I have taken classes related to statistics in college. I view this idea of using a small sample size and having it be an accurate representation as a theory. It can never be prov-en, because you do not know what those who were not asked would say. The larger the sample size, the more likely you will get an accurate representation of prevailing opinion. 10% of the population is the standard benchmark. I just don't believe that the opinion of 100 or even 1000 people can accurately represent the opinion of 290,000,000 Americans.
Of course, it isn't feasible to poll 290,000,000 Americans, or even 29,000,000. Therefore, I take all poll results with a grain of salt. They may or may not be accurate.
You still haven't explained where the 10% figure came from -- except to say somebody once told you that. Until you can give a coherent explanation for why 10% is necessary (and no, 'it just makes sense' is not sufficient), I'm going to dismiss the claim with a grain of salt.
I view this idea of using a small sample size and having it be an accurate representation as a theory. It can never be prov-en, because you do not know what those who were not asked would say.
On the contrary, it can be proven by simple laws of probability. The question comes down to how certain you want to be. If you want to be 95% certain the answer falls in the margin of error (which is the standard), you're still allowing that one in twenty polls falls outside the margin of error. Moreover, large margins of error make polls meaningless, because they indicate trends that may not be happening.