That is an enormous claim and there are reams of research on this topic - your assertion is not supported. It doesn't even stand up to the most cursory scrutiny - if it were true, then societies and states with harsh punishment would have lower crime - and this is very, very, very obviously not the case.
https://www.nij.gov/five-things/pages/deterrence.aspx
https://www.psychologytoday.com/blog/ethics-in-question/2015...
http://www.sentencingproject.org/wp-content/uploads/2016/01/...
https://undark.org/article/deterrence-punishments-dont-reduc...
tl;dr Social norms, accepted membership in 'legal' society and education are the best ways to deter crime, followed by certainty of punishment - not its severity. The reason people commit crimes is, in rough order, usually out of desperation, social norms that lead them to believe the prohibited act should be acceptable or ignorance of the knowledge that the prohibited act is illegal, for greed, and, lastly, then for the sheer thrill of it. Severity of punishment doesn't act as a good deterrent for any of those categories - certainty of punishment acts as a deterrent for the latter two, but for the first two, desperation and ignorance, are fairly well inoculated against rational counsel.
Before you start arguing the philosophy regarding merits of punishment v. deterrence, I am going to put it bluntly: the claim at issue - that severity of punishment is a deterrent for crime - is an evidentiary claim and it cannot be proven from first principle. It must be supported evidence, and as far as I can tell, the numbers are in, and they do not appear to be on your side. Unless you have studies that support your conclusion, the philosophy is totally irrelevant.
"Sentence Enhancements Reduce Crime"
http://www.nber.org/digest/oct98/w6484.html
"Longer prison sentences deter re-offending, study shows"
http://www.telegraph.co.uk/news/uknews/law-and-order/8504923...
Longer sentences deter crime up to a point
http://www.economist.com/blogs/freeexchange/2016/03/criminal...
"Longer prison terms really do cut crime, study shows"
https://www.theguardian.com/law/2012/jul/07/longer-prison-se...
"the average add-on gun law results in a roughly 5 percent decline in gun robberies within the first three years"
https://www.law.upenn.edu/cf/faculty/dabrams/workingpapers/D...
Note also that 2 of the 4 links you provided are comparing certainty-of-punishment vs harshness-of-punishment. This is a false dichotomy. There's no reason you can't have both. Having harsh punishment doesn't reduce the certainty of punishment in any way.
Is there a lot of contentious debate on this topic, and a lack of consensus on this topic? Of course. But given the lack of clear answers, I'd much rather err on the side of preventing victimization.
In America, we have historically low crime rates and historically low violent crime rates. Simultaneously, we have an insane crisis of prison overpopulation that leads into multi-generational cycles of poverty.
I too would rather err on the side of preventing victimization.
Right now, from where I sit, over-criminalization is a bigger problem than violent crime.
You say that your comment will be very unpopular with HN, but it seems to me that it's actually very unpopular with facts and statistics.
Now, one of the hard things to measure, is whether the sentences does deter everybody who doesn't commit crimes. I assume that there are crimes you and I have had the opportunity to commit, but weighed the odds of being caught and decided that the outcomes from committing the crimes were not worth it. It's difficult to measure that, but it's also not very useful, because it is hard to say whether the deterrent came from the punishment, or from the fact that it was lawbreaking in the first place, or that the label of "felon" is risky enough given the known outcomes.
In the place I'd argue we want the most deterrence - violent crime - our harshest punishment seems to have no real deterrent value. (I would be interested to see a review of this using more modern statistical / ML techniques to examine the data, though).
https://www.dartmouth.edu/~chance/teaching_aids/books_articl...
https://www.nij.gov/five-things/pages/deterrence.aspx
(NIJ is research arm of the DOJ)
When I look at crimes of passion or necessity, these cannot be stopped by harsh penalties. A fit of jealous rage doesn't consider the prison term. Hunger won't stop theft. The only place harsh punishments could stand to be effective are crimes which have no moral component. For such crimes ALL persons make an expected value calculation, like a sociopath makes for crimes than an ordinary person would consider immoral.
Harsh punishments work exceedingly well as a deterrent.