Bargaining in bicameral legislatures: When and why does malapportionment matter?

Malapportionment of seats in bicameral legislatures, it is widely argued, confers disproportionate benefits to overrepresented jurisdictions. Ample empirical research has documented that unequal representation produces unequal distribution of government expenditures in bicameral legislatures. The theoretical foundations for this empirical pattern are weak. It is commonly asserted that this stems from unequal voting power per se. Using a noncooperative bargaining game based on the closed-rule, infinite-horizon model of Baron and Ferejohn (1989), we assess the conditions under which unequal representation in a bicameral legislature may lead to unequal division of public expenditures. Two sets of results are derived. First, when bills originate in the House and the Senate considers the bill under a closed rule, the equilibrium expected payoffs of all House members are, surprisingly, equal. Second, we show that small-state biases can emerge when (1) there are supermajority rules in the malapportioned chamber, (2) the Senate initiates bills, which produces maldistributed proposal probabilities, and (3) the distributive goods are "lumpy."