Unmanipulable majority criterion

The unmanipulable majority criterion is a strategy-resistance voting system criterion devised by Chris Benham. It states:

If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.

A looser way of stating this is that if A wins and also beats B pairwise, then the voters who prefer B to A can't manipulate their votes to get B to win without executing a compromise strategy for B. In particular, methods that meet unmanipulable majority resist burial completely in such cases.

Very few methods pass unmanipulable majority. Chris Benham described one, SMD,TR, in the post where he defined the criterion.

Failures

Condorcet methods that reduce to Minmax (wv or margins) in the three candidate case fail unmanipulable majority:

93: A
09: B>A
78: B
14: C>B
02: C>A
04: C

B is the Condorcet winner and thus wins. Since B is the Condorcet winner, it beats A. Then 82 A-first voters decide to bury B:

82: A>C
11: A
09: B>A
78: B
14: C>B
02: C>A
04: C

and Minmax elects A.