Bsphil wrote:
How can you know there isn't a 5/5 split but yet not know how it may result any other way? How does that relate to the topic of public opinion polling?
Just hold your horses.. I'm getting there.
It's the condition of the example.
Bsphil wrote:
To answer your other question, 5. If you meant to say "what's the maximum number of draws you'd need to determine which is the majority", that answer would be 9.
I had more questions, but since you've been so cooperative, I'll just get to the point from here. The reason why the scenario couldn't be a "5/5" split, because I think it's safe to say that with the tens of millions of possible people to poll, it is very unlikely that it would be a dead tie. It will favor one way or the other even if by only a few hundred people.
If 8 out of 10 of your marbles are blue, then the probability without replacements of choosing a blue marble is greater than choosing a red marble. That means, the likelihood of you picking up 5 blue marbles (one by one or all at once) before picking a red marble is significant.
On the other hand, if you only have 6 blue marbles and 4 red marbles then the above probability decreases. The likelihood of you picking up 5 blue marbles (one by one or all at once) before picking a red marble is much less. In this scenario, you might end up having to get 9 marbles before determining which one is greater.
In the first scenario, the percentages were so heavy in one way, that only a small percentage of the marbles was necessary to show which one was greater. This correlates to my example on a poll of "Do you support rape?". That answer is probably so heavy in one direction, that the absolute least amount of people necessary to conduct a poll is probably more than enough to determine how the majority of the people feels about rape.
In the other scenario, the percentages of marbles were closer together. Because of this, the probability of determining the majority in the absolute least amount of marbles (50% of the marbles) decreased. So, while it was still statistically possible, only a 90% sample absolutely guaranteed you a majority. While it may not be 90%, the likelihood of it being anywhere from 60-80% is higher than 50% as in the above example. This correlates to my argument that the closer the percentages are, the larger the sample needs to be in order to guarantee a determination of the majority.
So, while 1,000 people might statistically be the absolute least amount of people necessary to conduct a poll to represent the nation, the more divided the percentages are, the least likely you are able to demonstrate the majority with the absolute least amount to poll.
P.S. I read over the "WLLN" and I didn't see any contradiction. It actually appears to me that you really don't grasp the concept of WLLN and you're just throwing it around as fictional support to seem more intellectual on the topic than what you really are.