@Andy-Dienes A thought occurred to me that makes me believe the sensitivity to Condorcet components is actually not odd at all.

The thought can be best illustrated with three candidates {x,y,z}. In this case, there are two kinds of balanced Condorcet cycles, namely (xyz+yzx+zxy), and (zyx+yxz+xzy). Individually, and even combined, these Condorcet components should indicate a tie by any reasonable deliberation, since the candidates are interrelated by perfect interchangeability.

For the same reason, a ballot set that is a scalar multiple of

(xyz+yzx+zxy)+A(zyx+yxz+xzy),

where A is a non-negative real number, should equally indicate a tie.

However, consider what would occur if one of the candidates, by new information that has a negligible effect on the relationship between the other two candidates, were discovered to be an invalid winner. Without loss of generality, we can say that candidate is z. It seems reasonable to simply remove z from every ranking in the ballot set, which would transform the ballot above into

(2xy+yx)+A(2yx+xy)=(A+2)xy+(1+2A)yx

At this point, it is clear that the preferable choice between x and y, conditional on the invalidation of z, can be decided from the information available in the combination of the two oppositely oriented Condorcet components. If 1>A we should prefer x, and if A>1 we should prefer y.

In other words, combinations of Condorcet components at least provide conditional information about the preferences between candidates. If this information is considered relevant, which I think it ought to be, then ignoring Condorcet components is improper.

Informally, while Condorcet components should indicate a tie, this can be considered due to a normative balance of potential marginal dissatisfaction among the voters. If some of this dissatisfaction is actualized as a sunk cost, then the margins are changed. In a sense, this is what is being analyzed by considering the pairwise electionsâthe normative marginal dissatisfaction of the electorate as a whole is being minimized when the Condorcet winner exists and is chosen.

This I think upholds the concept of the Condorcet winner as a canonical choice, given that one exists.