Coalitional Instability and the Three‐Fifths Compromise

Were the initial apportionments of the U.S. House of Representatives and the U.S. Senate inevitable? This article determines the coalitional stability of apportionment rules considered at the Constitutional Convention assuming the Convention limited itself to the rules proposed. Using each state's vote share as a measure of state preference, we find that the stability of legislative apportionment depended upon the states making decisions. Equal apportionment was in equilibrium with 13 states present, as in the Continental Congress, but when Rhode Island and New Hampshire were absent during the first third of the Convention, all rules were in a top cycle. With New York departing near the middle of the Convention, equal apportionment and the Three‐Fifths Clause both became stable, and the Great Compromise was reached. We conclude that the Great Compromise was partly the result of historical contingency (i.e., which states participated), rather than necessity.