Most studies of party competition in multidimensional spaces look at the strategies parties choose to influence their voters. There is, however, no good reason to only assume a unidirectional causal arrow. To fill this gap, this thesis proposes a theory that sets out how parties are influenced by their voters when choosing a strategy (ignoring, positioning/emphasising, blurring, or embedding) on an issue dimension. In this Constrained Strategies theory, the distinctiveness and salience, as well as the divisiveness, of the opinions of those voters likely to vote for a party are pertinent. I call these variables the electoral potential and dividing potential of an issue dimension. In addition, issue ownership and the risk of voters changing allegiance to competitors, called competition exposure, are crucial. Combined, these variables influence why parties choose a particular strategy. I apply this theory to parties' interaction with immigration and European integration. By combining data on voters' and parties' positions, I find that electoral potential leads to emphasising, whereas dividing potential is associated with blurring and ignoring. Furthermore, using a regression discontinuity design, I focus on competition exposure. By exploiting exogenous variation associated with electoral thresholds, I show that radical right parties entering parliament cause other parties to emphasise and blur on European integration and immigration. Overall, my results indicate that the strategic behaviour of parties in multidimensional competition is constrained by their voters.
