Okay so you understand why the covariance is important. Have some fun and read this article. It’s a sobering lesson,
Recipe for Disaster: The Formula That Killed Wall Street
http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all
The problem with applying the central limit theorem is that even if the covariance is zero (in which case the CLT can still apply), you don’t have an estimate of the variation, only the mean. The sampling error that the pollsters report is an estimate of the uncertainty of the mean. It is not an estimate of the variation.
Note that there are TWO kinds of statements that the pollsters make. One is an estimate of how individual races will go. The second is the total number of seats that will turn over. Each estimate requires TWO different models with different, proprietary, assumptions. You are mixing apples and oranges.
What the pollsters are telling us is, if the election were held today this would be the result, with a range of error around each candidate's result. If the result that they publish is really a mean of repeated sampling, with some error of the location of the mean represented by the margin of error, so be it. All I care about is that this is the expert's prediction of the result if the election were held today. I take their predictions, and use the margin of error around that prediction to create a probability of the leader actually winning. That is all.
I don't think I'm mixing apples and oranges.
-PJ