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In many environments, the majority voting rule maximizes agentsʼ ex-ante expected utilities among all anonymous and dominant-strategy implementable choice rules.
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We show that the set of implementable social choice functions (SCFs) is independent of the upper bound k.
We show that there exist two Nash implementable social choice correspondences defined on an environment with strict preferences for which the intersection is not Nash implementable.
If the planner is endowed with the knowledge of the rule, this might expand or shrink the set of implementable social choice correspondences depending on the particular rule used by the agents.
Counselling by telephone has proven to be an effective, easy implementable alternative [ 19, 20].
Any Nash-implementable social choice rule must satisfy a condition of "monotonicity".
20) Effective and implementable are alternative measures?
We show that any implementable and neutral social choice function must be a weighted welfare maximizer if the type space of every agent is an m-dimensional open interval, where m is the number of alternatives.
Whether or not a social choice rule is implementable may depend on which game-theoretic solution concept is used.
By contrast, precise information on reciprocity types may imply that all efficient social choice functions are implementable.
A social choice function is approximately implementable if it is correctly implemented an arbitrary large number of times with arbitrary high probability in all (communication) equilibria.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com