Via Tam I came across an article on the Dunning-Kruger Effect, which you should go read before going any further in this post. It won't take long and it is fascinating.
In FM 5-0 "The Operations Process" there is a good section on problem solving. According to this doctrine there are three types of problems and they are defined by the difficulty in framing the problem and how "obvious" the answers are.
A well defined, well structured problem allows non-experts to agree on a workable solution. Problems like "the roof leaks" is a good example, the obvious answer is that the roof needs repair and the steps necessary to accomplish that are straightforward.
A poorly defined, poorly structured problem allows experts to agree on a workable solution after they can come to terms with the problem. When someone from marketing asks the engineering department to come up with a new product that does some thing do you really think that the marketing department is going to get back exactly what they envisioned?
An ill defined, ill structured problem will cause disagreements among experts in the field and require many iterations of problem solving to come to a workable solution. Is green energy a viable alternative? Does man made global warming actually exist?
The more complex the problem, the more you need disagreement to drive the process of defining the issue and discovering a solution. During this disagreement process you will normally grab hold of solutions as they come, try to work those solutions into the cycle, and end up abandoning those solutions as the problem becomes more clearly defined.
Think guns. What is the problem? If you ask the Brady Bunch they will tell you that as long as one person dies from a gun shot wound there is too much "gun violence" and it has to stop. Ask a conservative and the problem is that machine guns and silencers are prohibitively expensive. No workable solution is possible because no agreed upon problem statement exists. This is why there can be no compromise with the Brady Bunch, they cannot work towards anything but total disarmament because of the way they "define the problem."
If you think about poverty you have to ask "what are the root causes of poverty?" and "once we find the root causes what can we do about it?" Clearly the "Great Society" and the "War On Poverty" have been abject failures, and if you actually want to SOLVE the problem you have to admit that the proposed solution didn't work and go back to more clearly define the problem and work through to a new solution. Unfortunately the Left believes that "if a million dollars of welfare didn't work" then clearly "a hundred billion has to work!" Failure to see the reality of a situation separate from any philosophy or ideology makes Leftists double down on their own failure like a gambling addict.
My point is that in an "ill defined, ill structured" problem where experts disagree there is no problem with amateurs in the field tossing out ideas. Einstein is a good example of an amateur who threw out ideas and helped advance his field. As Physics moved along a lot of Einsteins work has been pushed into the dustbin of history, but that is how science works towards truth. A scientist must abandon a theory when evidence shows that theory false. Scientists cannot afford the luxury of "doubling down" on an idea that reality has proven false.
However for a true solution to come out of an "ill defined, ill structured" problem people must abandon the dogmatic solutions. If someone refuses to abandon a course of action that has historically failed then they are not a part of the solution. And if you aren't a part of the solution, you are a part of the problem. Unless you are a chemist, then if you aren't a part of the solution you are a part of the precipitate.