Dodgson Winner (COMSOC)

Definition

Dodgson Winner ( COMSOC)

A Dodgson winner is an alternative with minimum Dodgson score in a profile $R$ over $C$:

$$x\in {\lambda }_{\mathrm{Dodgson}}(R)⟺\forall y\in C:{\mathrm{Dodgson}}_R(x)\le {\mathrm{Dodgson}}_R(y).$$

The Dodgson rule selects all alternatives attaining this minimum. They require the fewest adjacent swaps to become Condorcet winners, but need not already be Condorcet winners in the original profile. Several alternatives may tie as co-winners; a unique Dodgson winner has strictly smaller score than every other alternative.