# [EM] Smith//MMPO

Fri Sep 23 21:07:10 PDT 2016

```Mike,

35 A>B
25 B
40 C

> A is the most favorite candidate without majority  pairwise opposition.

C: Fortunately Smith//MMPO   meets  Irrelevant Ballots Independence, so
let's make a slight
change to the example so that there is no  voted "majority" for anyone

35 A>B
25 B
40 C
21 D

Smith//MMPO  still  elects A.  Your explanation to the C supporters as
to why their favourite lost
to A is now what?

As is often the case with failures of the Plurality criterion, the the
example is also an outrageous
failure of Later-no-Help.  If the A supporters had truncated like
everyone else, then C would be
the CW (and the only possible winner).

Why should their ranking of B make their favourite (A) the winner?
Especially since the method
has some random-fill incentive, why should we assume that their ranking
of B is sincere?  What if their
sincere preferences are  just A or even A>C ?

Part of your justification for Smith//MMPO  is that it meets "Weak CD".
But in a recent post on that
criterion you wrote:

> Not reassuring enough to be of much use.

C: So I assumed that it was an idea you were just toying with before
rejecting.

> Evidently MAM -like strategy is incompatible with CD.

C: What is "MAM-like strategy" and what do you think is so good

> C: Also (like WV) it fails  Mono-switch-plump.
>
> M: That's widely accepted, if wv does it.
>

IRV and Benham also fail the criterion, but they (unlike all the other
proposed Condorcet methods I'm aware of) meet
Unburiable Dominant Mutual Third (UDMT), which says that if the winner X
is a member of a set S of candidates who are voted
strictly above all outside-S candidates on more than a third of the
ballots and who all pairwise beat all the outside-S
candidates, then it isn't possible to cause the winner to change from X
to some outside-S candidate Y by just altering some
ballots that vote Y above X.

So one of my current standards is that a method should meet at least one
of Mono-switch-plump and UDMT.

Is it one of your prejudices that anything that is  "widely accepted",
should be accepted?

Chris Benham

On 9/22/2016 11:05 PM, Michael Ossipoff wrote:
>
>
> On Sep 21, 2016 7:50 PM, "C.Benham" <cbenham at adam.com.au
> >
> >
> > Mike,
> >
> > You recently wrote:
> >>
> >> Smith//MMPO has replaced Plain MMPO as an advocacy of mine.
> >
> >
> > Do you still advocate  Smith//MMPO ?
>
> Yes I do. Though it doesn't meet CD, it meets Weak CD.
>
> Evidently MAM -like strategy is incompatible with CD.
> >
> > It seems very similar to Winning Votes  (MAM, Schulze, River,
> Smith//MinMax)...
>
> Yes. If shares their optimally unproblematic strategy.
>
> You continued:
>
> ...except less decisive.
> (endquote)
>
> It can be decisive. If 2 candidates have the same max  pairwise
> opposition, compare their next-largest pairwise opposition...& so on.
>
> You left out a property: Weak CD.
>
> >
> > 35 A>B
> > 25 B
> > 40 C
> >
> > B>C 60-40,   C>A 40-35,  A>B 35-25.     MPO scores:  A40 = B40 < C60
>
> A wins.
>
> > WV elects B...
>
> ...rewarding defection.
>
> but MMPO gives an A=B tie.
>
> ...solved as described above. A wins
>
> You continue:
>
>  B winning fails CD and A winning fails Plurality.
>
> (endquote)
>
> A is the most favorite candidate without majority pairwise opposition.
>
> If the Plurality Criterion says A shouldn't win, then the Plurality
> Criterion is mistaken.
>
> Plurality is a positional criterion. A positional standard won't give
> the desired properties.
>
> > Also (like WV) it fails  Mono-switch-plump.
>
> That widely accepted, if wv does it.
>
> > 25 A>B
> > 26 B>C
> > 23 C>A
> > 22 C
> > 04 A
> >
> > C>A  71-29,   A>B  52-26,   B>C  51-49.     MPO scores: C51 < B52 < A71
> >
> > MMPO  and WV elect  C,  but if  the 4A ballots change to 4C then
> they both elect B.
> >
> > 25 A>B
> > 26 B>C
> > 23 C>A
> > 26 C
>
> Of course, as you know, rank methods have faults like that.
> Participation is another example.
>
> Avoid them with Approval.
>
> Michael Ossipoff
>
> > C>A  75-26,   A>B  48-26,   B>C 51-49.     MPO scores: B48 < C51 < A75.
> >
> > In my view C, being both positionally dominant and uncovered, is the
> prettiest winner.
> >
> > Chris Benham
> >
>
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