Timeline for Why should/does(?) statistical sampling work for politics (e.g. Gallup)?
Current License: CC BY-SA 3.0
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| Nov 7, 2016 at 18:19 | comment | added | hmakholm left over Monica | I am 100% confident that candidate Awesome's support is not exactly 52.0932840985028390984308%. The smallest electorate in which any integral number of voters round to that percentage would have 1,575,117,129,781 voters (of which 820,530,241,301 support Awesome). | |
| Nov 7, 2016 at 7:22 | history | edited | Alecto | CC BY-SA 3.0 |
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| Nov 7, 2016 at 6:00 | comment | added | user541686 | Wait, but if you take the random variable to be the person selected, then its expected value will be the average person... which is what you'd now be computing, but not what you are trying to compute. You're trying to find the average vote, not the average person. And the vote of the average person isn't necessarily the average vote of all the people (E(f(x)) != f(E(x)) and all that business). (Ok, I'll continue in chat) | |
| Nov 7, 2016 at 5:59 | comment | added | Alecto | Let us continue this discussion in chat. | |
| Nov 7, 2016 at 5:59 | comment | added | user541686 | "But If I took a random poll of people in America, wouldn't you agree that I could judge the top favorite ice-cream flavours in America?" No, actually; I would have the same problem with that example as here. | |
| Nov 7, 2016 at 5:58 | comment | added | Alecto | The "random variable" is which person is selected by the pollster to be asked their preference. The preference of an individual is not random; which individual the pollster selects is random. | |
| Nov 7, 2016 at 5:57 | comment | added | Alecto | Lets look at something other than politics with people. Someone's favorite flavour of ice cream depends on just as many things as their political views. It could depend on the preferences of their friends, fond memories of their childhood, good or bad experiences at the ice-cream parlour. Perhaps they like one flavour because they got it on their first date with their wife or husband. Perhaps they dislike a flavour because it reminds them of their ex. But If I took a random poll of people in America, wouldn't you agree that I could judge the top favorite ice-cream flavours in America? | |
| Nov 7, 2016 at 5:56 | comment | added | user541686 | Are you not treating each individual vote as a random variable here? If not, what are you treating as each random variable for your law of large numbers? | |
| Nov 7, 2016 at 5:52 | comment | added | Alecto | Distributions aren't applied to individual votes. Individual votes aren't random. They're applied to the voting behavior of the population as a whole. It's like drawing colored balls from an urn - each ball is predetermined to be red or blue, but you can have a probability of drawing each color and so you can construct a distribution for the likelihood of drawing a certain color of ball based on a sample of the balls in the urn | |
| Nov 7, 2016 at 5:48 | comment | added | user541686 | Also, I'm not even sure the law of large numbers justifies the thing you were trying to justify even if its assumptions are satisfied. The question is about sample sizes which the law of large numbers doesn't really address (at least not in the fashion you suggested); we need some notion of the variance or convergence rate here, not just the convergence of the mean at infinity. Maybe you meant to invoke the central limit theorem rather than the law of large numbers? (Though please see my previous comment since this is probably moot.) | |
| Nov 7, 2016 at 5:43 | comment | added | user541686 | I appreciate the response, but it's a little bit elementary relative to the question I was trying to ask and my background (not sure if you noticed, but I'm not exactly new to the basics of probability/stats); I don't think the answer to my question here is as basic as yours. For example: an assumption for the classic law of large numbers is that we have random variables with identical distributions... but I fail to see a justification for it in a political context: why should the distribution you put on my vote and yours be the same at all? | |
| Nov 7, 2016 at 5:11 | review | First posts | |||
| Nov 7, 2016 at 7:45 | |||||
| Nov 7, 2016 at 5:11 | history | answered | Alecto | CC BY-SA 3.0 |