  In the eyes of a rationalist like Descartes or Spinoza, human reasoning is
flawless, marching toward uncovering ultimate truth. A few centuries later,
however, culminating in the work of Kahneman and Tversky, human reasoning was
portrayed as anything but flawless, filled with numerous misjudgments, biases,
and cognitive fallacies. With further investigations, new cognitive fallacies
continually emerged, leading to a state of affairs which can fairly be
characterized as the cognitive fallacy zoo! In this largely methodological
work, we formally present a principled way to bring order to this zoo. We
introduce the idea of establishing implication relationships (IRs) between
cognitive fallacies, formally characterizing how one fallacy implies another.
IR is analogous to, and partly inspired by, the fundamental concept of
reduction in computational complexity theory. We present several examples of
IRs involving experimentally well-documented cognitive fallacies: base-rate
neglect, availability bias, conjunction fallacy, decoy effect, framing effect,
and Allais paradox. We conclude by discussing how our work: (i) allows for
identifying those pivotal cognitive fallacies whose investigation would be the
most rewarding research agenda, and importantly (ii) permits a systematized,
guided research program on cognitive fallacies, motivating influential
theoretical as well as experimental avenues of future research.
