Is the Condorcet method suitable for IFcomp?

I haven’t learned how to deal with blanks in matrices before but from your posts, I understand that it corresponds to treating unplayed games as neither higher or lower than any played game, which is what we want.

You referred to the Wikipedia article on ranked pairs which uses the assumption we want: “unstated candidates are assumed to be equal to the stated candidates.” so that’s good.

However, the main Wikipedia article on the Condorcet method did not mention this assumption. Instead it mentions this assumption twice: “Usually, when a voter does not give a full list of preferences they are assumed, for the purpose of the count, to prefer the candidates they have ranked over all other candidates.” This assumption would favor games which get played a lot over those which don’t.

Thus whoever applies the method on IFcomp data should understand this difference.

The main article mentions a matrix method which is rather simple. Unfortunately it is not described how to handle ties and unplayed games, i.e. unstated candidates.

In contrast the article on ranked pairs seems to apply some graph theory(?) to find the winner.

I don’t have the prerequisites when it comes to graph theory, so I am hoping someone can describe the corresponding matrix method, which I believe more people can understand.

Zarf, I understand that from one of your posts, that the simple matrix method shown in the main article in the section “Pairwise counting and matrices” can be applied if the unplayed games are treated correctly, i.e. you leave the relevant matrix fields blank, which is different from using zeros somehow.

Zarf, using the matrix example from “Pairwise counting and matrices” is there any chance you could explain what would happen to the matrices below if voter 1, who made ballot 1 below, had not played game D?
Thanks :smiley:

Ballot 1:
	A	B	C	D
A	—	0	0	1
B	1	—	1	1
C	1	0	—	1
D	0	0	0	—

Sum matrix (3 voters):
	A	B	C	D
A	—	2	2	2     6 points (winner)
B	1	—	1	2     4 points (3rd)
C	1	2	—	2     5 points (runner-up)
D	1	1	1	—     3 points (4th)

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