ECON3029 DD - Group Preferences

Imposing single-peaked preferences in pairwise majority voting

Universal Domain

Rational, Paretian, Nondictatorial, Based on Universal Domain, Irrelevance of Independent Alternative

The unique winner that emerges in pairwise comparisons when individual preferences are single-peaked

to lead to a single social preference relation/

It is impossible to obtain a rule that doesn’t violate independence of irrelevant alternatives - choice between A and B should not depend on the quality of a third, unrelated outcome C

Arrow's Impossibility Theorem

voting for one's most preferred preference

The agenda is not predetermined and can include any topic

Not in terms of pairwise majority voting

To obtain a single social preference relation.

Any method of aggregating preferences must violate one of the specified properties of a 'good' social rule

By demanding more information on individual preferences or dropping/weakening some properties (UD or IIA)

It is uncertain if the group always decides rationally.

the failure of majority rule to produce transitive preferences for society

Individual rationality may not guarantee rational group decisions.
Single peaked preferences (linear order and 1 local maximum) and pairwise majority voting are the only way to ensure a rational group.