Democracies are more supportive of US positions on important votes in the UN General Assembly than of nondemocracies. Is this because democracies share common perspectives, or does this pattern reflect coercion? Since 1985, US law has stipulated that the US State Department identify important votes and that aid disbursements reflect voting decisions. To unravel these alternative explanations, we introduce a strategic statistical model that allows us to estimate voting preferences, vulnerability to influence, and credibility of linkage, which are theoretical quantities of interest that are not directly observable. The results reject the hypothesis of shared democratic values: poor democracies have voting preferences that are more oppositional to US positions than autocracies, and they are more willing than autocracies to take symbolic stands that may cost them foreign aid. Democracies support US positions, however, because US aid linkages are more credible when directed toward democratic countries. Splitting the sample into Cold War and post–Cold War segments, we find that the end of the Cold War changed the way US linkage strategies treated allies and left- and right-leaning governments, but the effects of democracy remained constant.