Klaus Nehring: Impartial Ordinalism – an Update

31 January 24

Wednesday January 31 2024 at 11:00am in room A711

Speaker: Klaus Nehring (UC Davis)

Title: Impartial Ordinalism – an Update

Summary: Impartial Ordinalism is based on a vector comparison of alternatives according to which an alternative ordinally dominates another if its majority margin with respect to any feasible alternative is greater. Impartial Ordinalism is based on a natural extension of ordinal dominance to lotteries and entails a representation of a Social Choice Rule as a Generalized Borda Rule (GBR). GBRs maximize the weighted average of majority margins, where the index weights can depend arbitrarily on the profile. The only known GBRs are the Borda rule, the Essential Set and Maximal Lotteries (as an SSCR). The Borda rule is "unreliable" (overly agenda-sensitive); in particular, it violates axioms of Independence of Clones and Independence of Pareto Dominated Alternatives. On the other hand, while Condorcetian choice rules such as the Essential Set, Maximal Lotteries (as well as non-GBRs Maxmin and its cousins) are reliable, they arguably sacrifice relevant ordinal information.

This intuition can be expressed by an axiom of Qualified Reinforcement which applies Reinforcement only to situations in which reliability issues are of no concern. Qualified Reinforcement is satisfied by any "proper GBR", i.e. for which the index weights depend continuously on the profile. Reliable proper GBRs thus reconcile minimal desiderata for reliability with desiderata for an adequate use of ordinal information; no SCR in the literature has achieved such reconciliation before. It is also shown that reliable proper GBRs are incompatible with standard social choice axioms such as Fishburnís C2 and Monotonicity.

I will argue that these implications are to be viewed as features, not bugs.