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The assumption is of uniform distribution. Doing more did not seem necessary.

In Tables 7 and 8 of the special masters' analysis can be found another way of estimating these probabilities. There they get 8/8 (100%) Republican majoritarian, 11/17 (65%) Democratic majoritarian. https://acefiling.wicourts.gov/document/uploaded/2023AP001399/760087#page=17

The Wilson score estimates on these probabilities are 94+/-6% and 64+/-11%, respectively.

In regard to symmetry, the PGP report card gives information that may help. https://gerrymander.princeton.edu/redistricting-report-card/?planId=recDBtvHPqc5gq8RJ

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