Congressional apportionment and the fourteenth amendment

This paper examines state interest in the nine bases of congressional seat apportionment considered for the House of Representatives as part of the Fourteenth Amendment to the US Constitution. We ask, what if voters preferred apportionments that delivered larger vote shares to their state? We then show that among all states, one basis of apportionment was a weak Condorcet winner, while the others were in a vote cycle. In both chambers of Congress, however, pure majority voting created orderings of the nine bases and a different Condorcet winner. Ironically, Congress did not select either Condorcet winner. Instead, a population-based apportionment was reported out of committee and passed both chambers as a consequence of agenda control and lack of pairwise voting. Our analysis provides an example of how agenda setting with incomplete information unintentionally can produce undesirable outcomes for a legislature.