The margin of error simply tells you from a statistical point of view what the sampling error of a theoretically representative subgroup being applied to larger group. That is not a belief system that is math and that is why it is called the law of averages and not the theory of averages. If you flip a coin a million times and the coin is perfectly balanced you will get very very close to 50% heads and 50% tails. That isn’t a theory it is a well understand and well proven mathematical theorem.


When you average multiple polls you increase the overall sample thus deceasing the statistical noise inherent in applying the results of sub set to larger group. The problem is that model is only theoretically representative of the larger group and the low margin of error is dependent on the accuracy of that model. Pollsters have a model of what they believe that larger group to look like and they weight their results to makes them match the model. Mostly they use previous election turnouts as a reference for those models. The problem is which election to use and how to tweak them to get a sample the pollster believes to be correct. Those model errors are not factored into the margin of error though because they are not noise and sample size isn't a factor.

For most of my adult life I have taken measurements for a living and I very familiar with noise in a measurement causing errors. The way to overcome that is to increase your sample and then average. It works and I have seen it work more than enough times to know it is not a belief system. Systematic errors on the other hand cause repeating errors in the measurement and no amount of sampling or averaging will correct for that. If your voltmeter reads 2% high then the average of all your measurements will be 2% off and more sampling will only get you closer to that 2% error. If a pollster were to sample 30 million people, 10% of the country, he would publish an error rate of virtually zero but that doesn’t mean his true error will be virtually zero since that error rate doesn’t take into account the errors in his model not to mention the errors created by the question order or wording. That is why two polls can differ by more than their combined margin of error.

You are putting way to much faith and weight into the idea of published margin of error and what it does or doesn’t tell us. Even with the margin of error and modeling errors we can get a good idea of the trajectory of a race and the impact of an event on the race. If next week the average of the polls show that Romney is doing 3 points better than he was doing this week then that is very strong evidence that the race has moved by about 3 points in his direction regardless of the margin of error or even the model errors, assuming they don’t tweak the models. How close those polls will end up being to the actual results is another story and much more dependent on modeling error than on the published margin of error. Many of the polls out there are being based on the 2008 exit poll numbers but that was a very unusual election and the inaccuracy of the exit polls tell us they were poorly done to begin with. Since both of those things tend to favor a model that favors Obama I predict he will underperform the polls, like he did in 2008. Now that is a belief and not a scientifically proven fact, likely to be right but still unproven.