
opposition, taking whatever definitions of fairness might be most convenient to maintaining
or implementing a power dynamic (Becker and Gold 2022).
Another straightforward idea of fairness is political representation. Presently U.S. politics is
dominated by two political parties, so with relatively little information loss, ensuring partisan
symmetry across population and representation is an ideal metric (Gelman 2002). In this
formulation, fairness of a particular redistricting plan can be quantified by the relationship
between a proportion of votes a party receives and the proportion of seats it wins. If a
state has ten seats and a perfect partisan split, one might expect that both parties have
five seats each. There are two versions of this formulation, one comparing the seat share
each party would win if support were shifted to 50% per party, and the second comparing
with a specific symmetry parameter ¯p. This enables us to evaluate and compare plans with
a mathematically rigorous definition of electoral responsiveness and bias. In addition to
partisan bias, political scientists have developed a quantifier termed the ”efficiency gap”
(Warrington 2018). Partisan bias quantifies the degree to which parties would win different
fractions of the total seats with the same original votes. The efficiency gap relies on the
concept of a wasted vote, these being votes that are cast over the majority required to win
an election. We can see this in a simple toy example detailed in Figure 2. Two districts 1
and 2 have ten voters each. One district is won by party A with 7 votes and the other by
party B with 6 votes. In district 1, every vote over 50% of the population is ’wasted.’ An
optimal outcome for party A would be to redistrict 3 of its voters into District 2, where,
despite holding 50% of the partisan vote across districts, party A would hold 100% of seats.
District Party A Party B
District 1 7 3
District 2 4 6
Figure 2: Two-district vote distribution (10
voters each)
Another requirement for our analysis is that we
have a frame of reference to compare different re-
districting plans. While we can quantify fairness
with regard to the voting populous or partisan
representation atomically using partisan bias or
the efficiency gap, these plans are often drawn to
maximize a power dynamic with respect to a set
of rules which vary by state. There is no baseline
for comparison. The ALARM Project (McCar-
tan, Kenny, Simko, Garcia, et al. 2022) proposes
a simulation-based approach to contextualize congressional district plans within the rules of
a state, enabling state-specific district simulations. The authors simulate possible district
plans based on the rules of a state, considering geography, demographics, institutions and
redistricting requirements that constrain the space of possible maps. Drawing possible sim-
ulated plans thousands of times, they are able to evaluate different quantifiers of fairness
over the generated set. This formulation allows for a counterfactual ”ground truth” distribu-
tion of possible plans which can be used to contextualize existing plans, and has been used
extensively in further literature.
The simulated plans take into account existing redistricting rules per-state, but lack more
complicated rules from the Voting Rights Act (VRA). These ensembles are still effective
baselines, but are ineffective for contextualizing proposed plans with regard to prohibitions
against racial gerrymandering and minority vote dilution, specifically the “Gingles factors”
3