1. Some things to talk about Social and political polarization A cool dynamic network simulation (which we haven’t done yet) Statistical cutoffs and p-values (work of Wald, Berger, …) Survey weighting and poststratification

2. Andrew Gelman Departments of Statistics and Political Science, Columbia University 7 Feb 2009 Also: Tian Zheng, Thomas DiPrete, Julien Teitler, Jiehua Chen,Tyler McCormick, Rozlyn Redd, Juli Simon Thomas, Delia Baldassarri, David Park, Yu-Sung Su, Matt Salganik, Duncan Watts, Sharad Goel Studying social and political polarization

3. Questions from sociology Questions from political science Sources of data Statistical challenges

4. Questions from sociology The “degree distribution” Characteristics of “the social network” Homophily Quantifying segregation Knowing and trusting

5. Questions from political science Polarization of Democrats and Republicans Polarization of political discourse How are people swayed by news media, talk radio, each other, … Geographic polarization Polarization and the perception of polarization

6. Sources of data Complete data on small social networks (schools, monks, …) Very sparse data on large social networks (Framingham, …) Complete data on other networks (scientific coauthors, …) Other network datasets (email, Facebook, …) From random sample surveys Questions about close contacts (GSS 1985/2004, NES 2000) Questions about acquaintances (“How many X’s do you know?”)

7. Statistical challenges: Misconceptions of others Examples Name Disease status Sexual preference Political leanings Challenge/opportunity: attributed and perceived attributes Appearance vs. reality How large is the “footprint” of a group?

8. Statistical challenges: Learning about small and large groups 1500 respondents x 750 acquaintances = 1 million Potential to learn about small groups Potential to learn about people you can’t interview Difficulty with large groups For example, “How many Democrats do you know” #known is too high to quickly estimate Potential solution: look at subnetworks “Cube model” (individuals x groups x subnetworks) Need main effects and two-way interactions

9. Statistical challenges: Network structure Social network is patterned Sex, age, ethnicity, SES, location Names, occupations, attitudes Correct for non-uniform patterns by using a mix of names Estimate non-uniform patterns using a conditional probability matrix for ages Overdispersion to model unexplained variation Can’t do much with triangles, 4-cycles, etc.

10. Statistical challenges: Recall bias Some people are easier to recall than others David, Olga, Sharad For some sets of names, can be quantified: Nicole/Christine/Michael Sliding definitions Who are your friends? Estimates of average #known range from 300 to 750 to … Estimates of average #trusted range from 1.5 to 15 to 150

13. Statistical challenges: Returning to the social science questions Polarization as political segregation in the social network Comparing polarization to perceived polarization Answering conjectures such as: People in big cities know more people but trust fewer people Getting geography back in the picture

14. Andrew Gelman Departments of Statistics and Political Science, Columbia University 7 Feb 2009 Forming Voting Blocs and Coalitions as a Prisoner's Dilemma: A Possible Theoretical Explanation for Political Instability

15. Dynamic network model for political coalitions Mathematics of coalitions Forming a coalition helps the subgroup (or they wouldn’t do it) But it hurts the general population (negative externality) Coalitions are inherently unstable Coalitions of coalitions Opportunistic acts of secession, poaching, and dissolution The simulation I want to do: Set up a political settings: “agents” with attributes and locations Payoff function for agents Locally optimal moves Scheduling Implementation

16. Andrew Gelman Departments of Statistics and Political Science, Columbia University 7 Feb 2009 Statistical cutoffs and p-values

17. Setting a cutoff for selecting patterns for further study Old problem in statistics: Neyman, Wald, Berger, … Also of interest to biologists! Some different goals: Finding patterns that are “statistically significant” Classifying into those to study further, and those to set aside Mathematical framework: distribution of a “score” Solution depends upon: Distribution of the score among “uninteresting” cases Distribution of the score among “interesting” cases Number of uninteresting and interesting cases Cost of follow-up of uninteresting cases Cost of follow-up of interesting cases

18. Andrew Gelman Departments of Statistics and Political Science, Columbia University 7 Feb 2009 Survey weighting and poststratification

19. Survey weighting and poststrafication General framework for adjusting for differences between sample and population Population estimate = avg over poststratification cells You might have to model: The survey response Size of poststratification cells Probabilities of selection Respondent-driven sampling example: Cells determined by “gregariousness” and “distance” Could approx correlations using clustering