The arithmetic of news

A reader has trouble reconciling the numbers reported in various news stories. "Something," the reader says, "doesn't add up." The problem, I think,  could be in the data sources and the news stories themselves.

It has always bugged me that the Obama campaign reported raising enormous, unprecedented sums of money from small donors. According this study, Obama's campaign reports that about 3 million people gave to his campaign, and about 2.5 million gave less than $200. This number sounds about right (I have a better estimate below) given than he raised about $335 million from under-$200s according to the FEC, meaning the average donation was $134. That sounds plausible.

However, I read on an Instapundit link to this story that he sent out emails to 13 million people asking them to sign a pledge in support of his budget, and got back 114,000 pledges.

Now, based upon FEC data, John McCain probably had about 650,000 individual donors, while Obama probably had about 2,850,000 - a difference of 2.2 million donors. But 2 million of that difference was in the under-$200s, or about 90% of the difference. And a huge number of these small donors gave through the internet, so they're presumable savvy enough to fill out an e-commerce form.

So here's the rub. My gut tells me that there is no way Obama had this many legitimate small donors. I can't quantify this - no one can since Obama has not released any data on the under-$200s. But we've been told that there was a huge surge of small donors, motivated for change.

The thing is that, intuitively, it should be harder to get someone to give you money than sign a pledge form. And, presumably, if you gave Obama money, you are motivated to help him. Moreover, you have to assume the 2.85 million donors were included on the 13 million-person list.

Now let's just ignore the other 10.15 million people on the list. If someone donated to Obama's campaign, and they get an email asking them to sign a simple pledge, wouldn't you expect a pretty high response rate? But 114,000 of 2.85 million is 4%. This seems really low. Only 1 out of every 25 donors signed the pledge (and this assumes none of the other 10.15 million signed - the more that did, the higher this ratio goes).

This super-low response from his most ardent fans is consistent with the hypothesis that Obama didn't really have that many small donors, but rather was taking in large amounts of money from phantom donors through the "hole" in his credit card processing form. If these people really existed, you'd expect more response from them on the budget pledge. But the scanty response raises serious red flags on how much of his money was legit.

Essentially the problem is this: why could Obama persuade nearly 3 million people to send him campaign contributions yet be unable to convince any more than 114,000 to send him back a pledge?  The reader says this means he got only one out of 25 donors to signify support for the budget.  (The 1:25 is the ratio between 114,000:2,850,000.) The reader argues that the two statistics are unlikely to come from the same sample and conjectures that Obama really didn't have that many small supporters,  just more big supporters who sailed through some kind of loophole.

The reader may be right, but there's a second possibility, one I will call the "Japanese Marine's Watch" problem.  When I was a child, many of the older people told me how during the Battle of Manila, the Imperial Japanese Marines went on an orgy of looting and roamed the battlefield with half a dozen watches strapped to each arm. Watches were then very valuable objects and prized for loot. But they had to be wound up in those days and were much more fragile than the waterproof, shockproof, no moving parts timepieces that we know today. In consequence the average Imperial Japanese Marine finished up with 10 or more watches all displaying different times, some being wound and others running down; some running slow and others running fast.  It was then very common to say, "if you have too many watches, like a Japanese Marine, then you won't know the time".

The analogous problem here is which of the numbers reported by the newspapers to believe. Which watch is telling the correct time? The alternative hypothesis to asserting that the number of Obama campaign contributors is inflated is that the newspapers simply reported wildly inaccurate or incomparable numbers.  Perhaps most of the mailers to 13 million people wound up in the junk mail bin whereas during the elections they more motivated to act and more efficiently harvested by a superior outreach system.  So we really are looking at two different yields on an identical physical base whose virtual size differs because of differences in marketing techniques.  Or maybe the numbers are so fudged we are really pulling numbers out of the air. For comparison consider the Lancet's survey of the civilian casualties in Iraq. According to the prestigious British medical jounral, 654,965 excess deaths were related to the war, or 2.5% of the population, through the end of June 2006. To put that number in perspective, the Lancet had accused the US war effort of killing about three times as many as the combined deaths at Hiroshima and Nagasaki in 1945 between the years 2003 and 2006. You would think it would be possible to find more than a half a million extra dead.  But controversy dogged it from the beginning. The study has become something of an embarassment to the journal. Wikipedia writes:

The Lancet surveys are controversial due to their methodology and because their mortality figures are higher than other reports that used different methodologies, including those of the Iraq Body Count project, the Iraqi Health Ministry and the United Nations, as well as other household surveys such as the Iraq Living Conditions Survey and the Iraq Family Health Survey. On the other hand the ORB survey of Iraq War casualties estimated more deaths than the Lancet survey. Out of all the Iraqi casualty surveys so far, only the Lancet surveys and the Iraq Family Health Survey were peer-reviewed. The Lancet surveys have triggered criticism and disbelief from some journalists, governments, the Iraq Body Count project, some epidemiologists and statisticians and others, but have also been supported by some journalists, governments, epidemiologists and statisticians.

In particular the Lancet survey attributed a whopping 13% of deaths to air strikes -- nearly the number of dead in Hiroshima. At the time I wondered how those huge numbers could be reconciled with the very low tonnage of bombs dropped in the theater and the absence -- you can crank up Google Earth -- of craters. Where are the craters? I asked myself. In some sense the reader is asking himself the same question: if Obama had nearly three million supporters, how come he can't get more than 118,000 to sign his pledge? It's one of those questions that turns out to have no good answers when you try to reconcile one set of figures to another. How many "small supporters" did Barack Obama really have or were they inflated? I don't know and I doubt the numbers will ever add up any better than the time told by the watches of the dead.  Maybe it really is better to pick one book of fiction and believe it.