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Author: Petros at Freelab
To: squatconf
Subject: [Squatconf] OT [long]: The two-step population or how big is small community?
I apologise for the OT, but this is about quantitative modelling of
small communities and it IS connected with hacking AND squatting so I
hope someone would be interested in helping me out.

tl;dr: I need a mathematical function to estimate a size of community,
based on (actual) Dunbar number and the percentage of shared social

My definition of small community is a community able to govern itself
without institutional structures, based on natural mechanisms of social
control and assessment. It means to me that the size of community must
conform two principles:

 1. A number of direct social contacts (one direct friends, relatives or
    acquaintances) stays within the limit of Dunbar number (strict: 150,
    generous: 250)
 2. Throughout the community only two degrees of social separation
    exist. That means that for every member of community all other
    members are either one's direct social contacts or direct social
    contacts of his/her direct social contacts (“friends of a friend”).

The effect of this is making all social interactions simple. I can
identify everyone as a member of community. If I need an interaction, I
can introduce myself, referring a common acquaintance. Most probably
(gossiping is an important social function) we already know each other's
reputation. In case of conflict, we can easily find one or more
mediators. Etc., etc.
A simple calculation tells us that absolute theoretical maximum size of
such community lays between 150^2 and 250^2 (22 500 and 62 500 people,
respectively). But this makes no practical sense, as it only happens if
we have no common (shared) contacts. Thus, actual size of the community
will depend of this very parameter: how many contacts (on average) we
share with our direct ones. In extreme, again, it will be 100%, making
the community size 152 or 252. But the real life spreads between extremes.
Now, what I need from my illustrious friends (and other social contacts)
are two things.

 1. Can anybody help me formulate a nice mathematical function, to
    estimate a size of community, based on the parameters listed above?
    Or perhaps (likely) such formula already exists, only I was unable
    to find it. Then, point me in the right direction, please.
 2. Can anybody help me establish what are empirical values of the
    shared contacts percentage in various communities and what
    influences that? Most probably it is known already, I am just unable
    to ask proper questions, while googling.

Having it all together, I will be able to declare what actually is (in
qualitative terms) a “community” I refer to so often in my musings on
confederated system.

Anybody, please?

Best, Petros