Sequential referenda with sophisticated voters

This paper extends the Romer-Rosenthal agenda setting model to a two-period setting with sophisticated Voters and uncertainty about Voter preferences. If the Setter’s first proposal is rejected, the Setter will make a second proposal. Sophisticated Voters will anticipate the second proposal in responding to the first proposal. The Setter takes their sophistication into account in making the first proposal. We compare outcomes when the Setter faces the same Voters in the two periods with outcomes when the Setter faces different Voters in the two periods, and compare both with the corresponding outcomes with naïve Voters. For some distributions of Voter preferences, Voter sophistication eliminates the benefit to the Setter from having two opportunities; for others, the Setter can exploit the sophistication of Voters to do even better than when Voters are naïve. Whether Voters are sophisticated or naïve, the Setter always does at least as well with two opportunities than with one, but does not always do better. Moreover, because the preferences of the Setter and of the Voters are not directly opposed, the Voters may also do better when the Setter has two opportunities rather than one.