Presentation on theme: "Defining and Measuring the Partisan Fairness of Districting Plans"— Presentation transcript:
1 Defining and Measuring the Partisan Fairness of Districting Plans Andrew Gelman, David Epstein, Sharyn O’Halloran and Jared LanderDepartments of Statistics and Political ScienceColumbia University8 Jan 2008
2 2003 Texas RedistrictingTexas House delegation went from Democrat in 2002 to Republican in 2004 (while voting 61%-38% for Bush)Is this an unfair partisan gerrymander?Supreme Court (Kennedy) said there is no workable standard
3 Outline: Standards of fairness Some historical backgroundThe proportionality standard and its problemsThe seats-votes curveThe symmetry standard and its problemsToward a comparative standard“Fairness” mattersFor the courtsFor democracyNeed fairness standard to determine what’s unfair
6 Some historical background “Gerrymandering” isn’t as bad as people thinkGelman and King (1994b)Empirically, redistricting decreases partisan bias and increases competitivenessWhy? Because redistricters work under many constraintsBut fairness is still a concern
7 The proportionality standard Popular in Europe, via PR electoral systems“Fairness” is If your party receives x% of the vote, it should receive x% of the seatsThis does not work, in general, with first-past-the-post systems such as the U.S.Can win 55% of the vote in every district,100% of the seats.In fact, can win a majority with ~25% of the votesIn general, bonus for majority party (e.g., cube law)So how do we describe the relation between voter behavior and electoral outcomes?
8 The seats-votes curveThis describes the function S(V), the seats won S for a given percentage V of the voteFor a single election, calculate this as follows:Take the vector of votes V = (V1, V2, …, V435), where Vi is the percentage of Democratic votes in district iFrom this get the average Democratic vote and percentage of seats won by the Democrats – this is the actual electoral outcomeNow consider the vector V+1% = (V1+1, V2+1, …, V435+1)I.e., a uniform partisan swing of 1% for the DemocratsPerform the same calculations for V+ x% for all values of xThis will fill out the range, yielding a nondecreasing function S(V)This is the seats-votes curve
10 The seats-votes curveTraditionally (since Edgeworth, 1898) thought of as a deterministic function: S(V)Actually it’s probabilistic: p(S|V)Usually summarized by its expectation: E(S|V)
11 The symmetry standard “Fairness” is . . . E(S|V) = 100 – E(S|1-V) For example, in 2008 the Democrats averaged 56% of the vote in U.S. House races and received 59% of the seats.This is symmetric (i.e., “fair”) if the Republicans would have received 59% of seats had they won 56% of the voteIn particular, symmetry requires that E(S|V=0.5) = 0.5King and Browning (1987): partisan bias defined as deviation from symmetryGelman and King (1990, 1994a): empirical estimate of partisan bias by extrapolation
12 Problems with symmetry standard Problem 1: Need to extrapolate to 50%Consider a state such as MassachusettsIt will never be 50-50, so how can we tell what’s fair?Problem 2: Mixing apples and orangesSeats-votes calculations use all districts at all points along the curve to estimate the relationshipSo we use Montana to estimate Massachusetts, and vice-versaReal problem is that the S(V) curve is designed to answer questions about the electoral system as a wholeE.g., bias (intercept at V=.5) and responsiveness (slope at V=.5)Less useful when we’re interested in behavior away from the markBut each election gives us 50 data points, not just one…
13 Toward a comparative standard Goal: to solve the “Massachusetts problem”Not merely an academic exercise!Consider the 2003 Texas redistrictingAvailability of computer programs will make this worseMethod of overlapFor any state, extrapolate a bit in either direction (based on historical levels of variation)Compare a state to similar historical casesA chain of extrapolations gets you to 50% (and symmetry)Symmetry is thus a baseline but not always a direct standard
14 Seats-votes curves from state congressional delegations For each state and each election, extrapolations +/- 5% using uniform partisan swingCreate hypothetical elections, adding x% to Dem. share in each district, with x = -5.0, -4.9, -4.8, , +4.9, +5.0Full implementation would also add noise (“JudgeIt”)These will overleaf with each other, creating an overall seats- votes curve with a range of variation at each pointVariation is within states with similar partisan makeupsThen can obtain semi-parametric confidence intervals, taking into account state size, incumbency, etc.
17 Overall, get something that looks like a confidence band Can use this to judge proposed districting plans
18 Overall, get something that looks like a confidence band TexasOverall, get something that looks like a confidence bandCan use this to judge proposed districting plans
19 DiscussionTraditional methods of analysis are not well-designed to assess the fairness of districting plans for states that are far from a partisan splitWe propose instead the aggregation of local seats-votes curves to provide variation across states and over timeThese can be used to estimate normal seats-votes relationships for states with high levels of partisanshipThen, define unfair districting relative to this standardSee if Kennedy goes for it…