I don't understand the problem. This is exactly what statistics addresses. Is that 9% a good enough random sample of the entire population, or not? If not, then what is the error 5%, 10%? Actually 9% is a really good sample.
The statistical idea that a small sample can accurately represent the whole is based on the assumption that the small number are largely indistinguishable from that whole. It's like taking a sample of
In this case, the people voting in primaries are a self-selecting group - people who are both relatively actively engaged with politics and members of one of the two main parties.
It's not unreasonable to think that the wider population (even the wider population of people who normally vote at an election) could behave vastly differently.
For instance, if you had a candidate who was so divisive that they were either loved or hated, then it wouldn't be overly surprising if the vast majority of their supporters had signed up to vote in the primaries, with little support outside of that core. Compare this to a more middle of the road candidate - they might struggle to get as many people out to vote in a primary, but might do far better in the wider population.
That theory is very relevant in the UK at the moment, with the leader of the Labour Party (Jeremy Corbyn) being very popular amongst grassroots party members, but with his enemies saying he could never win a general election as this level of support would never be reflected outside of party supporters.
I don't understand the problem.
This is exactly what statistics addresses.
Is that 9% a good enough random sample of
the entire population, or not?
For a proper bayesian result like you are suggesting participation would have to be randomly decided, and representative proportioinally of demographics (economic background, ethnic, educational, age, etc.), which it isn't.
Voters are more often then not. Old, affluent (I.E.: Can afford to take time off of work to vote, or has a job that permits them to take time off to vote, or have time to research+register for absentee voting), black, educated. Under-educated, immigrant, and younger backgrounds are heavily under represented in the voting process currently, and for most modern records keeping. Furthermore some local governments have laws that discourage particaptation for some ethnic-minorities.
Of whether the people choosing the candidates have to be or even should be statistically representative of the whole population can be argued. The choice of candidates or order on ballots in many countries is decided by various less-than-representative groups.
That's pure conjecture as the article doesn't address the sample at all. It just basically says "The sample is 9%". It doesn't say why this is bad.
Either that, or the best candidate for president out of 300 million is the wife of the president three terms ago. Bush, Clinton, Bush, Obama, Clinton? This has nothing to with issues.
If X is 10% then its an excellent measure of the will of the actively thinking electorate and its not the fault of the statistician that Americans don't care about politics.
If X is 50% or so then there's 4 semi-motivated voters per primary voter which is getting fuzzy.
Note that about 20% of the population vote in non-presidential elections and 50% vote in presidential elections. I'd propose that the delta is due to tradition and heavy social signalling to get out the vote, but that 30% don't really care and absent intense PR activity in support of voting, would not vote. Unfortunately 20% is too high to clearly support the first criteria and 20% is too low to support the second criteria.
I think its really annoying that there is no mathematically trustworthy answer to is 9% enough. Annoyingly its probably good enough to not be ridiculously far off and bad enough to not be correct a significant amount of time.