In presidential elections in the United States, such as the one that will be held in November of this year, the outcome is not directly determined by the numbers of ballots that individual citizens cast for the various candidates, but by the votes of members of the Electoral College. In each state, the persons who are elected or appointed to membership in the Electoral College are supposed to cast their votes for the candidate who received the plurality of the votes of the citizens of that state. (For example, in 1996, more Iowans voted for Bill Clinton than for any of the other presidential candidates, so the seven persons chosen as members of the Electoral College all cast their ballots for Clinton.)
Because the candidate who receives the plurality of popular votes is awarded all of the state's electoral votes, regardless of the margin of victory, it is widely believed that the Electoral College system is biased towards populous states. Here's the reasoning: It is far more likely that the outcome of the presidential election will depend critically on which candidate wins a plurality in, say, California (which chooses fifty-four members of the Electoral College) than on the outcome in, say, Vermont (which chooses only three). The effect of bloc voting by state in the Electoral College, therefore, is that a voter in California is far more likely to participate in determining the outcome of the election than a voter in Vermont.
On the other hand, skeptics have argued that the Electoral College system actually favors less populous states, for two reasons: (1) The Electoral College representation of a state is not directly proportional to the state's population, but rather is set equal to the size of the state's Congressional delegation. Since each state, no matter how small, sends two senators to Congress, small states choose more members of the Electoral College per capita than large ones. (2) Although achieving a plurality in a larger state causes a bigger swing in the Electoral College, the larger number of voters in a larger state makes it more difficult to win a plurality. Winning several small states, therefore, is a task that is comparable in difficulty to winning one large state.
The project this time is to develop some evidence relevant to this dispute by estimating the voting power of an individual voter in each state -- the likelihood that that individual's vote has a share in determining the outcome of the election. We can compute such an estimate in two steps:
If a state elects or appoints v members of the Electoral College, the contribution of that state's electors to the outcome of the presidential election is proportional to v3/2.
Every registered voter in a state has an equal power to determine the plurality winner in that state. The state's voting power, therefore, is divided equally among the registered voters of that state.
For instance, for a state that has two million registered voters and chooses eight members of the electoral college, we'd compute the voting power of each voter as 83/2/2000000, or about 0.0000113. A voter in a state that has seven million registered voters and chooses twenty members of the electoral college would have a voting power of 203/2/7000000, or about 0.0000128.
Since only the ratios between these voting-power statistics are significant -- their relative magnitudes, not their absolute values -- it is convenient to normalize them in some convenient way, such as dividing each one by the least one in the group.
The file /home/stone/courses/scheme/data/electoral.dat contains fifty-one lines, one for each state and one for the District of Columbia. Each line contains the name of the state (in the first twenty columns), the number of persons from that state the Electoral College (in the next three columns), and (in the remaining nine columns) the number of voters registered in that state at the time of the 1998 Congressional elections, as determined by the Federal Election Commission and presented in their report ``Voter registration and turnout -- 1998''. (North Dakota does not require voters to register, and in Wisconsin one registers on election day, so in both of those states the estimated voting-age population at the time of the 1998 Congressional elections is listed instead.)
The exercise is to write a Scheme program that reads in these data and creates a file named voting-power.dat, again consisting of fifty-one lines. Each line should begin with the name of a state, and this should be followed by the computed voting power of one registered voter in that state. The lines should be arranged in descending order by voting power -- that is, the first line of the file should be the entry for the state in which an individual voter has the greatest voting power, and that last line the entry for the state in which the individual voter has the least voting power. The voting-power statistics should be normalized as multiples of the least. (So, for instance, the voting-power statistic on the last line should be exactly 1, and on all the other lines it should be greater than or equal to 1.)
The question of whether the Electoral College system is biased in favor of small or large states can then be resolved by seeing whether small or large states appear at the top of this list.
This exercise is due on Friday, April 28. Please submit your source code
and a copy of the voting-power.dat file that your program
generates.
This document is available on the World Wide Web as
http://www.cs.grinnell.edu/~stone/exercise-4.xhtml
created April 20, 2000
last revised April 20, 2000