Steve Ansolabehere and Shiro Kuriwaki write:
The premise that constituents hold representatives accountable for their legislative decisions undergirds political theories of democracy and legal theories of statutory interpretation. But studies of this at the individual level are rare, examine only a handful of issues, and arrive at mixed results. We provide an extensive assessment of issue accountability at the individual level. We trace the congressional rollcall votes on 44 bills across seven Congresses (2006–2018), and link them to constituent’s perceptions of their representative’s votes and their evaluation of their representative. Correlational, instrumental variables, and experimental approaches all show that constituents hold representatives accountable. A one-standard deviation increase in a constituent’s perceived issue agreement with their representative can improve net approval by 35 percentage points. Congressional districts, however, are heterogeneous. Consequently, the effect of issue agreement on vote is much smaller at the district level, resolving an apparent discrepancy between micro and macro studies.
That last point is worth saying again, and Ansolabehere and Kuriwaki do so, at the end of their article:
Our findings also help reconcile two observations. On the one hand, individual con- stituents respond strongly to their legislators’ roll call votes. But on the other hand, aggregate vote shares are only modestly correlated with legislators’ roll call voting records. This is a result of aggregation. Many legislative districts are fairly evenly split on key legislation. A legislator may vote with the majority of her district and get the support of 55 percent of her constituents, but lose the support of the remaining 45 percent. Those with whom the legislator sides care deeply about the issue, as do those opposed to the legislator’s vote. But, in the aggregate the net effect is modest because much of the support and opposition for the bill cancels out. Aggregate correlations should not be taken as measures of the true degree to which individuals care about or vote on the issues. By the same token, in extremely competitive districts, representatives have a difficult time satisfying the majority of the voters back home.
This is thematically consistent with Ansolabehere’s earlier work on stability of issue attitudes, in that details of measurement can make a bit difference in how we understand political behavior.