That's a very wide reach. Are you sure you're not using "rationality" just as a synonym for "doing something really well"?

I mean do well in the areas I talked about before. In summary, I basically mean do well at coming up with solutions to problems or choosing/being able to go through with the best solution, out of all of the solutions you have come up with, to a problem.

I will try to define it again.

First off, there is comprehensive rationality or normative rationality. This does not consider agent limitations. It can be thought of as having two types.

• Prescient - outcomes are known and fixed. The decision makers maximise the outcomes with the highest utilities (discounted by costs).
• Non-prescient - like the prescient model, but it integrates risk and uncertainty by associating a probability distribution with the models where the probability is estimated by the decision maker.

In both cases, choices among competing goals are handled by something like indifference curves.

We could say that under the comprehensive rational model a rational agent is one that maximizes its expected utility, given its current knowledge.

When we talk about rationality, though, we normally mean in regards to humans. This means that we are talking about bounded rationality. Like comprehensive rationality, bounded rationality assumes that agents are goal-oriented, but bounded rationality also takes into account the cognitive limitations of decision makers in attempting to achieve those goals.

Bounded rationality deals with agents that are limited in many ways which include being:

• Unable to determine all outcomes. Organisms with cognitive limitations have a need to satisfice and an inability to consider long sequential outcomes that are inextricably tied. There is also a tendency to focus on a specific set of the overall goals or outcomes due to priming.framing.
• Unable to determine all of the pertinent information.
• Unable to determine all of the possible inferences.

The big difference between bounded rationality and normative rationality is that in bounded rationality you also consider the agent improving its ability to choose or come up with the best outcomes as rational as long as there are no costs or missed opportunities involved.. Therefore, a rational agent, in the bounded sense, is one that has three characteristics:

• It has a honed ability to return decent sets of outcomes from its searches for outcomes
• The expected utiltity it assigns to outcomes accurately matches the actual expected utiltity
• It chooses the best outcome returned by its searches for outcomes. The best outcome is that one with the highest expected utiltity (discounted by costs)

Do you think it could be reformulated in the framework where values form tree-like networks with some values being "deep" or "primary" and other values being "shallow" or "derived" or "secondary"? Then you might be able to argue that a conflict between a deep and a shallow value should be resolved by the declaring the shallow value not rational.

I think that once a value is in. It is in and works just like all the others in terms of its impact on valuation. However, a distinction like the one you talked about makes sense. But, I would not have 'deep' and 'shallow' because I have no idea how to determine that. Perhaps, 'changeable' vs 'non-changeable' would be better. Then, you can look at some conflicting values, i.e. ones that lead you to want opposite things,  and ask if any of them are changeable and what the impact is from changing them. The values that relate to what you actually need are non-changeable or at least would cause languishing if you tried to repress them. I think the problem with the tree view is that values are complex, like you were talking about before, one value may conflict with multiple other values.

So how to avoid being caught in a loop: values depend on values which depend on values that depend on values..?

I don't see the loop. This is because there is no 'value'. There is only coherence which is just how much it conflicts with the other values. I don't know how to describe this without an eidetic example. Please let me know if this doesn't work. Imagine one of those old style screensavers where you have a ball moving across the screen and when it hits the side of the screen it bounces in a random direction. Now, when you have a single ball it can go in any direction at all. There is no concept of coherence  because there is only one ball. It is when you introduce another ball that the direction starts to matter as there is now the factor of coherence between the balls. By coherence I mean simply that you don't want the balls to hit each other. This restricts their movement and it now becomes optimal for them to move in some kind of pattern with vertical or horizontal lines being the simplest,

What this means for values is that you want them to basically be directed towards the same or similar targets or at least targets that are not conflicting. A potential indicator of an irrational value is one that conflicts with other values, Of course, human values are not coherent. But, incoherence is still an indicator of potential irrationality.

Unrelated to the above examples is that you would need to think about if the target of the value is actually valuable and is worth the costs you have to pay to achieve it, this is harder to find out, but you can look at the fundamental human needs. Maybe, your deep vs. shallow distinction would be useful in this context.

I am not sure I understand -- is "most trusted source" subjective? What if Jesus is my most trusted source? And He is for a great deal of people.

I don't think I am conveying this point well. I am trying to say that we only have an incomplete answer as to what is rational and that science provides the best answer we have.

One very common way of making a definition is to point to a well-known class,

I think instead of that type of defintion I would rather say that rationality means doing well in the areas of X, Y and Z. and then have a list of skills or domains that improve your ability in the areas of rationality.

Do you think that there are many types of rationality? I think that there are many types of methods to achieve rationality, but I don't think there are many types of rationality.

So if we were to try to give an is-a-kind-of defintion of rationality, what is the super-class? Is it reasoning? Is it skills? Something else?

I would say reasoning or maybe problem solving and outcome generation/choosing better convey the idea of it.