The Art of Compromising: Voting with Interdependent Values and the Flag of the Weimar Republic

We model a situation where ex ante opinions in a legislature are dichotomous but cross traditional left-right party lines, e.g., crucial decisions on ethical issues such as gay marriage and abortion, or joining/exiting an economic/political union. In addition to the two "extreme" positions on the left and on the right, we consider the effect of a compromise alternative whose location may be endogenous. We compare sequential, binary voting schemes conducted by privately informed agents with interdependent preferences: the voting process gradually reveals and aggregates relevant information about the location of preferred alternatives. The Anglo-Saxon amendment procedure (AV) always selects the (complete-information) Condorcet winner. In contrast, the continental successive procedure (SV) does not. This holds because AV allows learning about the preferences of both leftists and rightists, while SV only allows one-directional learning at each step. Moreover, under SV, the agenda that puts the alternative with ex ante higher support last elects the Condorcet winner more often than the agenda that puts that alternative first. The optimal compromise location for various goals is also shown to differ across voting procedures. We illustrate our main findings with a fascinating historical episode, the vote on the flag of the Weimar republic.