On the (mis)measurement of legislator ideology and shirking

In this paper, we show that current statistical measures of legislator's shirking are implicitly based on the electoral concept of a unique majority rule equilibrium point in the policy space where elections are contested. We note that such equilibria do not exist generically and present statistical results showing that cross-sectional regressions where legislators' voting indices are predicted by district average demograhic and economic data are mis-specified. We also discuss a weaker equilibrium construct, the uncovered set, and present statistical evidence showing that differences in voting behavior between Senators from the same state are positively related to the heterogeneity of the electorate. We argue that current evidence alleged to show shirking by Senators is equally consistent with Senators who perfectly represent an idiosyncratic constituency that cannot be represented by district average data.