[EM] alternative Smith?

[Chris Benham]

James,
James Green-Armytage wrote:

>Anyway, Nicolaus Tideman called me this afternoon to tentatively
>recommend a mixture of the Smith rule and the IRV rule:
>1. Eliminate non-members of the Smith set.
>2. If >1 candidate remains, eliminate the plurality loser.
>3. Repeat steps 1 and 2 until one candidate remains.
>

The method Tideman  suggests is Smith//IRV.
 
"X//Y" means "first eliminate and drop from the ballots the X losers, 
and then elect the Y winner from those
remaining", whereas   "X,Y"   means  "X losers are not allowed to win 
but are not dropped from the ballots.
Elect the X non-loser who is highest-ordered by  Y on the original ballots."
(The method some here rated highly was  "CDTT,IRV".)

The point of the distinction is that if it is possible for the two 
versions to give different winners, the comma
versions have less of a monotonicity problem.  In  this case Smith//IRV  
but not Smith,IRV  fails both  Mono-add-Plump
and  Mono-append.

Douglas Woodall gives this demonstration:

>abcd 10
>bcda  6
>c     2
>dcab  5
>
>All the candidates are in the top tier, and the AV winner is a.  But
>if you add two extra ballots that plump for a, or append a to the two
>c ballots, then the CNTT becomes {a,b,c}, and if you delete d from all
>the ballots before applying AV then c wins.
>
(By  "top tier" he means the Smith set, and  "AV" stands for 
"Alternative Vote" aka IRV.
"Plump" means the same as  "bullet-vote".)

James Green-Armytage wrote:

>His arguments in favor of this method included the following:
>1. It passes Smith, and therefore Condorcet, mutual majority, Condorcet
>loser, etc.
>2. It is likely to be less manipulable than other Condorcet methods. For
>example, it seems to be non-manipulable in cases where the Condorcet
>winner has more than 1/3 of the vote. (I'm not sure, but I think that this
>is the case in most or all of the real elections NT is examining in his
>investigation of strategy.) 
>
Smith,IRV  shares all  these same advantages.


Chris  Benham