  Winner selection by majority, in an election between two candidates, is the
only rule compatible with democratic principles. Instead, when the candidates
are three or more and the voters rank candidates in order of preference, there
are no univocal criteria for the selection of the winning (consensus) ranking
and the outcome is known to depend sensibly on the adopted rule. Building upon
XVIII century Condorcet theory, whose idea was to maximize total voter
satisfaction, we propose here the addition of a new basic principle (dimension)
to guide the selection: satisfaction should be distributed among voters as
equally as possible. With this new criterion we identify an optimal set of
rankings. They range from the Condorcet solution to the one which is the most
egalitarian with respect to the voters. We show that highly egalitarian
rankings have the important property to be more stable with respect to
fluctuations and that classical consensus rankings (Copeland, Tideman, Schulze)
often turn out to be non optimal. The new dimension we have introduced
provides, when used together with that of Condorcet, a clear classification of
all the possible rankings. By increasing awareness in selecting a consensus
ranking our method may lead to social choices which are more egalitarian
compared to those achieved by presently available voting systems.
