Incredible Illinois

[Little Star]

Incredible Illinois, or fun with percentages that can be larger than 100
Tyler Cowen links to a calculation by Tom Elia that "of Sen. Obama's 711,000 popular-vote lead, 650,000 -- or more than 90% of the total margin -- comes from Sen. Obama's home state of Illinois, with 429,000 of that lead coming from his home base of Cook County." This is interesting, but it's more a comment on how close the (meaningless) total popular vote count is, than a reflection of something funny going on in Cook County.

Put it another way. Suppose Obama's total margin was only 111,000 votes instead of 711,000. Then his 650,000 vote margin in Illinois would represent a whoppin 580% of the total margin, and Cook County would represent 390% of the total margin! But wait, how can a part be 390% of the whole??

What I'm sayin is, the "90%" and "60%" figures are misleading because, when written as "a percent of the total margin," it's natural to quickly envision them as percentages that are bounded by 100%. There is a total margin of victory that the individual state margins sum to, but some margins are positive and some are negative. If the total happens to be near zero, then the individual pieces can appear to be large fractions of the total, even possibly over 100%.

I'm not saying that Tom Elia made any mistakes, just that, in general, ratios can be tricky when the denominator is the sum of positive and negative parts. In this particular case, the margins were large but not quite over 100%, which somehow gives the comparison more punch than it deserves, I think.

P.S. Elia's comment that "Sen. Obama's 429,000-vote margin in Cook County alone is larger than the winning margin of either candidate in any state" is more directly interpretable because it's a difference, not a ratio. Obama won Illinois by a 32-percentage-point landslide. (By comparison, Clinton won New York with a 17-point margin and California with a 9-point margin.)

http://www.stat.columbia.edu/~cook/movabletype/archives/2008/03/incredible_illi.html

[Joe the Revelator]

1. What would the difference be without NY?

I mean, as long as we're playing pointless games with numbers...

[Hailtothechimp]

4. I doubt Clinton got ZERO votes in any part of Illinois

And yet lots of places in New York City gave Obama a big old bagel.

Nothing fishy about that, is there??

www.nytimes.com/2008/02/16/nyregion/16vote.html?_r=1&ex=1360904400&en=6114699040e9bc82&ei=5088&partner=rssnyt&emc=rss&oref=slogin

[judaspriestess]

2. kick

[AX10]

3. K & R!