# [EM] Mono-switch-plump criterion

Sun May 11 08:12:44 PDT 2014

```> I'd say Schulze, RP, and River can't satisfy it in any case, since X's
> election might depend on tracing a win through a victory of non-X over
> some third candidate. Then when non-X loses some ballots, he can lose that
> victory, making X lose.

Kevin,
I see.  But in the case of Margins a failure example would have to have
a Smith set with
more than 3 members.

And I think with my MMLV(erw)M suggested way of weighing defeats, making
a failure
example would be still more difficult.

I am doubtful that with more than 3 candidates it is possible to make an
example of the
Score  Margins Sort version  (of MMLVerwM) failing mono-switch-plump.

If I'm right about that, then that would be a case for just sticking
with Margins Sort
(and not bothering with Beatpath or Ranked Pairs or River). If I'm
wrong, just meeting
it in the case when the Smith set has fewer than 4 (or some higher
number?) candidates
is still worth a lot (i.e. 'close enough').

Chris Benham

On 5/11/2014 5:59 AM, Kevin Venzke wrote:
> Hi Chris,
>
>
>
>
>> ----- Mail original -----
>> De : C.Benham <cbenham at adam.com.au>
>>>    Mono-switch-plump:
>>>
>>> *The probability of candidate X winning must not be reduced if one or
>>> more ballots that
>>> plump for any not-X  are replaced by an equal number of ballots that
>>> plump for X.*
>> Previously I showed that this is failed by the following methods:
>>
>> Schulze (aka Beatpath), Ranked Pairs, River, MinMax (all equivalent with
>> 3 candidates) if they use Winning Votes to weigh pairwise defeats.
>>
> I'd say Schulze, RP, and River can't satisfy it in any case, since X's
> election might depend on tracing a win through a victory of non-X over
>
> some third candidate. Then when non-X loses some ballots, he can lose that
>
> victory, making X lose.
>
>
> Any kind of path tracing is likely to be an obstacle.
>
> Kevin
>
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>

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