Governments are confronted with a wide range of issues, from international affairs, to social security, to the economy. We develop a model of accountability to study policymaking in this multidimensional world. Our aim is to tackle several questions: When do officeholders address all policy dimensions that are relevant for the voters, and when do they instead focus on a subset of them? What types of reforms do policymakers pursue when they have broader versus narrower policy agendas? How do interconnections across dimensions impact policymaking? We begin with the observation that policymaking is complex, due to uncertainty about policy consequences. Voters observe outcomes and adjust their beliefs about optimal policies. When different policy issues are connected in voters’ minds, learning spills over from one issue to the others. In this context, trailing incumbents tend to adopt comprehensive policy programs covering interconnected issues, while leading incumbents prioritize fewer, more independent dimensions. Additionally, we identify a substitution effect between highly connected dimensions in voters’ minds, where multidimensionality can lead to either moderation or extremism in the primary policy dimension, depending on the incumbent’s electoral prospects. Our results challenge the notion that a unidimensional model adequately represents policymaking in a multidimensional world where preferences across dimensions are correlated.