We introduce an attractor model of political competition in which the distribution of voters’ ideal points is endogenous. Two candidates for office select policies they intend to pursue in office. They also select a range of voters they will attempt to persuade of the merits of their policies. Finally, the opinion formation process, where each voter is influenced by neighboring opinions, determines the distribution of ideal policies. Our main insight in this paper is that despite the endogeneity in the distribution of voters’ ideal points, candidates will adopt policy positions equivalent to the median voter’s ideal point before the communication processes take place. This outcome is termed the “median attractor” result and shows that democracy possesses an inherent resilience. We also show that candidates choose smaller influence ranges to attract voter groups, as such strategies will trigger the most favorable shift in ideal voter distribution towards the candidates’ policy positions.
Hoferer et al. (Fri,) studied this question.