Monday, September 06, 2004

The Electoral College

As everyone knows from the 2000 election, the United States does not use a majority rule to choose the president, rather they use a more complicated system known as the Electoral College. With some calls for the abolishment of the Electoral College, let's take a look at the College from a computer science point of view and see the rather clever device our founding fathers have created.

In short the Electoral College works as follows: 538 electors are allocated to states as the sum of the senators (2 for each state) and representatives (proportional to population). In most states, each voter picks a single candidate and the candidate that wins the most votes receives all of the electoral votes for that state. The candidate winning the majority of the electoral votes becomes president. More details here.

In computer science terms (assuming two candidates), we have a weighted majority of majorites or a depth-2 neural net. It has some properties that you would want:
  • Monotonicity: If a candidate wins the election and more people vote for him, he will still win.
  • Fairness: Barring a tie, if all the votes were switched the other candidate would win.
The College does lack symmetry, a permutation of the voters could lead to a different result. Only the simple majority function has symmetry, monotonicity and fairness. But symmetry is not necessary for an election scheme.

The United States is just that, a collection of fifty states each with their own laws, cultures and economies, united under some common principles. A simple majority would have the large populations centers overwhelm the rest of the country in choosing our leader. A majority of majorities would give some states far more power than their size would dictate. So a compromise was formed, a weighted majority of majorities to give small states some but not too much influence. The fact that this process does not always agree with majority is not a bug but a feature that preserves the balance between small and big states, rural and urban America. It also keeps balance between states of the same size, an lopsided vote in California would not overwhelm a closer vote in New York.

Some things I would change in the Electoral College: Electors should be required to vote for the candidate they represent; for each state we should have a ranked voting method instead of plurality takes all; the tie-breaking rules should be changed, now they give too much power to the small states.

The winner of the World Series in baseball is not the team that scores the most runs but the team that wins the most games, a majority of majorities and most people feel it gives a better indication of the better team. Why shouldn't elections deserve a system at least as sophisticated?


  1. >A simple majority would have the large populations centers
    >overwhelm the rest of the country in choosing our leader

    I can be a little na�ve, I am not American, but what about the president deciding to engage in war? Does not it affect all people same way? It's just an example, I think there are several issues distributed over people, not states.

    I'm just trying to understand it, not making critics to you. :)

  2. But is the election really a game? The World Series is won (in theory) by the team that best plays the game of baseball. Is the election then supposed to be won by the candidate who plays the win-a-state game the best? Why not just say the election should be won by the candidate who gets the most votes? Should the election be a game--a challenge in which the players' performances are judged and rewarded, like the Olympics--or an opportunity simply for candidates to be introduced and for voters to declare their preferences?

    I think the real issue is whether the United States are or the United States is. One may argue that different states have different characters or that small states would otherwise be overwhelmed by larger states (although some argue that the electoral college actually favors large states), but does any of this matter? States are constructs created by people, to serve their ends. Aren't people's rights the ones that matter, ultimately, not states'?

  3. But this doesn't at all address the issues of Gerrymandering that seem to have occured. In the more popular states, like New York, California, or Illinois you have a melting pot of so many different ideologies. We call them "blue states" but being "blue" is actually what America really is: A centrist hue of blue that would perfer a Clinton (minus the sex scandals).

    Except for in some big cities like Atlanta the lack of diversity (of thought) in the South is just shameful. I wouldn't want the majority of a population to have the same genetics (one virus could seriously wound such a population), but why do we think it's ok for such a large portion of our voters to have the same ideas?

    Without proportional representation, the two-party system is going to be relatively unchanged no matter what voting system is used: the gerrymandering of the states only brings it closer to the right.

    I think the representational democracy aspect of the EC failed us in 2000. Some of the electors should have "seen" that there was mass error and discrimination in Florida and put their votes to Gore. However, such decisions would have been unpopular to almost half of the voters, so it's clear to see why they can't even use their right to vote intelligently instead of always going with the crowd.

    What I'd like to see help build democracy is to make voting day a national holiday and to have same-day registration.

  4. Lance, another factor is that the small-population states get a minimum of 3 electors each, which increases their power relative to the big-population states. This could give quite an advantage to the Republicans. Partly for that reason, I would *love* to see the Electoral College abolished -- but it will never happen, because it would take a 2/3 majority of the Senate and 3/4 of the states to ratify, once again putting the decision disproportionately in the hands of small-population states.

  5. Is it only me or are many of the comments on the line of "the system has failed because Bush has won"?

    At any rate, I actually quite like the "win-a-state" analogy. Some management aspects do not scale to a country as big as the entire United States, so the intermediate decision level (the local majority) helps in my opinion. I cannot honestly say that I always know what is best for the entire world (apart from "try not to destroy it all at once" generalities), but it is easy for everyone to know what is good for one's own medium-sized state.

    If ever there is a Star-Trek like Federation of Planets, I believe it would need three or four nested decision levels, not just the two that the US now has.

    - Eldar.

  6. > A simple majority would have the large populations
    > centers overwhelm the rest of the country in choosing
    > our leader

    Why is this a bad thing? The "large population centers" aren't the ones doing the overwhelming; it's people versus people. If supporters of Alice overwhelm supporters of Bob on election day, why shouldn't we just declare Alice the winner, rather than trying to take into account the hometowns of said supporters?


  7. Eldar, if the fact that it helps Bush isn't reason enough to dislike the Electoral College system, there's another reason that's right up your alley. A tree of majority functions has greater average sensitivity than a single majority function on the same number of variables. Therefore a "Florida" is much more likely to happen than a comparable disaster with a national vote. (Disclaimer: Political comments are made in my capacity as a private commenter, not a former Guest Blogger. :) )

  8. Scott, you have actually just strengthened my convinction that the EC is a better system for the US. It is true that there is more of Florida in an increased sensitivity situation, but on the other hand, some sensitivity is good: If the US had a simple majority election system, the law of large numbers would have made the outcome very predictable. This is not as good as it seems at first sight, because then the two candidates would have eventually converged on a Nash equillibrium, which I believe would have been one in which their views are virtually identical. In the current situation there is more incentive for a candidate to distinguish oneself - and indeed, in this election it resulted in the voters having a choice between two diverging viewpoints concerning the war in Iraq.

  9. > Except for in some big cities like Atlanta the lack of
    > diversity (of thought) in the South is just shameful. I
    > wouldn't want the majority of a population to have the same
    > genetics (one virus could seriously wound such a population),
    > but why do we think it's ok for such a large portion of our
    > voters to have the same ideas?

    Could you cite some data here? Because it sort of seems like you're making armchair overgeneralizations. I have to say that I found this statement rather offensive.

  10. Here's an interesting article:

    Perhaps even Eldar could see the EC isn't so hot.

  11. I agree largely with Lance's assessment that a weighted majority of majorities is a good compromise between a simple majority and a majority of majorities.

    However, I would like to see at least some proportional representation among the electors for each state. Correct me if I'm wrong, but both ranked and plurality-take-all voting methods select a single winner who controls all electors for a given state.

    Systems of this kind invariably force a two-party race. The only way for a "third" party to exert influence is to win a high concentration of support in a small geographical area, which usually leads to provincialism. Conversely, parties with limited support that is nonetheless consistent across the country remain totally unrepresented in government, even if they actually win more votes nationwide than our hypothetical one-state-wonder provincialist party.

    That said, *pure* proportional representation is not the answer (Italy is a good example of why). But I believe that some hybrid of winner-take-all and proportional representation would be best.

  12. The REAL secret of the 2000 was that Gore won about 22% of counties. He got a plurality by rolling up margins of 75-90% in large urban areas. If the EC were apportioned according to congressional district (similar to Maine & Nebraska) it would be a truer representation of the nation as a whole. In 2000, Bush would have won around 290 electoral votes using that method which demonstrated his national appeal (I did not vote for Bush by the way).

    And I want to thank all those "open minded" folks who blast the South for "thinking alike". Oddly enough, no objections were raised when the segregationist South voted Democrat from 1870 - 1956. Wonder why?

  13. more discussions on voting schemes:

  14. this websight stinks