WELCOME TO THE GEOMETRY OF REDISTRICTING WORKSHOP

Transcription

1 WELCOME TO THE GEOMETRY OF REDISTRICTING WORKSHOP Metric Geometry and Gerrymandering Group

2 THANKS TO OUR PARTNERS AND SPONSORS Lawyers Committee for Civil Rights Under Law Jonathan M. Tisch College of Civic Life, Tufts University Alfred P. Sloan Foundation Educational Foundation of America Scholars Strategy Network College of Arts & Sciences, Tufts University OneVirginia2021 and many individual donors

3 ORGANIZING TEAM MGGG: Mira Bernstein, Moon Duchin, Ari Nieh, and Justin Solomon Photo: Yugo Nakai LCCR: Kristen Clarke, Megan Gall Tisch: Deena Alexander, Jennifer McAndrew Our wonderful summer interns: Assaf Bar-Natan, Tali Falk-Judson, Nathan Foster, Emily Sim Specialized session trainers: Geoff Cohen, Kareem Crayton, Bob Kengle, Jennie Lusk, Oren Sellstrom, Jeff Wice, Jim Bozeman, Alfonso Gracia-Saz, Sam Gutekunst, Yvonne Lai, Nina White, Mike McDonald

4 SITUATING REDISTRICTING AS A PROBLEM IN LAW, MATH, AND POLITICS Moon Duchin Tufts University

5 CONGRESSIONAL REPRESENTATION People have to be counted (Census) Congressional Reps have to be apportioned to the states States have to be divided up into districts

6 REDISTRICTING AS A MATH PROBLEM One mathematical formulation: partitioning with attributes Consider a set ( population ) of nodes, each with attributes whose values are drawn from a finite set. For instance, color (red/blue) and number (0/1). Partition the set into blocks ( districts ). How does the pattern of attributes at the district level compare to the pattern at the population level? has 45% of pop but 25% of districts now try with tens of thousands of census blocks per district! red has 52.5% of pop but 75% of districts

7 GOALS AND CONSTRAINTS We can define several goals with this setup, e.g., Proportionality: make districts representative Gerrymandering: choose partition to extremize some attribute at the district level To make the goals harder, add contraints: Equal-population districts Districts described by connected regions with no holes Not too eccentrically shaped???!

8 BUT THE MATH SITS IN CONTEXT How do these activate political values? Equal population representational equality cf. Law of Large Numbers Geographical division bare majorities shouldn t dominate Shape detects gerrymandering and other extremization agendas What other values / principles / normative commitments? Proportionality Competitiveness Partisan fairness Governability What are our legal parameters? None of those. (Yet.)

9 HOW TO GERRYMANDER Packing and cracking :

10 *CLASSICAL COMPACTNESS Many metrics exist: Isoperimetry 0 400πA/P Convexity How indented? Dispersion How spread out? but perimeter is problematic there are many legitimate reasons for non-convexity and all of this is 19th century mathematics!

11 THIS MATH RISKS LOSING CONTACT WITH THE POLITICAL CONTEXT Let s look back at some facts on the ground.

12 MINORITIES VOTE D People of color vote D, especially Black voters

13 CITIES VOTE D Top 40 cities by est population table credits: CITYLAB Correlation coefficients data credit: DecisionDeskHQ

14 CAN WE PUT THE MATH BACK IN CONTACT WITH THESE ELEMENTS? Yes.

15 DENSITY AND SPLITTABILITY Q: Is density itself to blame for gerrymandering? We are studying splittability of shapes through their packing and cracking loci. Dallas C P & C P San Jose Phoenix

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17 THINKING ABOUT THE GUTS OF A DISTRICT What is the right abstraction to capture the relevant information? (i.e., what object should we study?) (Perhaps all squares are not created equal) The census data comes in discrete units: census blocks (0-100 people), block groups ( ), and tracts ( ) Could break down a state into its census units, form graph to see the guts of a state and its district plan Q: What are the edges adjacency? distance/travel time? commonalities?

18 NC-1 AT THE CENSUS TRACT LEVEL Durham

19 NC-12 AT THE CENSUS TRACT LEVEL Winston-Salem Greensboro Charlotte

20 AND NC-8 FOR CONTRAST Charlotte

21 CURVATURE: A NEW APPROACH TO COMPACTNESS? Graphs have shape, and that shape reveals both isoperimetry and dispersion. Example: triangles arranged around a central vertex. Negative curvature 0 Positive curvature Saddle shapes; high perimeter, high sprawl

22 CURVATURE OF MAPS

23 THANKS! We re MGGG, the Metric Geometry and Gerrymandering Group a small team studying applications of math and computing to redistricting Research & publication Interdisciplinary collaboration Outreach & education We could use your support! sites.tufts.edu/gerrymandr/ Image: OpenHatch

24 Questions? Ask on paper, or tinyurl.com/askgerry