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Andrew Gelman, David Epstein, Sharyn OHalloran and Jared Lander Departments of Statistics and Political Science Columbia University 8 Jan 2008 Defining and Measuring the Partisan Fairness of Districting Plans

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2003 Texas Redistricting Texas 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

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Outline: Standards of fairness Some historical background The proportionality standard and its problems The seats-votes curve The symmetry standard and its problems Toward a comparative standard Fairness matters – For the courts – For democracy – Need fairness standard to determine whats unfair

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Some historical background

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Gerrymandering isnt as bad as people think Gelman and King (1994b) – Empirically, redistricting decreases partisan bias and increases competitiveness – Why? Because redistricters work under many constraints But fairness is still a concern

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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 seats This 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 votes – In general, bonus for majority party (e.g., cube law) So how do we describe the relation between voter behavior and electoral outcomes?

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The seats-votes curve This describes the function S(V), the seats won S for a given percentage V of the vote For a single election, calculate this as follows: – Take the vector of votes V = (V 1, V 2, …, V 435 ), where V i is the percentage of Democratic votes in district i – From this get the average Democratic vote and percentage of seats won by the Democrats – this is the actual electoral outcome – Now consider the vector V+1% = (V 1 +1, V 2 +1, …, V ) – I.e., a uniform partisan swing of 1% for the Democrats – Perform the same calculations for V+ x% for all values of x – This will fill out the range, yielding a nondecreasing function S(V) This is the seats-votes curve

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The seats-votes curve

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Traditionally (since Edgeworth, 1898) thought of as a deterministic function: S(V) Actually its probabilistic: p(S|V) Usually summarized by its expectation: E(S|V)

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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 vote In particular, symmetry requires that E(S|V=0.5) = 0.5 King and Browning (1987): partisan bias defined as deviation from symmetry Gelman and King (1990, 1994a): empirical estimate of partisan bias by extrapolation

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Problems with symmetry standard Problem 1: Need to extrapolate to 50% – Consider a state such as Massachusetts – It will never be 50-50, so how can we tell whats fair? Problem 2: Mixing apples and oranges – Seats-votes calculations use all districts at all points along the curve to estimate the relationship – So we use Montana to estimate Massachusetts, and vice-versa Real problem is that the S(V) curve is designed to answer questions about the electoral system as a whole – E.g., bias (intercept at V=.5) and responsiveness (slope at V=.5) – Less useful when were interested in behavior away from the mark – But each election gives us 50 data points, not just one…

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Toward a comparative standard Goal: to solve the Massachusetts problem Not merely an academic exercise! – Consider the 2003 Texas redistricting – Availability of computer programs will make this worse Method of overlap – For any state, extrapolate a bit in either direction (based on historical levels of variation) – Compare a state to similar historical cases – A chain of extrapolations gets you to 50% (and symmetry) Symmetry is thus a baseline but not always a direct standard

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Seats-votes curves from state congressional delegations For each state and each election, extrapolations +/- 5% using uniform partisan swing Create hypothetical elections, adding x% to Dem. share in each district, with x = -5.0, -4.9, -4.8,..., +4.9, +5.0 – Full 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 point – Variation is within states with similar partisan makeups Then can obtain semi-parametric confidence intervals, taking into account state size, incumbency, etc.

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Overall, get something that looks like a confidence band Can use this to judge proposed districting plans

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Overall, get something that looks like a confidence band Can use this to judge proposed districting plans Texas

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Discussion Traditional methods of analysis are not well-designed to assess the fairness of districting plans for states that are far from a partisan split We propose instead the aggregation of local seats-votes curves to provide variation across states and over time These can be used to estimate normal seats-votes relationships for states with high levels of partisanship Then, define unfair districting relative to this standard See if Kennedy goes for it…

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