Comment Re:A partial solution: (Score 2, Informative) 629
You are quite right to point out the role of "weighting". One does not simply take all the observations, place them in a machine, and let the conclusion fall out. We make personal choices about what to observe and what to ignore, which things are important and which aren't, and so on. The article does not demonstrate faulty reasoning on anyone's part when it says, "they reject the information that is contrary to what they would like to believe, and they glom onto the positive information." This merely demonstrates subjective values-based weighting of incoming data -- an unavoidable necessity in many cases.
That's not to say that people are always consistent in their application of weighting. There are examples aplenty of people misunderstanding measurement data (particularly statistical data) such that they reach exactly the wrong conclusion given their stated intentions. You're probably familiar with the examples, like the problem of dealing with false positives when testing for a rare condition, or whatever. In these cases, mathematics has something to say about how you apply your weights -- maybe you need to use Bayes' theorem -- and people are notoriously bad at reaching the right conclusion intuitively. This brings me to...
One is not arrogant for believing one's reasoning is reliable, that is a necessity and a consequence of reasoning itself.
It would be a necessary consequence for an agent capable of perfect reasoning. We humans, on the other hand, tend to make incomplete arguments, admit unnoticed errors, and generally overlook faults so long as the conclusions came out the way we wanted or were expecting. One should therefore append the caveat, "but it's likely I've screwed up somewhere AGAIN, so please check my reasoning" to all one's conclusions.