# [EM] Earlier-no-harm

Kevin Venzke stepjak at yahoo.fr
Mon Dec 29 22:45:02 PST 2003

```Anthony Duff wrote:
>I made the suggestion on the basis of:
>where Markus Schulze wrote"
>"In another paper, Woodall proves that no election method can
>simultaneously meet later-no-harm, later-no-help, monotonicity,
>and mutual majority. Therefore, the fact that Minimax(pairwise
>opposition) violates mutual majority in such a drastic manner
>can be considered a consequence of the fact that it meets
>later-no-harm, later-no-help, and monotonicity."

I see; I didn't think you might be talking about opposition instead
of defeats.  Sorry.

Seems clear to me now.  Inserting a strict preference among candidates
otherwise ranked last can only hurt the candidates who remain last.

--- Markus Schulze <markus.schulze at alumni.tu-berlin.de> a écrit :
> Hallo,
>
> suppose N is the number of candidates. Suppose d[i,j]
> with i <> j is the number of voters who strictly prefer
> candidate i to candidate j. Suppose d[i,j] : = 0 for i = j.
> Suppose d[i] : = max { d[i,j] | j = 1,...,N }.
>
> Then Minimax(pairwise opposition) chooses the candidate i
> with minimal d[i].

Perhaps I am a flaming idiot, but shouldn't it be
d[i] := max { d[j,i] | j = 1,...,N }
?  You want votes against i, not i's votes against others, don't
you?

>
> Minimax(pairwise opposition) satisfies later-no-harm because
> ranking an additional candidate can only increase but not
> decrease d[k] for every not ranked candidate k. However,
> my claim that Minimax(pairwise opposition) satisfies
> later-no-help was incorrect.

I can see this now, too.  Worsening someone's score could happen
to make a preferred candidate into the winner.  That is surely why
random filling always makes more sense than truncation.

Kevin Venzke
stepjak at yahoo.fr

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