M ODELING FAIR R EDISTRICTING C OMMISSIONSHenry Fleischmann and Pingbang Hu
henryfl@umich.edu and pbb@umich.edu
University of Michigan

GerrymanderingResults

How can we ensure that independent
redistricting commissions really work?

Every ten years, we redraw our voting maps. When these maps
are drawn by politicians to maximize their electoral gains, thisis known as partisan gerrymandering.

Theorem 1 (Balanced Mechanism). In commissions withequal numbers of partisans and some member preferring
a neutral map, the positional-scoring voting rule with scores⟨1, 0, −1⟩ is group strategy-proof and selects a neutral map.
Theorem 2 (Unbalanced Mechanism). As long as somecommissioner prefers a neutral map, the following groupdependent positional scoring rule is group strategy-proofand chooses a neutral map:D:11, R:, 0, −nDnD





11,I:
, 0, −nRnR11.
, 0, −nRnR

Theorem 3 (Robustness to Misevaluations). Let x and y be
the number of wD Democratic commissioners and wR Republican commissioners, respectively. If nD ≥ nR, thenTheorem 2 is robust up to k ≤ nI /4+ nnDR ·x+y commissionermisevaluations.

RIn the below, p is the probability a commissioner misevaluates
the maps.

DIElbridge Gerry’s Original Gerry-mander.
• In response to this anti-democratic process, fourteen states,
including Michigan and California, have adopted a new redistricting protocol.

In our model, the commissioners decide between a Republican-biased, neutral, andDemocrat-biased map. The true biases of the maps are known to the commissioners but unknown to the mechanism.
• The Michigan Independent Citizens Redistricting Commission is composed of fourRepublicans, four Democrats, and five Independents.
• After a year of learning about redistricting, the commission selects a voting map.
• Our mechanism leverages their acquired insight into the true biases of the maps toensure the selection of a truly neutral map, even if partisan commissioners preferbiased maps and commissioners make mistakes.

Our Model• Commissioner types: D for Democrats, R for Republicans, and I for Independents.
• Every redistricting cycle, a commission of volunteer citizens
form to draw the maps without the input of elected politicians.

• Commissioner sub-types: partisans are either weak or strong, and independents
lean weakly toward either Democrats or Republicans.

RThe state constitutions outline every aspect of these commissions. But, when the commissioners eventually choose amap to enact, how can we be certain that they will actuallychoose a fair map?

sR

IwRwRwDsDwD• The commissioners decide between three categories of maps: D (biasedDemocrat), N (neutral), and R (Republican-biased). Their preferences are:wD : N ≻ D ≻ R,Future WorkD• All commissioners prefer a neutral map over a map biased toward the other party,
but strong partisans prefer a biased map over a neutral map.

sD : D ≻ N ≻ R,For small enough p, it is better to have a big commission.
For large p, it is better to limit the commission size.

sR : R ≻ N ≻ D,

wR : N ≻ R ≻ D.

• The most well-known strategy-proof voting rule is the median voting rule on single-peaked domains.
• This voting rule can be generalized to restricted higherdimensional domains.
Is there a reasonable function from the space of redistricting
plans to a domain where the median rule applies?