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I think your analysis is mathematically flawed. Trouble with independent events and all that. For instance, "YES" and "NO" are not independent. The stated margin of error (MOE) in a poll is purely the 95-percentile sampling error. It is only a statement of the uncertainty attributable to a finite sample size.

The bigger problem with polls is systematic error. People who take time to talk to pollsters (I'm not one of them) are not representative of the population. An honest poll works to suppress systematic error, there are so-called "push polls" designed to produce a certain result where every attempt is made to build in systemic error.

To illustrate MOE: If there are one million red balls and one million black balls and you draw 1000 balls "at random" the 95-percentile sampling error is about 31. This means 95% of the time you draw between 468-532 red (or black) balls, even though the though the "expected" number is 500. Given that you drew 47% red balls (with a MOE of 3.1%) you would also report 532 black balls with the same MOE. The two events are not independent.

An honest poll works to suppress systematic error, there are so-called "push polls" designed to produce a certain result where every attempt is made to build in systemic error.

But what is a push poll anyway?

Fundamentally, what people label a push poll isn't a poll at all. A push poll is political telemarketing masquerading as a poll. No one is really collecting information. No one will analyze the data. You can tell a push poll because it is very short, even too short. (It has to be very short to reach tens of thousands of potential voters, one by one). It will not include any demographic questions. The "interviewer" will sometimes ask to speak to a specific voter by name. And, of course, a push poll will contain negative information - sometimes truthful, sometimes not - about the opponent.

http://www.cbsnews.com/stories/2000/02/14/politics/main160398.shtml

MOE's are given as PLUS or MINUS a percentage. So that I don't have to repeat myself, please be kind enough to see my posts #31 and #33 on this thread. Now, I don't claim to be a whizbang mathemetician. I try to reduce things down to a place where I can understand it, and assume that if I understand it, most others will, too.

If someone tells me they offer, say, a 45% prediction of something occuring, plus or minus 3%, that tells me they give themselves a range of seven percentage points within which they can claim to be right. Given an objective actual against which to compare the prediction, I can then see whether or not it was accurate. Very simple. Very clear. Very straightforward. The numbers speak for themselves.