Well, let me start off my first post by taking an inclusive definition of IR and including social networks as part of IR. (In fact, Aditya’s thesis is primarily based on the assertion that IR is generally a social activity rather than a database query).
There are these axioms in the theory of rational choice:
Rational choice theory makes two assumptions about individuals’ preferences for actions. First, is the assumption of completeness, that is that all actions can be ranked in an order of preference (indifference between two or more is possible). Second, is the transitivity, the assumption that if action a1 is preferred to a2, and action a2 is preferred to a3, then a1 is preferred to a3.
(Source: Wikipedia page http://en.wikipedia.org/wiki/Rational_choice_theory)
Focus on the second axiom. If you observe me choosing a1 over a2 whenever presented a choice between a1 and a2; and choosing a2 over a3, whenever presented a choice between a2 and a3, you conclude that I would prefer a1 over a3 whenever presented a choice between a1 and a3.
If instead, I choose a3, when presented a choice between a1 and a3, you conclude that I am irrational.
I. don’t. think. so. 
Hint: Especially when a1, a2 and a3 are people, rather than inanimate things.
We had a long debate about it yesterday in the lab and I finally found an example. Later over dinner, my wife found many more examples — all involving people, though. Not inanimate things.
Let me not give out the examples right now, just to let your minds get tickled a bit..
2 Comments
Rock, Paper and Scissors
Assumptions:
The universe of comparison has only three elements; rock, paper and scissors. Each of them is defined as a vector of properties, in my case a 3-tuple (a,b,c).
Definitions:
Rock a=1, b=0, c=0
Paper a=0, b=1, c=0
Scissors a=0, b=0, c=1
Comparison function:
element comp (element i, element j)
{
if (i.a*j.b > j.a*i.b) return j;
elseif (i.a*j.b < j.a*i.b) return i;
else ;
if (i.b*j.c > j.b*i.c) return j;
elseif (i.b*j.c < j.c*i.c) return i;
else ;
if (i.c*j.a > j.c*i.a) return j;
elseif (i.c*j.a < j.c*i.a) return i;
print “Not from my universe”;
}
Explanation:
The first assumption holds in this universe, the second does not. This happens because we are looking at each element as a single dimensional element, rather we are looking at each element as a multi-faceted (3 in this example) entity.
Just after posting the previous comment I found a problem with my approach.
I’ve explicitly given the ordering for the three elements. The comparison function actually states that Rock < Paper < Scissors < Rock, therefore making the transitivity fail. I should look into this theory and maybe there are more (trivial) assumptions which I’m missing.