We extend the estimation of the components of partisan biasd, undue advantage conferred to some party in the conversion of votes into legislative seats to single-member district systems in the presence of multiple parties. Extant methods to estimate the contributions to partisan bias from malapportionment, boundary delimitations, and turnout are limited to two-party competition. In order to assess the spatial dimension of multi-party elections, we propose an empirical procedure combining three existing approaches: a separation method (Grofman et al. 1997), a multi-party estimation method (King 1990), and Monte Carlo simulations of national elections (Linzer, 2012). We apply the proposed method to the study of recent national lower chamber elections in Mexico. Analysis uncovers systematic turnout-based bias in favor of the former hegemonic ruling party that has been offset by district geography substantively helping one or both other major parties.
We analyze sixty-six Ohio congressional plans produced during the post-2010 census redistricting by the legislature and the public. The public drew many plans submitted for judging in a competition hosted by reform advocates, who awarded a prize to the plan that scored best on a formula composed of four permissive components: compactness, respect for local political boundaries, partisan fairness, and competition. We evaluate how the legislature’s adopted plan compares to these plans on the advocates’ criteria and our alternative set of criteria, which reveals the degree by which the legislature placed partisanship over these other criteria. Our evaluation reveals minimal trade-offs among the components of the overall competition’s scoring criteria, but we caution that the scoring formula may be sensitive to implementation choices among its components. Compared to the legislature’s plan, the reform community can get more of the four criteria they value; importantly, without sacrificing the state’s only African-American opportunity congressional district.