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Gibbard's Theorem vs Stable Matching | by Chris Smith | May, 2021


Gibbard and Roth face off!
Gibbard’s Theorem: Strategy is Inevitable
The first theorem, initially by Allan Gibbard and generalized by later work by Gibbard and others, showed that any collective decision-making process must have one of three properties:
There are only two possible outcomes.
There is a dictator, who can choose the outcome regardless of any choices made by anyone else.
It is strategic, meaning that the best way to get what you want depends not just on your preferred outcome but also on anticipating what others will do.
This is a pretty big deal. Think about elections, for example. Assuming we have more than two candidates and don’t have a dictatorship, strategic voting must be possible. That’s too bad, because we’d like to be able to tell people that they can always just vote for their favorite candidate. Alas, this can never be the case. It’s widely known that hopeless third parties can “spoil” the election ....

Alvin Roth , Allan Gibbard , Deferred Acceptance , ஆல்வின் ரோத் , ஒத்திவைக்கப்பட்டது ஏற்றுக்கொள்ளுதல் ,