Effectively governing environmental and social externalities throughout the global economy poses challenges for democratic policy-makers in the court of public opinion. Following the median voter model, as the stringency of policy proposals increases, support rises amongst some citizens and falls amongst others. We argue informational disclosure-based governance presents a potential strategy to mitigate this zero-sum logic as citizens discount policy costs while expecting substantive benefits. We focus on political efforts to increase sustainability throughout global supply chains, drawing on two original survey experiments with representative samples in the 12 largest high-income importing economies (N=24,000). Indeed, at higher levels of policy stringency, citizens expect greater benefits than costs. Further, we find that expected benefits are more strongly associated with support than costs. Lastly, we note how policy stringency promotes convergence of expected benefits across the political ideological spectrum. Hence, our findings provide insights into public preference formation towards the globalization-sustainability nexus.