A published poll reports a figure for a whole population from a sample of a few thousand people. The steps between the raw answers and the headline number involve considerable judgement.
Random sampling is the theoretical basis
The statistics that make a small sample informative assume every member of the population has a known chance of being selected.
Under that assumption, sampling error can be calculated, which is where the quoted margin of error comes from.
True random sampling has become extremely difficult, because reaching people at all now depends on which contact methods they respond to, and response rates have fallen sharply.
Weighting corrects a sample that is not representative
Raw samples over-represent people who are easy to reach and willing to answer, which skews them by age, education and political engagement.
Pollsters correct this by weighting, giving under-represented respondents more influence in the total so the sample matches known population figures.
The choice of which characteristics to weight on is a judgement, and two firms weighting the same raw data differently can publish different results.
The margin of error covers only one problem
A quoted margin describes sampling variation alone, assuming everything else in the process was perfect.
It says nothing about whether the sample was reachable, whether questions were understood, or whether the weighting model was right.
This is why polls sometimes miss by more than their stated margin: the error that mattered was not the one the margin measures.
Question wording changes the answer
Small differences in phrasing produce measurably different results, as do the order of questions and the options offered.
A question that follows others on a related theme is answered in the context those questions created, which is why professional polls rotate the order.
Comparing across pollsters therefore compares different instruments, and tracking one firm's series over time is more informative than comparing two firms on one day.
Turnout modelling is the hardest step
Election polls must estimate not what people think but what those who actually vote think, and voting intention is a poor predictor of attendance.
Models use stated likelihood, past behaviour and demographic patterns, and each approach produces a different electorate from identical responses.
Most of the divergence between polls in the final weeks of a campaign comes from this step rather than from any disagreement about what respondents actually said, which is why headline figures can separate while the underlying answers barely move.