How do foreign interests influence the setting of policies by particular countries? What are the implications of such foreign influence? In this paper we develop a theory of foreign influence and apply it to the study of optimal tariffs. We develop a two-country probabilistic voting model of electoral competition, where we allow the incumbent party in each country to take costly actions that affect the election outcome in the other country. We show that policies end up maximizing a weighted sum of domestic and foreign welfare, and study the determinants of this weight. We show that although foreign influence is zero in equilibrium, its "threat" may be welfare-enhancing from the point of view of aggregate world welfare. This is because foreign influence helps alleviate externalities arising from cross-border effects of policies. We apply our model of foreign influence to the study of optimal trade policy. We derive a modified formula for the optimal import tariff and show that a country's import tariff is more distorted whenever the influenced country is small relative to the influencing country and whenever natural trade barriers between the two countries are small.
