Lets imagine a population within a large rectangle. As it turns out most people live within a small circle toward the lower left edge of the rectangle. If one distributes the samples geographically (evenly over the rectangle) then one does not get an accurate sampling of the majority population's opinions.
This is a bogus issue. The researchers are sampling the
population, not the geography. To the extent that they use geographic methods, they have to take into account local population densities so that there will be a random selection from the population.
How does one get an adequately random sample for a heterogenous population distributed unevenly across an area?
This is a known and well studied problem. There is published research in the area. Here is a link to a
professional organization in the discipline. It is sensitive to social trends - a sampling method that works today might not work next year.
I am suggesting that with such vast numbers over such vast terrain, which allows for many "clumps", 2000 is going to be too small for an adequate sampling such that one can get good representational results.
If the sampling is done reasonably well, then 2,000 is sufficient. If it is done poorly, a larger sample size won't solve the problems of poor sampling.
I feel my gut instinct on this is backed up by failures of polling.
Overall, the experience pubic opinion survey organizations to rather well. Amateurs are more prone to poor experimental design.
Poor sampling is only one of the problems. The wording of the questions asked can be important. Poorly chosen wording can result in misunderstood questions or can stimulate emotional responses. This is a harder problem than the sampling problem. Using a larger sample size does nothing to avoid this problem. Incidently, a survey about attitudes toward atheism may be particularly sensitive to problems associated with how the questions are worded.
This would suggest that voting is a less efficient and accurate way to pick representatives, than simply polling 2000 people.
Elections are not public opinion surveys. In an election, you are expecting the voters to make some sort of committment to support the legislature that they elect.
It also suggests that the national census would be less accurate than polling.
I think there is some evidence to support this. However, the national census does provide basic data that can be used in polling - local population densities, for example.
Kinsey's research did not try to get a bare minimum sampling, but as much sampling as could be gotten.
Polling works best when you have clear issues. That is, you know what you are looking for and just need the opinion data. As far as I know, Kinsey and associates were looking for more basic data, such as would be required before you could even design a statistical experiment.