Fairness in plurality systems with implications for detecting partisan gerrymandering (Q2673691)

Proportionality cannot be a standard of fairness for first past the post (FPTP) elections. All the same, the drawing of district boundaries is very important in determining the overall outcome, and thus much has been written about the fairness of proposed maps. The game-theoretic approach of \textit{W. Pegden} et al. [``A partisan districting protocol with provably nonpartisan outcomes'', Preprint, \url{arXiv:1710.08781}] (described as ``I cut, you freeze'') and the idea of jurisdictional partisan advantage of \textit{J. Eguia} [``A measure of partisan advantage in redistricting'', Elect. Law J. 21, No. 1, 84--103 (2022; \url{doi:10.1089/elj.2020.0691})] lead to the construction of ``fair'' seats-votes baselines. The author also constructs a seats baseline based on three assumptions about ``fair'' FPTP systems, for both two-party and multiparty elections. One of the assumptions states that in seats that the larger party must win, the winning party and losing party should have equal numbers of unnecessarily wasted votes. The construction is tested with U.S. and Canadian elections. The actual seats obtained in an election are explained as the sum of four sources: the fairness baseline proposed, political geography (the location of the voters of every party), the map-drawing rules, and gerrymandering (the intentional drawing of district boundaries to favour certain political parties over others). The fairness standard is applied to detect partisan gerrymanders in the two-party case; expected real maps are flagged as problematic. The criterion of long-term persistence of a large discrepancy between seat distributions and the baseline is relied upon.