Sunday, September 12, 2004

Paradoxes in the proposed Colorado Amendment 36

The scheme on Colorado's November 2 ballot to amend the state constitution to do away with the winner-take-all awarding of the state's electoral votes in favor of a proportional system tries to do something that is arguably laudible, but unfortunately it turns out that there is no "fair" scheme to do this. Much like the subtle mathematical problem of the decennial apportionment of the House of Representatives (see either a brief history or for a more detailed history, the book Fair Representation by Balinski and Young) this seemingly simple task of splitting 9 things based on a proportion in a fair manner can be quite tricky.

The Colorado scheme proposed by Make Your Vote Count works like this. Take the percentage of the state's popular vote received by each candidate, multiply it by the number of electoral votes, and then round to the nearest integer. This makes sense, but this does not guarantee that the number of electoral votes will sum to the number that the state has, which for Colorado is 9. If the sum is more than 9, then electoral votes are subtracted from the candidate getting the fewest popular votes but still receiving an electoral vote. If the total is less than 9, then the candidate receiving the most electoral votes gets the unawarded electoral vote. This seems reasonable.

Suppose in the November election results look like this:





Candidate
Popular Vote %Electoral Vote (Not Rounded)Electoral Vote (Rounded)
George Bush 48%4.324
John Kerry 46% 4.144
Ralph Nader 6% 0.541


However, does the following seem fair? Consider what happens if Colorada actually had 10 electoral votes. For the same popular vote it would look like this:






Candidate
Popular Vote %Electoral Vote (Not Rounded)Electoral Vote (Rounded)
George Bush 48%4.85
John Kerry 46% 4.65
Ralph Nader 6% 0.61


But this totals to 11 eleven electoral votes, and so Nader, the candidate receiving the fewest popular votes, loses his. Thus giving Colorado one more electoral vote to award takes away an electoral vote for Nader to award one more to both Bush and Kerry!

Now consider a second example. Return to 9 electoral votes but modify the popular results taking votes from Kerry and giving them Bush to give this:




Candidate
Popular Vote %Electoral Vote (Not Rounded)Electoral Vote (Rounded)
George Bush 50%4.505
John Kerry 44% 3.964
Ralph Nader 6% 0.541


Again there are more than the alloted electoral votes and Nader's is taken away. Therefore Nader's getting an electoral vote is not only a function of how many people vote for him, but it also depends upon the margin of victory of the first place finisher over the second place finisher! That does not seem fair at all.

I have no idea whether this Amendment will pass, and then whether it can constitutionally be applied to this year's election, which will of course be over before we know whether or not this will pass. But we could get into another mess in the courts. And it will certainly make it more difficult for the networks to call the results with only a mere 99% of precincts reporting in. It's possible for Nader to have an electoral vote based on the 99% report, but lose it with the results of that last precinct, despite increasing his total percentage of the popular vote.


Saturday, September 11, 2004

Atlas of US Presidential Elections

Want a color-coded map of how each county voted in the presidential election of 1960? Or how about a congressional district map reflecting the 2004 Oklahoma Democratic presidential primary? Then you need to check out Dave Leip's Atlas of U.S. Presidential Elections. I think it's fascinating. His blog is interesting too. He has maps of various possible scenarios for the 2004 election that result in a 269-269 tie in the Electoral College.

His blog also made me aware of the Colorado referendum on Novermber 2 to amend the state constitution to do away with the winner-take-all system of awarding electoral votes in favor of a preportional system. Click here for the Amendment. It's an interesting idea which I'll spend the rest of the night crunching numbers on.