Being Unbiased When Base Includes Individuals Unwilling to Share Personally Identifiable Information

Lets say we want to perform a survey. It is on a politically sensitive topic. 75% of the people (made that up out of thin air) are willing to share some personally identifiable information (PII) if they know it is anonymized (e.g. no easy way for their feedback to be tracked back to them). But there are 10% who are unwilling to share any PII.

One can survey the 75% and the results may be an adequate approximation of what PII-resistant individuals would have contributed to the survey…or it might not be.

This becomes even more problematic when the individuals who are PII-resistant come from a single minority background – e.g. racial, political, socio-economic, etc.

One could accept anonymous survey responses but then one has no way to guarantee that the surveys actually represent the opinions of unique individuals. Any person could (theoretically) submit many anonymous responses.

So what are best practices currently and are there theories/research which potentially offer better options in the future?

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