Reply #92: You are intuitively asking exactly the right question!

[Sancho]

For one example, two decades ago a well-known statistician described your question (including election polls as one example) in a popular published article that was reproduced in several journals and reports:

"Eelworms, Bullet Holes, and Geraldine Ferraro: Some Problems in Statistically Adjusting for Survey Nonresponse"
Wainer, Howard, 1987
Abstract:
There is no safety in numbers. When data are gathered from a sample in which the selection criteria are unknown, many problems can befall the unwary investigator. This paper explores some of these problems and discuss some solutions. The authors explore methods of covariance adjustment as well as more explicitly model-based adjustment methods. Among the latter, Heckman's Selection Model, Rubin's Mixture Model, and Tukey's Simplified Selection Model are discussed.

The conclusion of the article is simple. All the "weights" and "transformations" will not give a satisfactory result to account for "non-ignorable non-response". The only solution is to use "heroic methods" to get a proper sample.

In this case, the pollsters avoid getting the proper samples and continue to produce non-generalizable results for many questions. Reliance on parametric distributions and corrections (called weighting in the case of exit polls) to estimate error becomes a wild guess when the underlying distributions of the non-respondents are unknown.

Sorry if that seems too technical...