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Rationality as conformity, Doctoral dissertation: School of Mathematics, The University of Manchester, (Successfully examined on 22 June 2005.)
Outline -- Full text (pdf)

Rationality-as-conformity begins with the idea that a ``rational", ``commonsensical", ``natural", or simply ``logical" choice is one which corresponds to the choice other similar agents would come up with in similar situations. Our aim is to model the choice processes leading to this sort of conformity. Consider the following example.
[Supermarket shelf arrangement.] There are numerous ways in which a supermarket manager might choose to arrange the shelves in her store, for example by alphabetical order of product name, by product size or weight, by price, by the package's colours, and so on indefinitely (not to mention the astronomic number of random orderings!). However when stepping into a new supermarket (i.e. one we have never visited before, and about which nothing is known to us, apart from the fact it is a supermarket) we expect to find teas close to coffees, pastas close to rices, nappies near to toilet rolls. At least we argue that it would surely seem natural to hold expectations of this sort. In fact, if after ten minutes searching we finally located the sugar among the washing powders, we might well be inclined to question the store manager's rationality! After all, we see this as a situation where, for mutual convenience, the store manager and ourselves are trying to conform on the selection of a common world, i.e. shelf arrangement.
Although this is the sort of situation we intend to model within our framework, it is not hard to see how rapidly the complications would arise, if we were to work with this informal problem. For instance it could be put forward that in fact there is no choice process to be modelled, but rather the appropriate use of common knowledge. The objection here would be that that there are in fact rules or conventions (arising in all probability from marketing research) that regulate what a ``rational" shelf arrangement is. [Surely there seems to be some cold-blooded form of logicality when it comes to shelving sweets right at the eyes-height of an invariantly bored child queueing at the till!] Hence, the objection would conclude, those rules or conventions are all that a ``rational" customer would have to learn to shop conveniently. This would surely work if there was something as a ``universal shelving rule" around. Yet, needless to say, this is utterly unreasonable. Therefore it is not hard to see that this possible objection just begs the question for ``the new customer" would still have to figure out which shelving convention the supermarket manager is in fact adopting.
The next objection then, might be to notice that supermarket managers might indeed fill up the store with signs and maps indicating to the unlearned customer where is what. An account of ``rational shelving" pursuing this line, however, would seem to be easily exposed to two sorts of shortcomings. Firstly, this rule would require an enormous amount of computational effort to be learnt. And surely the vast majority of this effort could in fact be spared if the manager would adopt the same rule she thinks the customer would utilize in the same situation. Secondly, what if the customer doesn't happen speak the language(s) chosen by the manager for the sings? What if the manager and the customer didn't in fact share any language at all?
In this thesis we shall consider an idealised and mathematically abstract situation where communication or knowledge of such rules and conventions are not available to the agents. Since it is assumed that agents' ultimate goal is that of conforming to the expectations of their peers, we shall refer to the overall approach as Rationality-as-conformity.
Rationality (or common sense - we shall not make a distinction among these terms) is, in its full generality an extremely complex and widely debated subject. Yet within the scope of our simple mathematical formulation we shall be able to provide what amounts to a characterization or definition of what it means to choose rationally. The hope is that such investigations will ultimately provide a way of viewing and understanding these notions in a much more general real world context.

A letter to an Editor (if only life was like this!)

Dear Sir,
We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reason to address the — in any case erroneous — comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere.
Respectfully,
Albert Einstein

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