I did take a statistics course, but too many decades ago. But if those "quantitative techniques" were able to "create fairly accurate predictions with deceptively small sample sizes", then why in 2020 and 2022 elections were so many polls wrong? Either those techniques are flawed, or the sample size is to small. Or the other factors I discussed have a significant impact. And are those techniques applicable to people vs say a manufacturing assembly process? There will always be a tolerance level during manufacturing that the techniques can compensate, but where/how people feel about a topic is more "touchy-feely" and may require a larger sample. Trying to avoid politics, but I know many conservatives absolutely hated Clinton for 2016, yet many people were concerned about giving Trump a second term for 2020. In both cases, many people crossed lines and may have voted against Clinton/Trump for President, but still backed candidates from the other party for Senate/Congress.
Again, going back to my points on permutations - trying to randomly select possibilities, how a young, poor, conservative, single, Jewish, unemployed, male may consider a topic can be totally different than a middle age, middle income, liberal, married with kids, agnostic, employed, female.
Per my discussion, I came up with nearly 1000,000 permutations of voters. But again, most poll sizes are typically only 1000 people, which is still only 1% of the possible permutations.