[EM] "DOC," A method meeting ENHarm and Majority

Kevin Venzke stepjak at yahoo.fr
Mon Dec 29 14:08:04 PST 2003

Here is a method that meets earlier-no-harm and Majority (or at least,
Majority Favorite).  It's called "Descending Opposing Coalitions" or
"DOC" and it's basically the flipped version of DSC.  Like DSC, I
believe it also meets Participation, Clone Independence, and a lot of

Every possible set of candidates is given a score equal to the number
of voters who voted that those candidates are strictly the worst of
all the candidates.  They're arranged in descending order of score.
The set of potential winners initially includes all the candidates.
Each set in the list is taken in turn, and all candidates in the set
are deleted from the set of potential winners, unless that would leave
no potential winners, in which case the set is ignored.  Last candidate
left is the winner.

If your ballot was A=B>C>D, changing it to A>B>C>D can only cause set
"BCD" to rise in the list.  All you're doing is making it more likely
that B, C, or D will be eliminated.  So DOC meets ENHarm but not ENHelp.

This meets Majority Favorite because if a majority rank A as their sole
favorite, then the set of all other candidates must be higher on the
list than any set which contains A.  I believe a similar argument can
be made that DOC meets Majority generally.

To my dismay, it seems that earlier-no-harm does not imply Strong FBC.

11 C>A
7 A
9 B
10 D>B

C wins this.  (I'm not claiming this is a GOOD method.)  Note that, in
accordance with ENHarm, the D voters can't get anything by voting "D=B."
To make B win, they have to insincerely rank B first.  This is not a
failure of ENHarm, but it is a failure of FBC.

Do methods which satisfy later-no-harm (or earlier-no-harm) necessarily
have order-reversal incentive?

Kevin Venzke
stepjak at yahoo.fr

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