Modeling the effects of changing issue salience in two-party competition

For an identification of other aspects of political competition neglected by the standard Downsian approach, see Skaperdas and Grofman 1995.

Work directly drawing on Rikerian insights about heresthetics includes Feld and Grofman 1988; Hammond and Humes 1993; Humes 1993; Humphreys and Garry 2000; Humphreys and Laver 2007; Moser et al. 2009; Schofield 2006; Schonhardt-Bailey 2006, and Patty 2007, to name but a few. Other relevant work includes Schattschneider 1980 on the consequences of changing the dimension of cleavage. See also Jones 1994.

We will have more to say about the empirical literature on priming in the concluding discussion.

Survey data on voter positions and candidate placement is taken from the National Election Study conducted under the auspices of the University of Michigan.

To avoid technical complexities caused by knife-edge results such as the possibility of ties, we assume that there are an odd number of voters and that no two voters are located at the same point, i.e., we assume that no two voters have identical preferences. The latter assumption can be dropped were we to look at weighted voting games.

Our formalization is a special case of specifying weighted distances between v=(x,y) and D=(D _x ,D _y ) by ∥v−D∥ _A =(x,y)A(D _x ,D _y ) ^T where , a ₁₁=w, a ₂₂=1−w, and a ₁₂=a ₂₁=0 (see, e.g., Enelow and Hinich 1984).

To derive Eq. (2), replace the inequality in Eq. (1) with an equality and solve for x and y, recalling that (D _x ,D _y )=(−R _x ,−R _y ).

If the candidate points lay instead in the upper right and lower left quadrants, the cleavage lines would rotate through the upper left and lower right quadrants.

The initial formulation of this equivalence between “spin angle” and salience weight was suggested to us by Guillermo Owen (personal communication, 2008).

An alternative geometric way to view changes in weightings of dimensions is in terms of “stretchings” or “shrinkings” of one or both issue dimensions. Such topological changes can be displayed visually, but we will not pursue this approach further here since it is essentially equivalent to weighting dimensions and thus adds nothing new.

We assume regularity conditions for the function f, namely that f is continuous and piecewise smooth. A function is piecewise smooth if it has left and right derivatives at every point and—except possibly for a finite number of points—these are equal and define a continuous derivative.

Because the three voters in Fig. 1(a) are not symmetrically spaced, more than one harmonic would be needed to represent voter preferences.

For an nth harmonic function f (where n is odd), the majority switches each time the cleavage line passes through a minimum or maximum value of the function f (a total of 2n times) and also when the cleavage line passes through the line between the candidates (2 times). Thus, there are typically (2n+2) cleavage regions and hence (2n+2)/2=(n+1) majority sectors for each candidate. This latter number may be reduced to n if the line connecting the candidates coincides with a minimum or maximum of f, as in Fig. 3(b).

Conversely, the Democrat can increase her vote share by giving more emphasis to the vertical dimension. Had the third bloc been centered at (−2,−1) in the lower left quadrant, then the favorable issues to prime for the two candidates would have been reversed.

We may also calculate the vote shares of each candidate at each angle of spin (see Fig. 5).

Of course, these probabilities are only suggestive, because the degree of priming is a choice of the two contestants.

Voter and candidate positions are on the conventional 1–7 Likert scale.

The Fourier coefficients c ₁, c ₃, c ₅, c ₇, c ₉ for the 2000 electorate are 0.018, 0.026, 0.046, 0.018, and 0.049.

Of course we recognize that the actual contest was fought at the state level, in terms of the Electoral College, but we are not alone in neglecting that complication when considering presidential elections in the United States. Indeed, there are only a relative handful of formal papers that allow for this complexity by going beyond the popular vote in looking at presidential election competition (see e.g., Owen 1975).

Cf. Grofman et al. (1989).

Our work is also directly related to the saliency theory approach to political competition (Robertson 1976; Budge and Farlie 1983) which highlights how parties employ selective emphasis on issues: rather than taking a (maybe unpopular) position on all issues, parties focus only on those issues where they are perceived as particularly credible (e.g., defense of the welfare state for leftist parties, law and order for conservative parties, etc.). In our opinion, though, the most interesting feature of saliency theory is one that is seldom mentioned in the literature: the (often successful) attempts of parties to convert a positional into a valence issue by carefully hiding the implied policy trade-off. As an example, a leftist party will emphasize its preference for a larger and better welfare state, but will hardly mention that this would imply higher taxes, while conservative parties will emphasize their promise of lower taxes, carefully hiding that this would imply a substantial reduction of welfare state provisions. In other words, the (selective) emphasis on only one side of a policy tradeoff is the tool that parties can employ to frame in valence terms (shared goals for the whole community) issues that in principle are inherently positional, i.e., with clearly defined policy alternatives.

There are many ways in which candidates and their supporters can seek to change the salience of different issues and thus to affect voter choices. For example, Salvanto (2000) has looked at the effects of ballot referendums in California on voter perceptions of the most relevant campaign issues. His analyses look both at the anticipated consequences of decisions to place particular referendums on the ballot and on the decisions of some candidates to identify their own campaigns with particular ballot issues, a practice he call “referenda as running mates”. In California in 1994, the incumbent Republican governor, Pete Wilson, ran an anti-illegal-immigration platform and strongly associated his campaign with the campaign to pass Proposition 187, a referendum proposing to eliminate state spending on public services for illegal immigrants. By associating himself with a YES vote on the referendum he increased the salience of the immigration issue for those voting on the governor’s race. While this strategy appeared to make sense for Wilson, in that a substantial majority of voters were in favor of Prop. 187, the results in this paper show that we must be cautious in assuming that being associated with the winning side of an issue necessarily benefits a candidate as the (relative) weight attached to that issue increases among voters.

There are also other literatures on persuasion in both political science and social psychology. Perhaps the most relevant for present purposes is the literature on campaigning that look, e.g., to the effects of negative campaigning (e.g., Ansolabehere and Iyengar 1995; Skaperdas and Grofman 1995; Ansolabehere et al. 1999; Sigelman et al. 1999), or to the effects of endorsement cues (e.g., Lupia and McCubbins 1998), or to selective information attention and retention effects (e.g., Zaller 1992).