us senate apportionment

Why U.S. Senate Apportionment Matters

This question has its foundation in legal history. During the constitutional convention, James Madison proposed Senate apportionment based on population rather than equality among the several states.  Alexander Hamilton joined Madison in calling for proportional representation, claiming that equal representation despite population inequality “shocks too much the ideas of justice and every human feeling” (The Avalon Project 2008).  This issue incited the most debate in the convention and threatened the creation of the Constitution.  Delegates were deeply divided on the issue and many small states let it be known that they would leave the convention should Madison’s plan be adopted.  That said, Madison and Hamilton had early success – state delegations originally voted 6-5 to implement proportional representation for the Senate. However, small states later reopened the issue and, with the votes of a few medium and large states, successfully adopted equal representation of states in the Senate.  In return, the House would be apportioned based on population.  This, along with other concessions between the two sides, resulted in the Great Compromise that held the convention together.

It is unlikely that the Founding Fathers anticipated the population disparity we see today.  After the convention, the smallest state – Delaware – had a little more than 8 percent of the largest state’s population.  Today Wyoming, the nation’s smallest state, has around 1.5 percent of California’s population.  Figure 1 plots the smallest state’s percentage of the largest state’s population as well as those states’ populations over time (note that the population of the smallest state barely registers on the graph).  The left-hand y-axis denotes state population while the right-hand y-axis shows the total population percentage of the largest and smallest states; the gray line represents the smallest-largest state population percentage, attained simply by dividing the smallest state’s population by that of the largest.

senate apportionment

Figure 1: The blue line denote the largest state’s population (left-hand axis) and the orange lines – barely noticeable – show the population of the smallest state.  The grey line depicts the smallest-largest state ratio.  Numbers derived from the U.S. Census and

Relative Senate representation is inversely related to state population.  As the smallest-largest population percentage decreases, representational inequality increases.  Over time, small states gained power over their larger counterparts as they maintained an equal voice in the Senate as their share of total population and largest-state population percentage shrank.  This can also be seen by examining whether state population percentage equates to its share of Senate seats.  Based on a one person, one vote principle, a state’s share of legislative seats will equal its share of the population.  Clearly, based on Figure 2, the Senate fails to meet such standards.

us senate apportionment one person one vote

Figure 2: Blue lines show the nation’s population share of the largest state and the orange lines, again hardly noticeable, show the population share the nation’s smallest state.  The grey lines picture each state’s Senate seat share.  Numbers again derived from Census data

The blue lines denote the population percentage of the largest state, the orange line the population percentage of the smallest state, and the grey line shows each state’s share of Senate seats.  Under perfect one person, one vote representation, the three lines should be equal.  Obviously, that is not the case.

Population inequality isn’t limited to the two extreme states – the unequal distribution of people across the country results in numerous low population states capable of controlling the Senate.  The smallest possible coalition that could sit 51[1] Senators consists of 26 states[2] comprising 55 million people, or about 17 percent of the total population.  By comparison, California and Texas – the two most populous states – have 64 million people but only four Senators.  A 60 seat supermajority can be attained through the votes of 72 million people, or 22 percent of the population.  While such coalitions are currently unlikely to happen – the likelihood that liberal Vermont elects senators from the same party (and with the same ideology) as deep-red Wyoming in the current political environment approaches zero – this examples demonstrates the extent to which the American senate can subjected to minority rule.  Considering the collapse of the two major parties onto the left-right ideological spectrum (McCarty, Poole, and Rosenthal 2006; Noel 2013), a small percentage of the population can impose their ideological tendencies onto the majority of Americans, either by electing a majority of Senators or enough to sustain procedural roadblocks (i.e., a filibuster).  Though political scientists have studied the impact of institutional design on the distribution of federal funds and representation of parties, they have not fully delved into how the Senate’s apportionment scheme impacts absolute party numbers and ideological composition of the chamber, and ultimately, how this affects policymaking.


In Reynolds v. Sims, Chief Justice Earl Warren found that the principle of one person, one vote serves as a basic democratic tenet.  It implies the inherent equality of all voices in a polity – regardless of class, gender, race, creed, religion, or geographic location, everyone has one equally weighted vote used as the ultimate show of support for a candidate or idea.  Chief Justice Earl Warren described the Court’s foray into the “political thicket” from which it decided that it had jurisdiction over redistricting cases despite their political nature (Baker v. Carr 1964), paving the way for the “one person, one vote” doctrine (Reynolds v. Sims 1964), as his tenure’s most influential decision (Ansolabehere and Snyder 2008).[3]  Yet despite the theoretic and legal justifications for one person, one vote, the American Senate does not – and cannot, per Article V of the Constitution – subscribe to the standard.  Given the vast state population disparities, there is sizable representational (and thus electoral) inequality in the Senate (Lee and Oppenheimer 1999; Griffin 2006).  On a one person, one vote basis, the Senate is the most malapportioned legislative chamber in the world (Lijphart 1984).

This representational inequality has the potential to generate undemocratic policy outcomes.  Overrepresentation of the least-populous states skews distributive outcomes by ensuring that small states receive larger amounts of federal dollars per capita than do large states (Lee 1999, 2000).  Senate apportionment also effects coalition building.  Those seeking to form a minimal winning coalition will seek to “buy” small state support rather than large state support because it is cheaper to earn small state backing.  For instance, a Senator seeking to pass a transportation appropriation will likely turn to small state Senators for support, wooing them with promises of money that, given the state’s small size, amount to little of the bill’s proposed budget.  Large states, having more roads than small states, would require a larger appropriation share, lowering the amount the sponsor could bring to his or her home state, thus making large state Senators unattractive coalition partners (Lee 1999, 2000).  Coalition strategies owing to Senate apportionment benefit small states and hurt large states (Lee 2000).

Following the Baker v. Carr and Reynolds v. Sims Supreme Court decisions ( 369 U.S. 186 (1962) and  377 U.S. 533 (1964), respectively), state legislatures adopted apportionment based on population, generating a natural case study to assess whether equal geographic representation noticeably and significantly impacts public policy.  Prior to the Supreme Court’s decisions, most state legislatures found themselves malapportioned – through deliberate efforts to thwart redistricting, rural counties often held disproportionate seat shares and thus had undue power and influence on state fund transfers.  Many rural counties thus received state funds per person than did urban counties.  When state legislatures moved to representation by population after Baker and Reynolds, state fund transfers largely matched population percentages (Ansolabehere and Snyder 2008).  Urban counties did not dominate the state purse, a fear many state legislators expressed during a House committee hearing regarding a constitutional amendment to allow states to choose how to apportion legislative chambers (Apportionment of State Legislatures: Hearing before the Committee on the Judiciary 1964).  While this does not speak directly to the Senate or Senate vote outcomes, it demonstrates that changing the apportionment scheme has substantial effects on public policy that would likely be borne out in the Senate.

Existing literature pens a persuasive analysis of the normative importance of one person, one vote and the distributional results of the Senate’s failure to adhere to the principle.  However, there has yet to be an extensive study into how Senate apportionment impacts Senate vote outcome and legislation ideology (i.e., content).  Existing research suggests that Senate apportionment does tend to overrepresent minority parties (Lee and Oppenheimer 1999, Griffin 2006), but may not have an effect on ideological representation (Griffin 2006).  The latter point likely needs to be revisited: since Griffin’s study the South and the Northeast have increasingly moved to single-party dominance.[4]  Furthermore, the continued collapse of party lines onto left-right ideology[5] (McCarty, Poole, and Rosenthal 2006; Noel 2013) furthers the likelihood that the over or underrepresentation of a party corresponds to the over/underrepresentation of an ideology.  The degree to which such representational disparities will hopefully be exposed in my research, which seeks to expand on existing studies by delving into Senate design and determining how it impacts vote and policy outcomes.

Analyzing senatorial outcomes and comparing them to the hypothetical Senate with proportional representation allows us to see the impact of rural overrepresentation in votes and legislation ideology. Recognizing the impact of equal representation in the upper chamber of Congress is crucial in assessing whether the Founding Fathers, in their strides to bolster equality in preference, perversely created a system in which the residents of the least-populous states can exert undue impact on national affairs. After all, can America truly be considered democratic if the will of the many is subverted by that of the few?

[1] Well, 52 given that each state elects two Senators

[2] Obviously

[3] To put this in perspective: Chief Justice Warren wrote the majority opinion in Brown v. Board of Education, which found school segregation to be unconstitutional

[4] In the 107th Senate, the last included in Griffin’s analysis, there were nine southern Democrats and six New England Republicans.  Today, those numbers are one and two, respectively.

[5] Across many political areas, including economics, race, and culture.

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