3
Once valence advantages are added to the Downsian model, though, the
predictions change. Ansolabehere and Snyder (2000) showed that valence advantages
(see Stokes 1963) work as a moderating force in candidate positioning. Specifically, the
advantaged candidate will typically take positions closer to the median voter than will the
disadvantaged candidate, though this relationship is not necessarily linear. Groseclose
(2001) extended these results, proving that if the valence difference is large enough, the
advantaged candidate will actually diverge towards her ideal policy-motivated position,
although the disadvantaged candidate will still be the more extreme contender of the two.
In sum, the valence predictions are non-linear. When an incumbent has a slight
advantage on valence (e.g., project allocations), then movement toward the median voter
is expected. When an incumbent has a large advantage on valence, then movement away
from the median voter is expected (see Figure 1).
1
Empirical research on position-taking and representation has often contradicted
these theoretical results. Candidates for Congress represent the views of their party rather
than the median voter in their districts (Ansolabehere, Snyder and Stewart 2001a;
Schraufnagel and Mondak 2002). Furthermore, the congressional literature on
constituency service, trust, and incumbency advantage produces two other competing
hypotheses separate from the valence hypothesis. First, a number of scholars have noted
that legislators build trust with their constituents through project allocations and
constituency service, and this district attention (which can be conceived of as valence)
1
In a number of instances, though not tested in this paper, there are no equilibria predictions when a
legislator has a fairly substantial valence advantage and is motivated primarily by office-holding.
Empirically, though, we think legislators and candidates are motivated by both office-holding and policy
goals.
Convention