[EM] Re: "Approval Later-no-Harm",

[Araucaria Araucana]

On  6 May 2005 at 10:44 UTC-0700, Chris Benham wrote:
> Ted, James (and anyone interested),
>
> In my last post (Thu.May5) I suggested this criterion:
>
>    "If x wins, and afterwards some identical ballots that approve x
>    are uniformly changed only so that they approve more candidates
>    than previously; then if there is a new winner it must be one of
>    the candidates approved on these altered ballots."
>
> This is supposed to be a simple test for the property that approving
> more candidates should never change the winner from an approved (on
> the original ballots) candidate to a disapproved (on both sets of
> ballots) candidate.
>
> This is very similar to this monotonicity-like criterion:
> 
>    "If x wins, and afterwards some ballots are changed only to
>    increase the approval scores of some other candidates; then if
>    there is new winner it must be one of the candidates whose
>    approval scores have been raised."

I was going to say that I didn't see why these were different.  But
now I see -- the difference is that in the first, the approval is
extended on ballots that approve X, and in the second version, it can
be any set of ballots, X-approving or not, and they don't have to be
identical.

>
> Or maybe it is better to put it the other way:
> 
>    "If x wins, and afterwards some ballots are changed only to
>    decrease the approval scores of one or more other candidates;
>    then x must still win."
>
> Yes, this seems more succinct. But what to call it, "Mono-reduce
> opposition approval"?

But you lost me here.  I'm don't think the two last definitions are
equivalent.  In the first mono-like criterion, X is the winner before
approval-extension.  In the second, X is the winner with expanded
approval.  Call the second winner Y instead, for clarity.

Then if Y is the new winner after the first definition, the only way
to go back is to remove approval for Y in the second definition.

Also, are you assuming that when approval is extended it is being
applied only to lower-ranked candidates than those already approved?
That would be normal for ranked ballots with approval cutoff.

>
> Another criterion that applies to rankings/approval methods
> interests me, which I might call "Disapproval Later-no-Harm":
>
>    "Ranking a disapproved candidate must never harm an approved
>    candidate".
>
> (A stronger version would add "or a higher-ranked disapproved
> candidate").  This is incompatible with Condorcet, and in a future
> post I'll suggest a method that meets it.

This goes around and around ... If you have such a method, I don't
think it will satisfy the Condorcet Criterion.

But I'm interested anyway ;-)

-- 
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