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There is statistically good evidence
To the extent that the evidence is any good (and I'm not coming down on either side of that question), it might lead to well informed people deciding to wear a helmet voluntarily. That is nothing to do with the legal compulsion question, which aside from the points introduced earlier about dissuading cycling and thereby causing more harm than good to population health, has a much more serious and for my money insurmountable problem; for all legal prohibitions, at the margin, the state must be prepared to kill citizens to enforce them. If you're going to start killing people for resisting your laws, you need to be absolutely confident that the public goods you are buying with those deaths are worth the price. There's no way even the most charitable reading of the possible benefit of making everybody who doesn't already voluntarily wear a helmet wear one under penalty of law amounts to a justification for killing people.
Perhaps its my fault for engaging with you, or not making things clear enough.
Either way we've now diluted the thread. So I refer people to the literature again:
There is statistically good evidence that helmets reduce risk:
-https://www.ncbi.nlm.nih.gov/pubmed/27450862
There is good evidence that in laboratory tests there is a reduction of instrument based replication of head injury in bike accidents:
https://www.ncbi.nlm.nih.gov/pubmed/24686160
There is limited evidence supporting reduction in cycling admissions following helmet legislation:
Against:
https://www.ncbi.nlm.nih.gov/pubmed/23674137
For:
https://www.ncbi.nlm.nih.gov/pubmed/26577650
Here's the study from mary's:
https://www.ncbi.nlm.nih.gov/pubmed/28945822
Here's a study from Taiwan with 'insignificant' increased hospitalisation for non-helmeted cyclists (I think)
https://www.ncbi.nlm.nih.gov/pubmed/29342208
Here's one showing reduction in facial trauma:
https://www.ncbi.nlm.nih.gov/pubmed/28751943
And here's one from Korea: " A lack of helmet use was significantly associated with serious outcomes"
https://www.ncbi.nlm.nih.gov/pubmed/28704554
Since I am not a helmet designer- and (I suspect based on the evidence provided) neither are you, the best we can come up with is second hand information garnered from equally polarised sites and conjecture- I really don't have any desire to continue.