Comments on: Rationality and social networks http://www.grok.in/blog/2007/05/05/rationality-and-social-networks/ (ignorance killed the cat, curiosity was framed) Wed, 16 Jun 2010 18:48:41 +0000 hourly 1 By: aditya http://www.grok.in/blog/2007/05/05/rationality-and-social-networks/comment-page-1/#comment-5 aditya Mon, 07 May 2007 18:47:51 +0000 http://www.grok.in/blog/2007/05/05/rationality-and-social-networks/#comment-5 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. 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.

]]> By: aditya http://www.grok.in/blog/2007/05/05/rationality-and-social-networks/comment-page-1/#comment-4 aditya Mon, 07 May 2007 18:34:29 +0000 http://www.grok.in/blog/2007/05/05/rationality-and-social-networks/#comment-4 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. 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.

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