[extropy-chat] Effective relationships

[Anders Sandberg]

Eliezer S. Yudkowsky wrote:
> Anders Sandberg wrote:
>> If another form of organisation was more stable or produced more
>> happiness
>> it would likely be fairly prevalent. Since triads or tetrads do not
>> occur
>> that often I would conclude that they are not stable in general.
>
> Second paragraph does not follow logically from first paragraph.  Since
> when is "happiness" a primary optimization target of the patterning
> processes in question?

OK, more properly: humans tend to move out of social relations that make
them unhappy (especially when there are alternatives around) with a higher
probability. So if a state of relationsship has probability P1 of ending
due to inherent instability, to this one can add an extra probability P2
of ending due to unhappiness.

My model would be a small Markov chain with three states: S, single, T,
triad/tetrad, and D for dyad. S can move to T with P(s->t) and D with
P(s->d). If there are transitions between all three it is nicely ergodic
and we can get a stable long term distribution just by calculating the
biggest eigenvalue of the transition matrix.

I'm sitting in an internet cafe right now so I can't prove anything
strictly, but I'm pretty sure that one can prove that if the steady state
distribution overwhelmingly promotes S and D over T, it implies that
either the probabilities leading to T are extremely low or that P(T->T) is
lower than P(D->D) and/or P(S->S). Hmm, sounds like entertainment for my
flight home.




-- 
Anders Sandberg,
Oxford Uehiro Centre for Practical Ethics
Philosophy Faculty of Oxford University