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# Mathematical Musings after Iowa

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The Democratic race in the Iowa caucuses the other night (I didn't follow the Republican one as closely) exhibited something that concerned me very much: a textbook example of the way in which the availability of earlier results can influence later ones.

I was at my desk until late that night working on a new short story, and -- in between searches for le mot just -- was logging on to the relevant CNN page pretty frequently all evening. (I'll admit it: The real reason I was going online so frequently was to keep track of the cricket between India and Australia. But I was checking the caucuses at the same time.)

Up until about 40% of the caucus results had been declared, you really could not have laid a sensible bet between Obama, Edwards and Clinton: the three were neck and neck, their "scores" spread over at most 2 percentiles, and they were often exchanging the leadership.

Between about 40% and 50% of the results declared, the situation looked much the same at a glance, but if you were following them even just a little more carefully it was evident that Obama was by now consistently the one who was just slightly in the lead.

Thereafter, very suddenly, Obama's lead began increasing dramatically, and indeed by the end of the tally there was about an 8% gap between him and the other two.

At first this might not seem too extreme a change, but consider it for a moment. To attain that 8% lead overall, during the second half of the evening Obama must have immediately achieved and then maintained for the duration a whopping 15% lead over Edwards and Clinton. That's an astonishing change from a consistently maintained 1% (or so) lead. I'm not enough of a mathematician to calculate the odds against it happened by chance, but it must be millions to one.

I deduced, therefore, that the later-deciding caucuses were hearing the results of the earlier ones. Those later decisions were being skewed by that knowledge in the manner well known to happen in elections if later voters learn what earlier ones have done (which is why most democracies ban the announcement of any results, even exit polls, until the final vote has been cast).

And indeed I discovered corroborative near-proof of that the following morning. According to Alternet's account of the caucuses, at about the same time as 40%-50% of the Democratic caucuses had reported, the networks called the result for Obama, even though at the time his advantage was, as noted above, extremely slender. It's my conclusion that this was the main reason why Obama's win was by such a wide margin.

In other words, yet again the decisions of the media have affected the functioning of this democracy. In a sense, this example isn't too important, because it looked as if Obama was going to win anyway; on the other hand, heading into NH with an 8% Iowa lead is a bit different from heading into the next primary with a 1% Iowa lead, no?

And, if the networks had declared for Edwards or Clinton instead -- as they could perfectly well have done when all three were still separated by at best a hairsbreadth in the extant results -- might we have had a different Democratic winner going into the next round?