Axiomatic Districting

In a framework with two parties, deterministic voter preferences and a type of geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts one party can win, given the distribution of individual votes (the \optimal gerrymandering rule"). As a corollary, we obtain that no districting rule can satisfy our axioms and treat parties symmetrically.

Axiomatic districting

In a framework with two parties, deterministic voter preferences and a type of geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts one party can win, given the distribution of individual votes (the "optimal gerrymandering rule"). As a corollary, we obtain that no districting rule can satisfy our axioms and treat parties symmetrically.

The Multiple Hierarchical Legislatures in a Representative Democracy: Districting for Policy Implementation

We build a multiple hierarchical model of a representative democracy in which, for instance, voters elect county representatives, county representatives elect district representatives, district representatives elect state representatives, and state representatives elect a prime minister. We use our model to show that the policy determined by the final representative can become more extreme as the number of hierarchical levels increases because of increased opportunities for gerrymandering. Thus, a sufficiently large number of voters gives a district maker an advantage, enabling her to implement her favorite policy. We also show that the range of implementable policies increases with the depth of the hierarchical system. Consequently, districting by a candidate in a hierarchical legislative system can be viewed as a type of policy implementation device.