I don't understand how. Aren't you suppose to study logic to be a a judge ? Surely laws and argumentation are a central topic, and they all require a brain. How somebody unable to understand simple concept like probabilities can be judge ?
How many smart people struggle with the Monty Hall problem? It's a fairly simple probability problem, overall, but it is very much unintuitive (mostly a matter of the difficulty of setting up the problem in the first place). Most people aren't very strong in mathematics, and even most scientists struggle to apply statistics correctly (see the commentary around the fMRI of a dead fish for an example). It's not surprising that judges and juries are going to have these same struggles.
Judges are lawyers, but the approval process and performance of judges who are willing to follow the rule of law and rule in ways that aren't simply in line with "nepotism" is significant.
Even existing supreme court justices appointed have not taken actions that the folks who appointed / approved them might wish... that's a good thing.
I don't think that's completely accurate. It's very much party politics at the local level. Party hacks are rewarded. (Which may look like friends and family, but party discipline is highly enforced AFAIK)
I think like diving into an actual scientific paper, it's actually quite hard to take issue with various things and understand them if you're not familiar with the science itself.
I feel like I can logic out some stuff reasonably well as say some doctor studying DNA (speaking very generally) but as far as DNA goes i'm straight ignorant as to what to weight and conclude.... the doctor presumably better, but I'd have no clue if he was wrong.
Some of this gets solved via the use of expert witnesses- people who weren't at the scene of the crime that have expertise in a related topic, and their job is, basically, to explain some part of what happened, or how something works, under oath- for instance, a computer forensics expert, who investigated the computer of a hacker, can, during testimony, explain how something works and why that's important. Because experts are under oath, and assumed to have a knowledge of the field they're representing, the judges (and jury, too) generally place trust in them. In this case, the defendant scientist was concerned because of a lack of data:
Ms. Stajic, 69, said she felt vindicated.
“As a forensic scientist, I am fully aware
of the importance of validating each study,”
she said in an interview. “My concern was if
that study was not done, there could be
wrongful convictions. And if the wrong people
were convicted, that would mean the wrong person
would be walking free.”
Low Copy Number testing involves very minute amounts of DNA —
often lifted from crime scene surfaces, such as weapon handles
or bicycle handlebars, that multiple people have touched.
The city first adopted this technique in 2006, and it is estimated
to have been used in thousands of cases before it was phased out
in January 2017. New York was the only crime lab in the country
believed to have used the method.
In conclusion- yes, logic is an important part of being a judge, and a part that you more or less have to have in order to get very far. Judges also trust expert witnesses to fill them in on what they don't know (such as how this exact model of car works, or what a particular weapon's spray is like, or if shells from bullets match the defendant's gun) and generally trust them. The problem in the article is that the NYC's science department was more or less in bed with its prosecutors, which is not fair, and that the science department was using less data than it ought to to produce often-damning evidence. It's not really the fault of the judge for not understanding that the shortcuts that the science department were using weren't good, especially when they're under oath, which is a HUGE psychological part of law.
Also, if it helps, here's a good overview of how a court case works, in the form of a movie scene critique (legitimately the best primer on how a court with a jury generally functions, or at least ought to):