Most models of candidate competition assume either that candidates can choose all of their positions (e.g., the classical Downsian model) or that candidates are exogenously endowed with certain fixed positions and characteristics so that voter preferences over candidates cannot be influenced by the candidates (e.g., the citizen-candidate model).
A differentiated candidates model is a hybrid of these two extreme assumptions. There are some positions or characteristics such as gender, race, professional background etc. that are unchangeable for the candidates, but there is also a meaningful policy choice that voters care about.
Core supporters and swing voters
Voters who prefer all fixed characteristics of candidate A over those of candidate B are candidate A's "core supporters." They are very likely to support A no matter what policies A (and B) propose on those issues where the candidates can choose a position.
In contrast, voters who like some of the fixed features of candidate A, but also some of those of candidate B are much more likely to be persuadable. When choosing their flexible positions during the election campaign, candidates will predominantly focus on these swing voters.
Stefan Krasa and Mattias Polborn, The binary policy model, Journal of Economic Theory, 145 (2), March 2010, 661-688.
Does political competition between office-motivated candidates lead to policy convergence?
Standard models of political competition are often interpreted as predicting very small differences between candidates, as long as candidates are primarily office-motivated. This is clearly true in the one-dimensional Downsian model, the most widely applied model of political competition. Conversely, if candidates are observed with widely different platforms, this is interpreted as evidence that candidates are policy-motivated (i.e. they are willing to accept a decreased chance of winning the election in exchange for the ability to implement a policy that is closer to their own ideal if they win).
These intuitions are derived in a particular modeling framework in which candidates do not differ in their fixed characteristics. Are they also true in more general differentiated candidate models?
It depends on the structure of voter preferences. There are conditions on voter preferences under which candidates' equilibrium policies generically converge. In contrast, whenever fixed characteristics such as competence influence a voter's preferred policy from a candidate, the condition is violated, and we show that policy divergence can arise in the unique and strict Nash equilibrium.
Stefan Krasa and Mattias Polborn, Political Competition between Differentiated Candidates, Games and Economic Behavior , 76 (1), 2012, 249-271.
Models of complementarity and competence
Candidates for political office often differ in their competence in different policy areas. For example, voters often perceive Republican candidates as "stronger" (more competent) on national security, and Democrats as more competent on many domestic policies (this is sometimes called issue ownership in the political science literature).
The standard way of modeling candidate quality (also called valence) used in most political economy models is as an additive term that is independent of the policies proposed by the candidates. This modeling applies best if we think of valence as charisma or physical appearance of the politician (and citizens prefer any policy to be delivered by a charismatic or good-looking candidate). It is less appropriate if the relevant quality dimension is the competence of the candidate to manage the provision of certain public goods, because a candidate's ability is complementary to the policy (say, the amount of money that the candidate suggests to spend on his area of expertise).
Stefan Krasa and Mattias Polborn, Competition between specialized candidates, American Political Science Review, 104 (4), November 2010, 745 -765.
The interaction of competence and ideology
Consider a model, similar to the one described just above, in which Democrats and Republicans have different capabilities in producing public goods. However, suppose that voters also care about ideology (a second dimension in which voters have preferences for either the Democratic or the Republican position).
In such a world, there are different types of swing voters (i.e., voters who are almost indifferent between candidates). Voters who are socially liberal but economically conservative like the social liberalism of Democrats, but also the economic conservatism of Republicans. Voters who are socially conservative but economic liberals are exactly the other way around. Candidates compete for these swing voters.
We analyze how an intensification of ideological preferences (or a change in the percentage of social conservatives) changes the candidates' economic policy platforms. Interestingly, candidates adapt to a more socially conservative electorate by adopting more economically liberal policies.
Stefan Krasa and Mattias Polborn, Social ideology and taxes in a differentiated candidates framework (American Economic Review)
Empirical estimation of candidate positions and electoral polarization
The differentiated candidate model is also the basis for our empirical project on the measurement of candidate positions and the analysis of electoral polarization.