The Borda rule and Pareto stability: a further comment

In their paper "The Borda rule and Pareto stability: a comment" published i n 1979 by Econometrica, Farkas and Nitzan revealed the "intimate relationsh ip" between the Borda rule and the Pareto criterion. The idea was the follo wing: in a profile of total orders, when there is a candidate who obviously wins under unanimous agreement of the voters, that candidate should be in the choice set. In a profile where there is no obvious winner, the candidat es that are the closest to unanimity should be chosen. According to this pr inciple, they defined a choice rule called "closeness to unanimity" and the y showed that it is equivalent to the Borda rule. In our paper, we give an equivalent result for a ranking rule. Then we try to obtain similar results when aggregating profiles of tournaments, weak orders, semiorders, fuzzy r elations,... and we show that the definition of an obvious winner is no mor e obvious. (C) 2001 Elsevier Science BN. All rights reserved.