Single Regression Estimates of Voting Choices When Turnout is Unknown

Abstract This paper demonstrates that conventional single regression estimators of voting preferences for groups within the electorate are unreliable when group-specific turnout rates are unknown. In this context, the relationship between voting choices and the composition of the electorate is defined by two applications of Goodman’s Identity. Several methods appear in the scholarly and litigation literature which attempt to estimate characteristics of this relationship with variants of “Goodman’s regression”, including “correlation analysis” and “homogeneous precinct analysis”. Most of these methods are inconsistent with the Identities. For all methods, the expected values and variances of the dependent variables and of all regression statistics are unknown. None of these methods are capable of identifying any of the underlying parameters, much less the statistical significance of any estimators. Consequently, none has any scientific validity.