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

Chris Benham chrisbenham at bigpond.com
Sun May 8 08:14:01 PDT 2005

```Ted,

>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."
>
>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"?
>

You responded (Fri.May6):

> 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.

Yes, the two definitions may not be exactly equivalent, but they convey
the same idea. I would say that normally a method that meets one would
meet the other.

Ted:

> 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.

Yes.

I also wrote:
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.

Ted:
"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 ;-)"

CB: The method I had in mind when I wrote that I've since rejected, sorry.
Also, sorry list for somehow accidentally sending my last post three times.

Chris Benham

```