Dynamics of Evolving Social Groups

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Model uses opinions in [0,1], two uniformly drawn candidates per round, members vote for the closer candidate (homophily). Under consensus rule the accepted-opinion intervals shrink to the extremes and the group polarizes; under majority rule the median converges to 1/2 and the empirical distribution approaches a triangular shape (simulation to 20,000 members); proof sketch shows doubling group size moves median by ≈2ε^2k w.h.p.; introducing a founder veto r yields a phase transition at r=1/2. Extensions and nonuniform draws remain open.

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1. 0:00Start
2. 0:17Evolving Social Groups Groups in which the group members decide which new members to accept.
3. 3:28Homophily the tendency of people to prefer and interact more with others who are more similar to them.
4. 5:50Consensus Admission Rule: A candidate is admitted if all group members prefer him over the other candidate.
5. 11:08Majority Admission Rule: The candidate that is voted for by at least half of the group is admitted.
6. 21:44More Admission Rules The group has a founder located at 1 that has special veto power-only the candidate preferred by the founder can be admitted
7. 25:07Summary We study a model in which members of a group select new members based on their similarity (homophily) In our model different admission rules have very different implications on the range of opinions in the group.