Mono-add-top criterion

Mono-add-top is a relative criterion which requires that if candidate X is the winner of the election, then adding additional ballots which rank X strictly above all other candidates must not reduce the probability that the winner is still X.

The name "Mono-add-top" was invented by Douglas Woodall.

Any method which satisfies the Participation criterion also satisfies Mono-add-top.

Woodall has shown that it is impossible for a method to satisfy all three of Condorcet, the Plurality criterion, and Mono-add-top. Minmax(margins) passes Condorcet and mono-add-top, but not Plurality.^[1] It is not known whether Mono-add-top is compatible with Smith.

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References

↑ Woodall, Douglas R. (1997). "Monotonicity of single-seat preferential election rules" (PDF). Discrete Applied Mathematics. Elsevier BV. 77 (1): 90. doi:10.1016/s0166-218x(96)00100-x. ISSN 0166-218X.

[Woodall_1997_pp._81–98-1] Woodall, Douglas R. (1997). "Monotonicity of single-seat preferential election rules" (PDF). Discrete Applied Mathematics. Elsevier BV. 77 (1): 90. doi:10.1016/s0166-218x(96)00100-x. ISSN 0166-218X.

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