## 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 [typo fixed] with a 9-point margin.)

1. Alex F says:

You might want to fix the last sentence.

2. Ken Houghton says:

So outside of his home state, Obama's massive popularity amounts to a 61,000 vote difference?

And Elia excluded Florida, where both candidates were on the ballot.

3. Jonathan says:

To put it another way, if you don't count his 429,000 vote margin in Cook County, you shouldn't count her 300,000 vote in New York.

4. sky says:

The habit of using percentages in journalism seems be related to decimal values being scary and 'scientific.' So, whenever it's a multiplier, we mostly see it as a percentage.

I don't think you can blame the rampant innumeracy on percentages–the world would be a better place if they stated their data in equations. Instead, journalists have forced the world back a few thousands of years.

5. You can't cherry-pick data like that. Let's see how Clinton's popular vote breakdown looks to us if we cherry-pick them:

Arkansas: Clinton wins by 44% margin and ~136,000 votes.

New York: Clinton wins by 17% margin and ~305,000 votes.

Hawaii: Obama wins by 52% margin and ~20,000 votes.

Illinois: Obama wins by 32% margin and ~639,000 votes.

Let's sum it up: