Unlike the large literature on 'democracy and trade', there is a much smaller literature on the effect of the level of democracy in a nation on the level of its foreign direct investment (FDI) inflow. These few studies reveal mixed empirical results, and surprisingly only one study has examined bilateral FDI flows. Moreover, few of these studies use multiple governance indicators separating the 'pluralism' effect of democratic institutions from the 'good governance' effect, there are no studies on democratic institutions' various effects on the level of FDI relative to trade, and there are no studies of democratic institutions' various effects on the selection of countries into FDI. We focus on three contributions. First, we examine the simultaneous effects of the World Bank's (six) Worldwide Governance Indicators (WGIs) - which allow separating the effects of pluralism from those of five other good governance measures - on bilateral trade, FDI and FDI relative to trade using state-of-the-art gravity specifications. Second, we find strong evidence that - after accounting for host governments' effectiveness in various roles of good governance - a higher level of pluralism as measured by the WGIs' Voice and Accountability Index reduces trade levels, likely by increasing the 'voice' of more protectionist less-skilled workers, but not FDI levels. Moreover, we find qualitatively different effects of other WGIs - such as political stability - on trade versus FDI flows. Third, we account for firm heterogeneity alongside a large number of zeros in bilateral FDI flows using recent advances in gravity modelling. We distinguish between the (country) intensive and extensive margins and show that pluralism affects FDI inflows negatively at the intensive margin, but positively at the extensive margin.