I asked Claude this question, and I thought the answer was pretty good: "What would be the margin of error in an average of polls"
Great question — the margin of error in an average of polls depends on several factors:
The Basic Math
When you average multiple polls, the margin of error shrinks because you're increasing the effective sample size. The formula is roughly:
MOE of average ≈ Individual MOE ÷ √(number of polls)
So if each poll has a ±3% MOE and you average 4 polls, the combined MOE drops to about ±1.5%.
Typical Individual Poll MOE
Poll of 600 likely voters → ~±4%
Poll of 1,000 likely voters → ~±3%
Poll of 1,500 likely voters → ~±2.5%
Polling Average MOE in Practice
# of Polls Averaged Approx. Combined MOE
2 polls ~±2.1%
4 polls ~±1.5%
8 polls ~±1.1%
15+ polls ~±0.8%
The Catch — Systematic Error
Pure math assumes polls are independent and unbiased. In reality:
Herding — pollsters adjust toward consensus, making polls correlated, not independent
House effects — pollsters with a consistent Republican or Democratic lean skew averages
Mode effects — phone vs. online polls have different biases that don't cancel out
Likely voter screens — different methodologies create systematic differences
The Real-World Lesson
In the 2016 and 2024 elections, polling averages were off by 3-4 points in key states — far outside the stated MOE — because of systematic bias, not random sampling error. The math-based MOE only captures random error, not structural polling problems.
Bottom Line: A good polling average of 8-10 polls might have a statistical MOE of ±1%, but a real-world uncertainty of ±3-4% once systematic errors are factored in.
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I would add that those averaging polls seem to have quite different methodologies. Some include all polls equally. Some try to weight polls by past accuracy or bias. There is no consensus on the right way to do it.
Here is Trump's net approval rating:
FiftyPLusOne -23%
Silver Bulletin -21%
RealClearPolitics -19%
New York Times -21%
That's a lot closer than the averages have been in the past.
FWIW, on August 1st, FiftyPlusOne had their average at -25%. Does that mean a significant change has taken place in the last 6 days?
I don't think it is safe to conclude that. It may simply be a artifact of the most recent polls released.