Presentation on theme: "Defining and Measuring the Partisan Fairness of Districting Plans"— Presentation transcript:
1Defining 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
22003 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
3Outline: 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
6Some 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
7The 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?
8The 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
10The 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)
11The 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
12Problems 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…
13Toward 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
14Seats-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.
17Overall, get something that looks like a confidence band Can use this to judge proposed districting plans
18Overall, get something that looks like a confidence band TexasOverall, get something that looks like a confidence bandCan use this to judge proposed districting plans
19DiscussionTraditional 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…