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JudgeIt is used to model two-party electoral systems; choose one party to identify as ``Party 1''. (All results for Party 2 are clearly the opposite for those of Party 1.)
In any particular election year, let be the share of the two-party vote received by Party 1 in district . We model the resulting vote share as
where is a vector of predictor variables with coefficient , and and are the systematic and random error terms. In this presentation, is the total error variance, and is the share attributed to the systematic error component. The error terms in each district are independent of each other and of those in each other district in the system.
The standard approach to estimating the unknown quantities is to model each year under the Bayesian framework, with noninformative priors on the and parameters in each year. To estimate , take the total variance estimate in each year and pool those estimates together; then use the mean of the pooled estimates as the value of as the value for each election.
To estimate for the electoral system, note that the systematic component of the error is proportional to the votes received in each district in two subsequent elections, yielding
where may include as many variables as are available from elections and . The value of used is the mean of these estimated values. Note that estimates of can only be obtained when two subsequent elections use the same electoral map, i.e. no redistricting has taken place.