Some things to talk about

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. Studying social and political polarization Andrew Gelman Departments of Statistics and Political Science, Columbia University 7 Feb 2009 Also: TianZheng, Thomas DiPrete, JulienTeitler, JiehuaChen,Tyler McCormick, RozlynRedd, Juli Simon Thomas, Delia Baldassarri, David Park, Yu-Sung Su, Matt Salganik, Duncan Watts, SharadGoel

3. Studying social and political polarization • 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. Forming Voting Blocs and Coalitions as aPrisoner's Dilemma: A Possible TheoreticalExplanation for Political Instability Andrew Gelman Departments of Statistics and Political Science, Columbia University 7 Feb 2009

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

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

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