for voters are constant, and it's the voter's opinion which are volatile or changeable. There's a theory out there which runs quite the other way (I don't know if it has been published somewhere, nor whether it's got a name).

It is based around the metaphor of an ice cream vendor and lots of potential customers spread along some 2km of a beach. Perhaps this model is too simple, but: which position is he most likely to choose?
Obviously, he will be found in the center, because everybody can reach him. If he were at one end of the beach then some customers on the opposite side could begin to trade off their efforts against the pleasure of an ice cream.

Now let's introduce a competitor and ask the same question again. To which the answer is that they /both/ will be found in the center, no more than a few meters apart! If they would divide the beach into two sectors of 1km each and position themselves in the centers of these sectors then they would perhaps give away the customers in the middle to the other one. Sticking to the center of the whole beach leaves them both a chance of 50%.

Now let's introduce a third ice cream vendor...
Result: the third one will be right in the center, and the others walk away some distance, but will keep not too far from the middle.
Two additional vendors will be found close to the very extremes of the beach, hoping to maintain a niche for themselves there.

Now let's assume the sun is going to set, which leaves half of the beach in the shadow of some rock, and the customers start moving into the other half...[and so on]

The point is: in this model it's the political parties who put themselves in the best positions and are adapting to changes in the overall situation. It's them who have to choose their political programs such that they gain maximum profit (ie: votes) out of it. It is /them/ who are actually performing the vote !?

Umm, weird, isn't it?

Hi there, thanks for the comments. It sounds like you're referring to "game theory", specifically the prisoner's dilemna. Have you heard of this? There seems to be a long entry on it at http://www.bbc.co.uk/h2g2/guide/A509690 (in case that gets censored, the entry is A509690). The second thing you mentioned (how it changes with time and so on) I'm not sure about. Perhaps there is a theory of continuous game theory under changing conditions? I don't know about it but it almost certainly exists and is heavily studied. I agree that Arrow's theorem is certainly not a complete analysis of voting and so forth, but it does answer one aspect of it rather well. Finally, yes it's all pretty weird stuff

Editorial Note: This conversation has been moved from 'The Writing Workshop' to 'Arrow's Possibility Theorem'.

There's a existing Edited Guide Entry on this topic already: http://www.bbc.co.uk/h2g2/guide/A509690