While "Two-Stage Electoral Competition" (Grofman and Owen) in important ways departs from the standard Downsian analysis (in both assumptions -- most obviously the "two-stage" contest -- and in conclusions), in a more fundamental way it retains a "Downsian" assumption that may be hard to justify.

        This basic assumption is that voters focus entirely on the ideological positions of the candidates (or parties) contesting the immediate (district-level) election. This is fine if the office at stake is an "elective autocracy," in which a single candidate is elected to an all-powerful office (as "Downsian theory" most often is implicitly presented) or in which a unified party team is elected to control an all-powerful government (as in Downs's own discussion or in the "Westminster model"). In this event, the single winning (in the general election) candidate or party straightforwardly enacts its policy platform, so (induced) voter candidate (or party) preferences are identical to (underlying) voter policy preferences.

        It has been noted that in the U.S. this "classical Downsian setup" applies best to the election of (unitary) executives, as opposed to (plural) legislatures (or to legislative-executive packages). But even here the application is far from perfect, because an executive cannot enact (most) policy outcomes independent of the separate legislature, which may lead to induced "office balancing" calculations by voters.

        It is commonly presumed that the "classical Downsian setup" applies within each of many U.S.-style single member districts. Thus district-level party competition should converge on the district median preference, with more or less indistinguishable candidates spitting the district vote about equally. But we observe, that (a) many districts are safe for one or other party, (b) candidates take distinctly divergent positions in many districts, and (c) when a Democrat replaces a Republican or vice versa in a given district, there is often an abrupt change in the district incumbent's roll-call behavior. These observations are commonly viewed as anomalous in the context of Downsian spatial theory.

        But this "classical Downsian setup," applied to a district election, assumes, in effect, that a single legislator, namely the one being elected from the focal district, can dictate policy so that, within each district, voter induced preferences over candidates is identical to voter policy preferences. But this legislator will in fact be only one member of a considerably larger legislature, and the legislature as a whole dictates policy. (Let's say there is no executive veto.)

        So to determine the preferences of truly sophisticated voters within a district, we need to model decision making within the legislature and to specify how legislative outcomes may be affected by the outcome of the election in the focal district. Obviously a realistic model would be very complicated, but we can consider two very simple ones.

        The legislature has weak to non-existent party discipline. In this case (which is probably approximated in the U.S.), we may suppose that the legislature enacts the legislative floor median. Thus the effect of the district election is only to shift the floor median a bit to the left or to the right.⁽¹⁾

Thus, for example, both left-wing and moderate Democrats (supposing that the latter are at least a bit to the left of the prospective floor median) equally want to shift the floor median to the left. Moreover, the election of a moderate Democrat accomplishes this just as well as the election of a left-wing Democrat (provided the moderate Democrat is to the left of the floor median). Of course, the moderates want to shift the floor median only a bit to the left, while the left-wingers want to shift it a whole lot to the left; but the point is that the outcome of the focal district election can shift the floor median only slightly, regardless of the ideological positions of the candidates. So there is no particular reason to expect the Democratic candidate to position himself near the center -- or for a Democratic primary with sophisticated voters to be won by a moderate candidate.

Obviously, parallel considerations apply on the Republican side. Basically the outcome of the district election depends on whether the median voter in the district is to the left or the right of the prospective legislative floor median. In the first case, a Democratic victory results; in the second, a Republican victory, and in both cases the margin of victory being a function of the number of voters in the district with ideal points closer to the prospective floor median than to the district median.

        Thus the implications of this "weak party" model are broadly compatible with empirical observations (a), (b), (c) note above.

        The legislature has strong party discipline. In this case (which is possibly approximated in the U.K.), we may suppose that the legislature enacts the median position of the majority party caucus. Thus the outcome of the district election has two quite distinct effects: (a) it adds one member to either the Democratic caucus or the Republican caucus, thus slightly affecting the probability that one or the other becomes the majority caucus, and (b) it shifts the median of the augmented caucus slightly to the left (or right), if the winning candidate is "extreme" within his party, or to the center, if the winning candidate is moderate. Clearly the interval between the medians of the party caucuses is likely to be much greater than the possible shifts of either median within a party caucus, so the former consideration will be dominant in the minds of voters. We would expect the district election to be won by the candidate whose (prospective) party median is closer to the district median and that the ideological positions of the district candidates themselves would have virtually no effect on voter calculations or the district election outcome. Within each district, we get something like the classical Downsian setup but with ideologically rigid non-vote-maximizing parties.

        Of course, national party leaders would, by the classical Downsian logic, seek to recruit and nominate moderate candidates in as many districts as possible, so as to shift their party caucus median toward the center and thus increase the chance that their party will become the majority party. Or perhaps more feasibly, they might simply impose a (probably more moderate) position on the party than its caucus median. Put otherwise, in the strong party discipline case, the legislature may enact the majority party caucus position but that position may not be the median position within the caucus but one dictated by national party leaders. In either event, we get back to something like the classical Downsian setup and its convergence result.
 

1. See attached note on "Candidate Non-convergence." There is obviously at least a bit of a conjectural variation problem across districts. Thus I refer a bit vaguely to the "prospective" floor median here, and focus on the example of a special election (so that the floor median is fixed apart from the outcome of the focal election) in the other note.