Definition of meta-problem
Definition: a meta-problem is about identifying the best problem to solve, knowing there is a tradeoff between the value of solving a particular problem and the effort it takes to solve that problem.
The best way to get started with the meta-problem is to recognize some situation which is complex and you need to make a choice. Think about the goals you hope to improve, and what choices you could make. Is there a different choice that helps you achieve your goals better? Are there goals that weren't top of mind but are also important?
Following this path can help you get clearer on what you want and how you can accomplish those things.
Now for the technical view
Incompletely-Defined Problems
Solving a meta-problem starts by defining an incompletely defined problem.
Definition: An incompletely defined problem is a problem where we have defined some of the criteria, but especially may not know how to trade off one variable versus another.
To solve an incompletely defined problem, we can make assumptions about anything that is not known. For example, we could assume some tradeoff between criteria and see what the result is.
Completely-Defined Problems
Incompletely defined problems are best explained by showing what they are not.
Definition: A completely defined problem is a problem where there is a right answer.
To solve a completely defined problem you have some flexibility, but the value of the answer will be the same no matter how you get there. Incompletely defined problems in a classroom setting often become completely defined through the power of the teacher telling students what assumptions to make.
For example, if the teacher just taught a class how to do division with a "remainder," the students assume they should not use fractions to answer the question. If I ask what 3 divided by 2 is and 1 with a remainder of 1 is correct but 3/2 is not, then this is a completely defined problem.
Assumptions
Assumptions fill the gap between an incompletely defined problem and a specific completely defined problem
Definition: Assumptions determine some unknown in an incompletely defined problem.
With enough assumptions, we can get a version of a particular incompletely defined problem which is completely defined. Those assumptions could include simplifications of the problem, models of uncertainty, predictions of the future, estimates of preferences, and anything else.
Using the term assumption comes from engineering where we acknowledge if something is known for certain or not. Models require a lot of elements to be known, many of which we do not in fact know. By explicitly stating those unknowns engineers can discuss if the assumption is appropriate or not. If not, we often need to consider different methods.
The Fundamental Trade-off
A Meta-Problem is the following pair of questions "How does the value of solving this particular problem compare to the effort of solving it? Is there a best problem to solve given the situation and that trade-off?"
Value on one side, effort on the other, assumptions to stick everything together, and an incompletely defined problem to focus our discussion and find the best completely defined problem to ultimately solve. That is the focus of this page.