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Well that seems like some untrustworthy bullshit. Give me a sample size of 100,000 and maybe I’ll listen. Fucking polls…
A thousand voters is actually a perfectly good statistical sampling for the US population.
What matters is that
A thousand people is enough to get you into single digit margin of error for a population the size of the US. If you find them by dialing random landlines, or mailing surveys to people with a voter history, your sample biases towards the demographic that still has landlines or that's willing to take the time to fill out a paper survey.
That's just an absurdly large sample size. 1000 is adequate if a little on the low side.
1000 daily mail readers isn't adequate
If the Daily Mail had been the complaint I might agree with you, it was the numbers though.
A 100,000 person response rate for a snap poll is basically impossible. Not enough people say yes to taking political polls. Most polling is done with 1000-1500, and if you want higher response rates, you have to look at aggregators like 538.