Letters to the Editor
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@JeffM23
Sorry, but you're wrong. It is not 97.whatever percent.
Assuming that the errors are Gaussian and they've corrected or accounted for all systematic effects (the real kicker in these polls), lets run through some examples.
Candidate A leads B by 2% and the margin of error is 2%. This means there is a 68% chance that A leads B by anywhere from 0-4%. There is a 16% chance that A leads B by more than 4%. There is a 16% chance that B leads A by some amount.
There is a 95% chance that the real results are somewhere in the range of A trailing B by 2% to A leading B by 6% (original lead +/- twice the margin of error).
I'd love to see a real examination of how often election results fall into the window suggested by polls. Not as often as they should based purely on the statistics, I bet. Which means that pollsters are constantly under estimating systematic effects.
Accounting for only statistical differences, you need to ask
1000 people to get 4.5% error
2000 people to get 3.1% error
4000 people to get 2.2% error
assuming two evenly matched candidates.