The poll that moved without changing opinions
A survey can be numerically precise about the wrong group of people.
The poll that changes without anyone changing their mind
Consider a fictional town of 10,000 people. Group A comprises 60% of residents and supports a proposal at a rate of 70%; Group B comprises 40% and supports it at a rate of 30%. Their opinions remain fixed throughout this experiment. We change only who responds.
True population support54.0%
Expected support among respondents62.7%
Selection discrepancy+8.7 points
Numerical table of expected counts
| Population | People | Expected respondents | Expected respondents supporting |
|---|---|---|---|
| Group A | 6,000 | 5,400 | 3,780 |
| Group B | 4,000 | 1,200 | 360 |
| Total | 10,000 | 6,600 | 4,140 |
Counts are mathematical expectations, not observed or simulated survey responses. The model assumes that, within each group, a person's response probability does not additionally depend on their support. Real nonresponse can be more complicated; an actual survey also has random sampling variability and measurement concerns. A larger response count does not by itself cure this bias.