Abstract
The topic of district size was so important in the early American republic that even before it passed what would become the first amendment, the 1st Congress approved an amendment to limit the size of constituencies in the House of Representatives. In contrast to the amendment providing freedom of speech, assembly and religion, this earlier amendment dictating a ratio of representation failed to receive the requisite support among the states. Absent this constitutional provision, the number of representatives and thus district population is governed by statute, the most recent of which caps the size of the House of Representatives at 435. With over 300 million people living in the United States, each representative is responsible for more than 700,000 constituents.
The framers were rightly concerned about how one person could provide adequate representation to so many people; however, the level of apportionment used by the United States has other ill-effects. In particular, we show that low levels of apportionment (a high ratio of constituents to representatives) exacerbates bias in electoral outcomes. We show that increasing the population while holding constant the number of representatives can lead to more bias in electoral outcomes. We test this claim using Monte Carlo simulations of hypothetical districts under varying levels of apportionment. Using a computer algorithm we produce tens of thousands of alternative maps of congressional districts under existing levels of apportionment and under levels of apportionment in which there are more members of the House. Using this large set of hypothetical districts, we find that as the number of representatives increases, the expected level of bias decreases.