"Typical applications of the law also generally assume no bias in the underlying probability distribution, which is frequently at odds with the empirical evidence"

I think I covered that very extensively and made it crystal clear that I was differentiating between true random errors (noise) and and underlying bias in the distribution, that was the part about models errors. If you don't like to use the lay term and prefer to use LNN that is fine but it really does nothing to undermine my previous argument. If the sample is larger, which it is in when you average more polls, then the margin of error will be reduced and the published margin of error of the individual polls are no longer valid since in effect you have a new poll with a larger sample. Errors in polls that are not the result of sample size will not be averaged out by multiple polls, which is where the bias in the underlying probability distribution part comes into play. If your model over weights or middle aged men living in their mom's basement no amount of sampling will overcome that but it also isn't reflect in the published margin of error and since it will be reflected in all of your polls so it won't affect your trends.

Using your example if one poll that gives you 48 to 52 and then you conduct that poll over and over multiple time and get and average answer of 50 to 50 then the true answer is much more likely to be 50-50 and the margin of errors for those combined polls will be lower than 4 points of the original poll. If your polls model is improperly weighted and gives one candidate an unearned 2 point advantage then your averages will end up closer to 48-52 and that will have nothing to do with your margin of error.

The margin of error is only where the results will be the majority of the time. If you have a poll with a margin of error of 4 it is completely within the realm of possibility that actual sample error is 15 but it is just very unlikely. It is representing a bell curve so while the margin may be 4 points statistically there is more likelihood that the error will be 1 point and the more polls you have the more polls you will have that are closer to the true number.

It is true that polls are only so useful and they have errors, some more significant than the sample errors, that make them of limited value. Just changing the time of day that you poll will change the results since different people will be available and give you different results. But they are still the best tool we have for judging the state of a race and they do show trends in support of the candidates. You can see trends show up in multiple polls as the result of real events in the campaign and if you average multiple polls you can see the trends in finer detail than any in any of the published margin of error of the polls.


This really is pretty straight forward stuff and sampling is a well understood science.