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Subject: Re: Interesting math / network challenge
From: Joshua O'Madadhain <[log in to unmask]>
Reply-To:[log in to unmask]
Date:Sun, 27 Jan 2008 19:22:21 -0800
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*****  To join INSNA, visit http://www.insna.org  *****

Scott:

It would be pretty easy to model this using JUNG
(jung.sourceforge.net)...given a model for the network itself, which
is not necessarily trivial (more on this below).  The algorithm is
similar to things like eigenvector centrality-based metrics (e.g.
PageRank).

One minor nitpick: if the probability of passing it on is exactly 1/k
(where 'k' is the number of people for whom you do favors), then there
is no growth: the expected number of active participants is 1 at any
given time (not counting deaths and other externalities).

You'd also need to make some other decisions, e.g.:

* do you ever do a favor for a given person twice?
* is the number of people for whom you do favors fixed, or probabilistic?
* if more than one person does you a favor at time t-1, how many
favors do you do at time t?
* how many "seeds" are there, i.e., how many people are doing favors
for altruistic reasons to start the model off?
* do people ever do favors for altruistic reasons other than at t=0?
* are all favors done in the time tick after a favor is received, or
can they happen later?

All of these could be made parameters of the model, of course.

Anyway, as I said, I think that the thorniest potential problem is
defining the connections in the first place; you have to make some
assumptions about who people will decide to do favors for, and
realistically that should be some combination of (a) people with whom
you have an established connection (for which there are a multitude of
models, some more realistic than others) and (b) people that you're
proximal to in some sense (either physically or in some other social
context).  I don't know what the connection model should look like.

If you want to give this a whirl using JUNG, let me know.

Joshua O'Madadhain

On Jan 27, 2008 5:20 PM, Scott Allen <[log in to unmask]> wrote:
> *****  To join INSNA, visit http://www.insna.org  *****
>
> In another discussion group I'm on, someone asked the question, "What's the
> future value of 'pay it forward'?".  In case you're not familiar, "pay it
> forward" is the idea, made popular by the movie of the same name, of not
> "returning" a favor, but rather "pay it forward" by doing three big favors
> for three other people. When they ask how they can pay you back, you say,
> "You can't. Pay it forward."
>
>
>
> Even if the trend is dampened with some kind of attrition rate, so long as
> the attrition rate is less than 66% (i.e., at least 1 out of 3 people
> continue the meme), it will continue to grow, exponentially.  Given a finite
> number of people in the world, plus the nature of networks, then it's
> obvious that sooner or later, you're going to get more favors coming back to
> you then you did in the first place.
>
>
>
> That got me to thinking. you could actually model this:
>
> .         Assume a network of n people.
>
> .         Assume some kind of attrition rate (not everyone pays it forward,
> or at least not three times).
>
> .         You don't pay it forward to the person who paid it forward to you,
> but once you get to 2, 3, 4 degrees of separation and higher, there's a
> certain possibility of paying it forward to someone who's already been
> "tagged" at least once, i.e., that person sees a "return" on what they paid
> forward.
>
> .         As more and more people get tagged, there's an increasing
> probability of tagging someone who's already been tagged.
>
>
>
> Frankly, I don't have the knowledge of how to model this correctly, but I'd
> love to work on it with someone who does - I've got some ideas about the
> factors that would need to be considered.  For someone who knows what
> they're doing, this isn't a very difficult model.
>
>
>
> I've been Googling this and can't find anything useful.  If anyone's
> interested in working with me on this, or if you know of any existing or
> current research on the topic, please contact me off-list.
>
>
>
> Scott Allen
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-- 
  joshua.omadadhain@gmail.com...................www.ics.uci.edu/~jmadden
   Joshua O'Madadhain: Information Scientist, Musician, Philosopher-At-Tall
It's that moment of dawning comprehension that I live for.  -- Bill Watterson
 My opinions are too rational and insightful to be those of any organization.

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