We present a class of orderings L for which there exists a profile u of preferences for a fixed odd number of individuals such that Bordas rule maps u to L.
Let g be a strategy-proof rule on the domain NP of profiles where no alternative Pareto-dominates any other. Then we establish a result with a Gibbard-Satterthwaite flavor: g is dictatorial if its range contains at least three alternatives.
Let g be a strategy-proof rule on the domain NP of profiles where no alternative Pareto-dominates any other and let g have range S on NP. We complete the proof of a Gibbard-Satterthwaite result - if S contains more than two elements, then g is dictat
orial - by establishing a full range result on two subdomains of NP.
