Disregarding the validity of your argument in itself, trust issues cannot be solved by black boxes. Humans laws have to be enacted by humans, because the real world is messy and rules and laws need "messy wiggle room".
I believe in the utility of separation of powers: a true democratic legislative branch, a provable executive branch, and a mechanically verifiable judgement branch.
I don't mind if you call the democratic facet of the legislative branch messy. Learning to make proper decisions for novel situations tends to be messy, because we learn from our mistakes, and mistakes are messy.
As long as the way the population would democratically prefer the case to be judged is captured/modeled accurately by the law, the formal mechanical law is suitable. If the way the mechanical law is applied does not capture the way we want things to be handled (what I presume you refer to with a messy case) the legislative branch should be activated to change the law, and we want the legislative branch to be democratic because it's what makes sure that the population consults their ethics and feelings (community taste can not be proven, except by poll).
So the mess is restricted to just the first instance of unforeseen situations. ("History repeats itself, the first time as a tragedy, and from then on as a farce")
I would hate to live in your world. The law is the way it is because it governs humans, and because legislation cannot capture every aspect of all facets of the law.
Mechanical application of the law is a pretty dreadful idea.
So it would still be decisions by humans, the resolution of the law would increase and capture more detail messy real world situations of our daily lives.
The only horror is that it would force us to either treat everyone as equals before the law, or force us to democratically change the law back and forth when we choose to be inconsistent, forcing us to realize we are discriminating on some (un)identified factor.
Neither can the current system, so any analysis would have to be comparative. I do believe we can approach such a state much quicker and more accurately through formalization.
>nor that mechanical application of such would be a good thing.
Was the formalization transistion from unwritten laws to written laws a good thing in your view? What makes quotability from a written corpus of law not horrible, but further formalization horrible?
With mechanical application I only refer to the end result taken after the verifier (judging algorithm, i.e. MetaMath or other) as a result of either a passing proof of guilt provided by prosecutor, or passing of a proof of innocence provided by defense. There is no imperative algorithm that maps cases to sentences, thats not how the law can work due to combinatorial explosion. The law is like philosophy or mathematics.
The society could unconditionally reward people for detecting inconsistencies in the law before we run into them during a trial after a tragedy thus potentially preventing it (i.e. finding a proof that the law simultaneously guarantees a right for a certain deed, yet also forbids it)
btw I enjoy this discussion, so if you can come up with more criticisms or examples please do!
Inflexibility. We humans are squishy and imprecise. Which is why the law is unlike mathematics, and I think efforts to make it so and to remove humans from its application are fundamentally misguided.
> The society could unconditionally reward people for detecting inconsistencies in the law before we run into them during a trial after a tragedy thus potentially preventing it (i.e. finding a proof that the law simultaneously guarantees a right for a certain deed, yet also forbids it)
My thoughts here go more to mitigating circumstances rather than inconsistencies. These are varied to the point of the near infinite, and people can judge these better than algorithms ever could as people can infer, empathise and extrapolate.
I think the iron answer from a judge is less flexible than the possibility to start a democratic petition against a scandalous oversight in the formalized law...
I was trying not to bring up mitigating circumstances, since many people don't see a good reason for their existence (I do!), but mitigating circumstances is actually one of the reasons I want formalization! The way society treats the law is highly oversimplified with one-liners like "the law is the law" and "innocent until proven guilty" and "every convicted person is guaranteed a just trial because the prosecution needs to prove their case"
But if mitigating circumstances should be brought into consideration, then in theory you can't convict a person with a certain level of punishment until you have also proven that there were no mitigating circumstances, and I am not aware of any binding rule to try and locate or identify the mitigating circumstances.
I.e. allow me to call a perpetrator "less guilty" if there are mitigating circumstances; if the prosecution wins a case in the current world without mitigating circumstances ever being brought up by the defense (because they might not be aware), we currently accept the "proof" by the prosecution, even though the punishment may be unjustly harder.
I.e. the idea that the burden of proof in the current system lies totally with the prosecution is false, because the prosecution is not trying to diminish the sentence of the defense.
By formalizing we would start a discussion on how exactly to formalize mitigating circumstances.
I might choose to commit a crime against the (much older) perpetrators of my youth trauma, and while in practice I might get mitigating circumstances, I currently have no such guarantee...
The judge has some flexibility in how exactly to apply the law, which an algorithm does not.
> less flexible than the possibility to start a democratic petition against a scandalous oversight in the formalized law...
You can already do such, should you wish.
> By formalizing we would start a discussion on how exactly to formalize mitigating circumstances.
I don't believe we can capture all of these, nor should we try to have an exhaustive list. Such a list would likely need frequent modification as societal mores change. Better to have humans involved in the process than trying to apply to fix it afterwards.
I'm, personally, not convinced any of this is crying out for a blockchain either, even if we were to grant that automation would be a positive.