PS. I am writing this as an example, and confess for not thinking it throught too much. Take it as an illustration etc. and do not sue me for every line. Comments and criticism are welcome, as always.
I had a freind that has a legal case. There were some documents that would inccrease the probability of the closure of a lagel case hanging above her head. Effort was not that big. She did not make the effort.
I tried to persuade her for that. She refused to take care. While screaming at me not to make her crazy, she explained:
"I know myself. Realistically, I will not do it. Only value of your nagging is making me angry".
So, given the fact that she will probably not do that, she is better off hanging up my phone calls, as far that this subject is the issue.
But she still sounds irrational. But only on the surface.
There was a psychological element here. In order to persuade herself to work on the issue, she should have adopt a different outlook at reality. A different way to go about her whole life. Would her whole life be better with a more "rational" management? Not so sure.
This is what Robert Aumann calls "rule rationality" when you make a very general decision how to decide your actions, instead of deciding for every case separately. Sometimes it is more optimal to have a rule to follow. Moreover, in some cases the decision involves complicated systems (emotinal, or perception mechanisms, and others) that force oyu to have a big decision about various cases instead of a local decison every time.
In such cases, local irrationality maybe a result of a rational decision about the rule.
Other issues are also involved, such as limits of life management. I guess that there is kind of natural limit of how many things one can "care for" in a day. having too much tasks has a high cost, and even impossible for some. It is not the local cost of the very task, but the space available in our psych's "do to" list. (It is not necessarily in the number of tasks but depends of their emotional current and more).
Here, too, there was a point in the above example. "being responsible" to gather the documents, would cost much more than its net working time. Most probably, the task would hang on her mind for a week or two, costing high amounts of energy and burdening her with stress all over. It was not so cheap after all.
Clarification arising upon discussin in the comments of the earlier post.
The definition problem of rationality
I am realizing that at the edge (i.e. with reductio de absurdum), if one says he is rational but has limits, there will be no use for the term rationality.
Example: on the reason-passion axis. Saying "the guy has strong passion which hings on his ability to be rational, but given his passions as constraints he is rational" is kind of making fun of the very saying "he is rational". Everything will be rational that way.
Intuitively, however, one can draw a line somewhere and maybe perserve some meaning for "rational". So that there is a decision maker that has rationality and limits, and tries nevertheless to achieve his goals. Not sure whether I make sense or just babbling.