The Borda rule and Pareto stability: a further comment
In their paper "The Borda rule and Pareto stability: a comment" published in 1979 by Econometrica, Farkas and Nitzan revealed the "intimate relationship" between the Borda rule and the Pareto criterion. The idea was the following: 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 candidates that are the closest to unanimity should be chosen. According to this principle, they defined a choice rule called "closeness to unanimity" and they 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 relations,... and we show that the definition of an obvious winner is no more obvious. (C) 2001 Elsevier Science BN. All rights reserved.
borda fuzzy relation pareto principle