How does sampling reduce selection bias?

#1
Hi everyone,
I'm struggling to understand theoretically how sampling reduces selection bias. Take the following example:

Supposing there is a population of 1000 people, and 200 of them have an axe to grind (for some reason). These 200 will respond to 100% of surveys. The remaining 800 are neutral and will respond to 50% of surveys. If you survey the whole population (all 1000), you'll have 200 axe grinders and 400 of neutral people. Now supposing you want to reduce selection bias by randomly sampling 500 from the population. 100 will be axe grinders and 400 will be neutral, and after you survey them (assuming the response rates from before) you will have 100 axe grinders and 200 neutral people. This is the same proportion of axe grinders to neutral people as before, which leads me to believe that random sampling does not reduce selection bias. However, I've heard (and believe) that it does.

Can someone help me to understand this theoretically?

Thanks!

PD
 

noetsi

No cake for spunky
#2
Why do you think that sampling reduces systematic error (that is bias) that exists in the population? I have never heard this suggested as a use for sampling. In fact the reverse is commonly seen as likely. People will respond to surveys because they have a bias (more so than people who don't have a bias) so you sample ends up with a more biased view then the regular population.

That is a frequent concern in polling.