Must humans obey the Axiom of Irrelevant Alternatives?
If someone picks option A from options A, B, C, then they must also pick option A from options A and B. Roughly speaking, whether you prefer option A or B is independent of whether I offer you an irrelevant option C. This is an axiom of rationality called IIA, and it’s treated more fundamental than VNM. But should humans follow this? Maybe not.
Maybe humans are the negotiation between various “subagents”, and many bargaining solutions (e.g. Kalai–Smorodinsky) violate IIA. We can use insight to decompose humans into subagents.
Let’s suppose you pick A from {A,B,C} and B from {A,B} where:
A = Walk with your friend
B = Dinner party
C = Stay home alone
This feel like something I can imagine. We can explain this behaviour with two subagents: the introvert and the extrovert. The introvert has preferences C > A > B and the extrovert has the opposite preferences B > A > C. When the possible options are A and B, then the KS bargaining solution between the introvert and the extrovert will be B. At least, if the introvert has more “weight”. But when the option space expands to include C, then the bargaining solution might shift to B. Intuitively, the “fair” solution is one where neither bargainer is sacrificing significantly more than the other.
Must humans obey the Axiom of Irrelevant Alternatives?
If someone picks option A from options A, B, C, then they must also pick option A from options A and B. Roughly speaking, whether you prefer option A or B is independent of whether I offer you an irrelevant option C. This is an axiom of rationality called IIA, and it’s treated more fundamental than VNM. But should humans follow this? Maybe not.
Maybe humans are the negotiation between various “subagents”, and many bargaining solutions (e.g. Kalai–Smorodinsky) violate IIA. We can use insight to decompose humans into subagents.
Let’s suppose you pick A from {A,B,C} and B from {A,B} where:
A = Walk with your friend
B = Dinner party
C = Stay home alone
This feel like something I can imagine. We can explain this behaviour with two subagents: the introvert and the extrovert. The introvert has preferences C > A > B and the extrovert has the opposite preferences B > A > C. When the possible options are A and B, then the KS bargaining solution between the introvert and the extrovert will be B. At least, if the introvert has more “weight”. But when the option space expands to include C, then the bargaining solution might shift to B. Intuitively, the “fair” solution is one where neither bargainer is sacrificing significantly more than the other.
See also geometric rationality.
How does this explain the Decoy effect [1]?
I am not sure how real and how well researched the ‘decoy effect’ is