"The law of averages is a lay term used to express a belief that outcomes of a random event will "even out" within a small sample."

"In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times."

Your analogy of the voltmeter readings to people being polled doesn't fit. With the voltmeter reading, there should be one answer, what the system is supposed to output at the point of measurement. Let's call it twelve volts. You're absolutely right that we will take a million measurements and by averaging them we will have a better idea of what the voltage is at the spot being measured and it will be closer to the expected value the more measurements we take. The problem with comparing this to people being polled is that there is not a right or expected answer. Obama is not the expected value and Romney the error or the other way around.

What the margin of error tells us is that if the same poll were run again with a different subset of the population then the results could vary by plus or minus the margin of error for each candidate. For example, if we run a poll, Candidate A gets 48 and Candidate B gets 52 and our margin of error is 4 it is very possible that if we conducted the poll again with a different subset of the population that our results could end up 50/50.

This is why when the difference between the two is within the margin of error, the result of one doing better than the other is insignificant.

As far as taking the results of multiple polls as indication that one candidate is doing better than the other despite the margin of error showing that the result is insignificant, this is where you and Joel are mistaking the law of averages for the law of large numbers.

In this case, the number of polls considered is a small data set.