How do senators vote? -Issues - Strategies -Affiliation - - PDF document

4/30/18 CSCI 3210: Computational Game Theory The Power of Context: Ideal Points with Social Interactions Ref: Irfan & Gordon Mohammad T. Irfan How do senators vote? -Issues - Strategies -Affiliation - Influence Voting Behavior 1

4/30/18 Stat: Ideal Point Models (Davis+, 1970) Parameters: § p i – ideal point of senator i § a d – polarity of bill d § b d – popularity of bill d Variable: § x id – yea (+1) or nay (-1) p ( x i,d = yea | p i , a d , b d ) = σ ( p i a d + b d ) . http://k7moa.com/images/ png/Sen114_Ideal_Point_Pl otB.png Linear Influence Game (LIG) (Irfan & Ortiz, 2014) 2

4/30/18 Strengths & Weaknesses of Models Mo Model: Strengths: St Weaknesses: We Linear Influence Strategic behavior Bill-specific voting Game (LIG) Ideal Point Bill-specific voting Strategic behavior Ideal Point Model with Social Interactions Idea: add ideal point parameters to LIG model Predict Terms Description Votes of senator i x i ∈ X w i, − i ∈ W Incoming influence on senator i from all other senators − i Learn Influence threshold of senator i t i p i Ideal point of senator i Polarity of bill l a l Observe m Number of bills The topics in each bill d (Sec. (3.2.2)) ` d ∈ D 3

4/30/18 Ideal Point Model with Social Interactions — Influence function of Senator i for bill l X f i ( x − i , l ) ≡ w ij x j − t i + ( p i · a l ) = j ∈ N i — Influence function > 0 è B.R. is vote yea — Influence function < 0 è B.R. is vote nay — Influence function = 0 è Indifferent Voting Data 4

4/30/18 Data Learn Parameters Model Compute Equilibria § Model does not immediately predict anything § Must compute equilibria first § NP-Hard (Irfan & Ortiz, 2014) 5

4/30/18 Implementation Issues: scaling Warren(D-MA) Sanders (I-VT) Shelby (R-AL) Cruz (R-TX) -4 -4 +4 +4 Implementation Issues: polarity of unseen bills Polarity = ? New bill Euclidean dist. to existing bills 6

4/30/18 0-500 500-1000 1000-1500 0-5 5-10 15-20 20-25 10-15 0-10 10-20 20-30 30-40 40-50 0.00045 0.00045 0.00045 0.000425 0.000425 0.000425 0.0004 0.0004 0.0004 0.000375 0.000375 0.000375 0.00035 0.00035 0.00035 0.000325 0.000325 0.000325 0.0003 0.0003 0.0003 rho' 0.000275 rho' 0.000275 rho' 0.000275 0.00025 0.00025 0.00025 0.000225 0.000225 0.000225 0.0002 0.0002 0.0002 0.000175 0.000175 0.000175 0.00015 0.00015 0.00015 0.000125 0.000125 0.000125 0.0001 0.0001 0.0001 rho rho rho Euclidean dist. Validation error # edges Se Selected M Model: ⍴ = 0.0225 ⍴’ = 0.004 ≈1000 edges 16% validation error Model Evaluation Our model vs. LIG model 7

4/30/18 Criterion: % data that are NE 100% Empty Test Model Accuracy Problem: large # of NE Want % data as eq. # eq. 8

4/30/18 Model Evaluation § True proportion of equilibria: π ( G ) ≡ |NE ( G ) | / 2 N § Proportion of equilibria in data: G ), we want § q = fraction of observed data captured as NE q q · m as |N E ( G ) | / 2 N . S log |NE ( G ) | Model Evaluation LIG model: § q = 20% 20 q log 10 |NE ( G ) | = log 287494 ≈ − 4 . 16 § |NE(G)| = 287,494 Our model: |NE ( G ) | = log 4 . 83 q log 10 3242 ≈ − 2 . 69 § q = 4.83% § |NE(G)| = 3,242 (Our model constrained to ensure similar graph size) 9

4/30/18 114 th U.S. Senate January 2015 – January 2017 − 4 − 2 0 2 4 GRASSLEY GRASSLEY MORAN MORAN CRUZ CRUZ SHELBY SHELBY COTTON COTTON SULLIVAN SULLIVAN MURKOWSKI MURKOWSKI TOOMEY TOOMEY LANKFORD LANKFORD VITTER VITTER WICKER WICKER INHOFE INHOFE COATS COATS CASSIDY CASSIDY HOEVEN HOEVEN SASSE SASSE BLUNT BLUNT BOOZMAN BOOZMAN FLAKE FLAKE ENZI ENZI SCOTT SCOTT CAPITO CAPITO JOHNSON JOHNSON PERDUE PERDUE ERNST ERNST FISCHER FISCHER PORTMAN PORTMAN HATCH HATCH THUNE THUNE HELLER HELLER ROBERTS ROBERTS RISCH RISCH TILLIS TILLIS MCCAIN MCCAIN ROUNDS ROUNDS CORNYN CORNYN CRAPO CRAPO BURR BURR BARASSO BARASSO SESSIONS SESSIONS LEE LEE ISAKSON ISAKSON RUBIO RUBIO DAINES DAINES PAUL PAUL CORKER CORKER COCHRAN COCHRAN GRAHAM GRAHAM COLLINS COLLINS KIRK KIRK GARDNER GARDNER AYOTTE AYOTTE ALEXANDER ALEXANDER MCCONNELL MCCONNELL DONNELLY DONNELLY CASEY CASEY HEITKAMP HEITKAMP MANCHIN MANCHIN BENNET BENNET WARNER WARNER SCHUMER SCHUMER MENENDEZ MENENDEZ HEINRICH HEINRICH CARDIN CARDIN MCCASKILL MCCASKILL MURPHY MURPHY FEINSTEIN FEINSTEIN KAINE KAINE KLOBUCHAR KLOBUCHAR STABENOW STABENOW SHAHEEN SHAHEEN MIKULSKI MIKULSKI MURRAY MURRAY PETERS PETERS UDALL UDALL TESTER TESTER COONS COONS REED REED BLUMENTHAL BLUMENTHAL REID REID HIRONO HIRONO BALDWIN BALDWIN GILLIBRAND GILLIBRAND BROWN BROWN WYDEN WYDEN MARKEY MARKEY BOOKER BOOKER FRANKEN FRANKEN WHITEHOUSE WHITEHOUSE CARPER CARPER BOXER BOXER MERKLEY MERKLEY LEAHY LEAHY NELSON NELSON DURBIN DURBIN SCHATZ SCHATZ CANTWELL CANTWELL KING KING SANDERS SANDERS WARREN WARREN − 4 − 2 0 2 4 Ideal Point 10

4/30/18 Most i influential s senators: group of senators who can enforce a desirable outcome CARPER D DE MCCASKILL D MO CARDIN D MD MENENDEZ D NJ SCHUMER D NY CRUZ R TX LEE R UT PAUL R KY PETERS D MI Most influential senators ( a l = 0) 11

4/30/18 Case Studies Three bills (Not in training set) 4 4 2 2 Polarity (a) Amdt. 777 Motion to Proceed 0 0 Keystone XL − 2 − 2 − 4 − 4 Bill polarities 12

4/30/18 Case Study: Keystone XL Pipeline § Passed 62 - 36 § Polarity: 1.426 § LIG Model: § 287,400 NE § Median correct votes: 50 § 0.005% of eq. had at least 90 § Our Model: § Only one possible NE § 91 correct votes Case Study: Amdt. 777 “To establish a deficit-neutral reserve fund to recognize that climate change is real and caused by human activity and that Congress needs to take action to cut carbon pollution.” § Failed 49 - 50 § Polarity: -3.705 § LIG Model: § 287,400 NE § Median correct votes: 50 § 0.005% of eq. had at least 90 § Our Model: § Only one possible NE § 92 correct votes 13

4/30/18 Case Study: Motion to Invoke Cloture § Passed 84-12 § Cruz, Paul, Warren, and Sanders voted yea § Polarity: -0.0297 § LIG Model: § 287,400 NE § Median correct votes: 44 § Our Model: § 3,200 NE § Median correct votes: 77 Main Take-Aways § Significant improvement in quality of equilibria § Stronger predictive power than LIG model § Ability to adjust for bills leads to specific NE § Improved computation time 14

4/30/18 Future Work § More efficient equilibrium computation § Topic modeling § Bayesian games 15