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I'm playing with the problem of community learning. I think this is pretty generic as it can be applied to economic development, investments and others. I want to know if there's a name for this and if there is previous work before delving further.

The problem goes like this:

  • You have 10 people with differing skills in math.
  • People may spend time by themselves and increase their skill level by 1/week
  • People may spend time with others and increase their skill level by some equation like e^(b-a) where a is the person's skill level and b is the other person's skill level. This means that by learning from someone far more skilled than you, you learn faster, but by teaching someone far less skilled than you you learn much slower.

How do you approach solving/optimizing this problem (total skill in the group) given a specific time range and initial skill levels?

How about if there are constantly new beginners coming in every week. How would you approach creating sustainable growth for everyone?

Axiverse
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  • More of a guess than anything else, but considering a simple case seems kind of helpful. Suppose you have two people, one at skill level 10 and one at skill level 1. Then there are two possibilities - work together or separately. If they work together, the new guy improves by a factor proportional $e^9$, which is pretty substantial growth. Likely after a few rounds of training, his rate of learning slows down, and the group benefits more by going their separate ways, as it is better for the group to get +2 by working independently. – A. Thomas Yerger Mar 30 '16 at 06:57
  • So in somewhat more generality, I expect it is best to let the best of the best train the worst in each round, to get the fastest growing community. If no new people come in, then eventually it becomes preferable for more and more people to work independently. – A. Thomas Yerger Mar 30 '16 at 06:59

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