24 July 2008

The 2000 election, eight years later

Outcomes of presidential elections and the house size, by Michael Neubauer and Joel Zeitlin. (It's in a journal, at PS: Political Science and Politics, Vol. 36, No. 4 (Oct., 2003), pp. 721-725 -- but that's not where I found it, and that's not where the link goes.) The link comes from thirty-thousand.org, a site which claims that congressional districts were never intended to be as large as they are; they advocate one per fifty thousand people, which is six thousand representatives. (Thirty thousand is approximately the original number of people per representative.)

The authors look at the 2000 U. S. presidential election and concluded that given the way in which seats in the House of Representatives are awarded, if the House had 490 members or less the election would have gone to Bush; with 656 or more, it would have gone to Gore; in between it goes back and forth with no obvious pattern, and some ties. The ties come at odd numbers of House members, which surprised me. But the size of the Electoral College is the number of House members, plus the number of Senators (always even, since there are two per state), plus three electoral votes for DC. So an odd number of House members means an even number of electoral votes, as in the current situation where there are 435 in the House and 538 electoral votes.

In case you're wondering why a small House favors Bush and a large house favors Gore, it's because the states that Gore won made up a larger portion of the population, but Bush won more states. In the large-House limit, the number of electoral votes that each state gets is proportional to the population, since the two votes "corresponding to" Senators are essentially negligible. In the small-House limit, each state has 3 electoral votes (I'm assuming that each state has to be represented) and so counting electoral votes amounts to counting states.

The states that Bush won had a total population in the 1990 Census (the relevant one for the 2000 election) of 120,614,084; the states that Gore won, 129,015,599. So 51.68% of the population was in states won by Gore, 48.32% in states won by Bush. Bush won 30 states, Gore 21. (I'm counting DC as a state, which seems reasonable, although the 23rd Amendment says that DC can't have more electors than the least populous state, even though it does have more people than the least populous state.)

So if there are N House members, we expect Bush to win 60 + .4832N electoral votes; the 60 votes are two for each state, the .4832N his proportion of the House. Similarly, Gore expects to win 42 + .5168N electoral votes. (The three are for DC; I'm assuming that DC would always get three electoral votes in this analysis, which isn't quite true. So Bush wins by 18 - .0336N electoral votes, which is positive if N is less than 535. The deviations between this and the truth basically amount to some unpredictable "rounding error".

If you look at the difference between the number of Bush votes and the number of Gore votes, you do see roughly a linear trend. To me it looks like a random walk superimposed on linear motion. This isn't surprising. As we move from N seats to N+1 seats in the House, 51.68% of the time the next seat should go to a Gore state; 48.32% of the time, to a Bush state. (The method that's used allots the seats "in order", i. e. raising N by 1 always adds a seat to a single state. Not all apportionment methods have this property; this is the Alabama paradox.) So the difference between the number of seats in Bush states and in Gore states will fluctuate, but the overall trend is clear. Of course the noise isn't actually random, coming as it does directly from the populations of the states, but the dependence on the state populations is so complicated that we might as well think of it as random.

I believe that something similar would happen with any set of election results in which more states voted for candidate A, but the states that voted for candidate B collectively had greater population. (Note that the latter criterion is not the same as candidate B winning the popular vote.)

Incidentally, I remember hearing in 2000 that if the House had had only a few more seats than it did, or even a few less seats, Gore would have won -- the implication being that N = 435 was a particularly fortuitous choice for the Republicans. This isn't true. But it's also possible that my memory is false.


J. E. Quidam said...

Our total number of Representatives to the U.S. House has been limited to 435 ever since 1913 (except for a four-year period when it was temporarily increased to 437). In 1929, this number (435) was made permanent by an act of Congress. During the debates preceding that act, Missouri Representative Ralph Lozier stated:
"I am unalterably opposed to limiting the membership of the House to the arbitrary number of 435. Why 435? Why not 400? Why not 300? Why not 250, 450, 535, or 600? Why is this number 435 sacred? What merit is there in having a membership of 435 that we would not have if the membership were 335 or 535? There is no sanctity in the number 435 ... There is absolutely no reason, philosophy, or common sense in arbitrarily fixing the membership of the House at 435 or at any other number."

The challenge posed by Representative Lozier in 1928 is still valid: is 435 a sacrosanct number or should it be subject to debate?

Please read the 15 Questions & Answers on the home page at:

Related to this subject, read about the now forgotten first amendment inscribed on our Bill of Rights:

Thirty-Thousand.org is a non-partisan and non-profit 501(c)(3) organization.

CarlBrannen said...

My feeling on the size of the House and Senate is exactly the opposite of the "30,000" group.

When the size of the deliberating body becomes too large, it becomes too political and it becomes impossible for it to find decent compromises. I would prefer that they cut the Senate down to 50 senators, and the house to around 100.

J. E. Quidam said...

Isabel, there is an important point to add to your observation, which was: "Of course the noise isn't actually random, coming as it does directly from the populations of the states, but the dependence on the state populations is so complicated that we might as well think of it as random."

There is something else happening that is little understood: because of the small number of congressional districts (435 relative to a population of 300,000,000) the districts are not equally sized nationwide (even though they are equally sized within each state). As a result, some districts are 25% to 80% larger than others (in violation of "one person one vote").

As an extension of that, various states are either over- or under-represented in the federal House relative to their populations. For example, Oregon's share of federal representation is 94.35% of their share of the states' total population (as a result of the 2000 apportionment).

Consequently, as the number of districts is increased, these discrepancies diminish and the electoral college vote approaches the popular vote asymptotically.

For anyone who is interested in learning more, I'm working on a paper which explains all this.

Michael Lugo said...

In response to your last comment, there seems to be another solution that doesn't require enlarging the House. Why not have Representatives be elected from districts that aren't entirely in one state?

Anonymous said...

Another, similarly directed possibility: do as Nebraska and Maine do, and elect 2 presidential electors at-large from that state, and 1 each directly from each congressional district.

Strange, that seems more direct, yet I have a funny feeling that it would not have moved the election (as so much of the Democratic vote is concentrated in lopsided urban districts).

But "why 435?" is a great question. Why have states at all may be a better one.


J. E. Quidam said...

Isabel, it would require a Constitutional amendment to create ├╝ber federal districts that cross state lines and, I can assure you, such an amendment would never be ratified in this country. The biggest opposition would come from the low-population states who would not want their federal representation subsumed into larger regions. If such districts were established, I believe that the smallest states (if not all states) would effectively cease to exist as sovereignties and the mega extra-state federal districts would eventually evolve into pseudo-sovereign entities. Consequently, myself, and many Americans, would oppose such a development using every possible means at our disposal, which is why such an amendment would never see the light of day.

In any case, it is generally becoming recognized that the number of congressional districts will have to be significantly increased in order to ensure the existence of Majority-Minority Districts (i.e., districts where the majority of residents are members of an ethnic minority). That is simply a mathematical urgency.

The fundamental objective of making the districts smaller (and increasing their number) is to take political power away from powerful special interests and return it to the citizenry. With respect to that objective, bloated equally-sized federal districts would accomplish nothing.

Most questions people have about this subject are answered in the 15 Questions and Answers on TTO's home page.

J. E. Quidam said...

Jonathan, you are correct. The states should eliminate the winner-take-all convention with respect to the Electoral College votes (and award the 2 "senator" electors to the winner of the state-wide vote). Maine and Nebraska are already doing that. That is a state-by-state decision (absent a Constitutional amendment to the contrary).