Theory: the logical model of minority representation

What is the logical model of minority representation?

The logical model formalizes a simple claim: minority representation requires a minority candidate to emerge and to win. Whether that occurs reflects both the district’s prior racial electoral environment and the minority group’s share of the electorate. The model combines those quantities to produce a district-level probability of minority candidate emergence and electoral success.

The package calculates

[ () = ( - 50), ]

where () is the standard normal cumulative distribution function, M is the adjusted racial margin of victory, and C is the minority share of the electorate. Both M and C are expressed from 0 to 100.

The adjusted racial margin of victory (M)

M summarizes the electoral environment from the vote shares of the top minority and White candidates in a previous election. If those vote shares are Vm and Vw, respectively, then

[ M = + 50. ]

Larger values indicate a more favorable prior environment for the minority candidate. Use comp_M() when the relevant vote shares are observed, or sim_M() when constructing a prospective scenario from voting assumptions.

Minority electorate share (C) and turnout

C is the minority percentage of the electorate. If the available value is a population or voting-age-population percentage and minority and White turnout rates differ, use gap = c(minority_turnout, white_turnout). Each turnout rate is a proportion from 0 to 1. minorep() and sim_redistrict() apply the turnout adjustment before calculating their predictions.

Interpreting a prediction

The output is a model-based probability, conditional on the inputs and assumptions supplied. It is not a deterministic forecast and should be read with the model’s scope in mind. The published article evaluates the model with Louisiana mayoral elections and state legislative elections; those results do not establish a universal accuracy guarantee for other places or future plans.

The application vignettes show how to choose inputs, calculate predictions, and use simulations and plots to compare scenarios.

Reference

Atsusaka, Yuki. 2021. “A Logical Model for Predicting Minority Representation: Application to Redistricting and Voting Rights Cases.” American Political Science Review 115 (4): 1210–1225. https://doi.org/10.1017/S000305542100054X