The Borda count, or average rank method, is said to satisfies the participation criterion.
This means that this ranking method is free from the "no show paradox".
Do you know any proof of this claim? Can you please link to a reference?
2026-03-25 20:34:57.1774470897
Does Borda count satisfies the participation criterion?
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The proof is fairly simple, so I don't know of any work that spells it out (though there might well be).
To satisfy the Participation Criterion, The following situation should be impossible:
Voter Anne prefers candidate $A$ over $B$.
With all votes tallied, $B$ wins the election.
Had Anne not voted, $A$ would have won.
For Borda count, the candidate with the most "points" is elected, where the points of a candidate are simply the sum of the points they get per ballot, in which a better place on the ballot gives more points. This means that with all votes tallied, $B$ has more points, but with Anne's ballot removed, $A$ has more points. This necessarily means that she assigned more points to $B$ than $A$, which is in contradiction with Anne preferring candidate $A$ over $B$.