[EM] Condorcet + IRV completion?

[Chris Benham]

Andrew,
Oops!  In my last message a reference to  "other IRV methods" should 
have read "other Condorcet methods".

> In common with IRV and Schulze it meets the Plurality criterion and  
> Clone Independence. In common
> with other IRV methods, we lose IRV's Later-no-Harm and  Mono-add-Top.

should read:

> In common with IRV and Schulze it meets the Plurality criterion and  
> Clone Independence. In common
> with other Condorcet  methods, we lose IRV's Later-no-Harm and  
> Mono-add-Top.


Chris Benham




The entire corrected message:


Andrew Myers wrote:

> Here's an obvious idea that must have been considered before. How 
> about using the basic Condorcet method, but running IRV on the 
> Schwartz set, if any? Are there any known results on how well this 
> works/vulnerabilities/etc.?
>
>
>  
>

Andrew,
Yes. Douglas Woodall has demonstrated that dropping the non-members of 
the Schwartz/Smith set
from the ballots and then applying IRV  causes the resulting method to 
fail both mono-add-plump
and mono-append, two very weak (normally easy to meet) criteria that I 
rate a essential.

He refers to IRV as "AV" (Alternative Vote) and the Smith set as "CNTT" 
(Condorcet(Net) Top Tier):

> 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.
>


But instead we don't need to even mention the Schwartz or any other set 
in the algorithm:

"Before the first and each subsequent IRV elimination, check to see if 
the there is a single candidate X
with no (among remaining candidates) pairwise losses. As soon as an X 
appears, elect X."

That *does* meet mono-append and mono-add-plump, with no disadvantage 
compared to the other
method.  Like IRV, it still fails mono-raise.

In common with IRV and Schulze it meets the Plurality criterion and  
Clone Independence. In common
with other Condorcet methods, we lose IRV's Later-no-Harm and  
Mono-add-Top.

I like it, with above-bottom equal preferences not allowed so as to make 
Pushover ("turkey raising")
strategy more difficult.

It has the property that when there are three candidates XYZ, and  X 
wins with more than a third of the
first preferences, then changing some ballots from  Y>X>Z  to  Y>Z>X 
can't change the winner to Y.

The other property that it has in common with IRV but not Schulze etc. 
is that in the zero-information case
regardless of how the voter rates the candidates the voter has no 
"strategy" that is better than sincere ranking.

Some dislike the fact that it fails Minimal Defense.

49: A
24: B
27: C>B

Here it elects A.

46: A>B
44: B>C  (maybe "was" B>A or B)
10: C

Here I like the fact that it elects A. Meeting both MD and the 
anti-burial property  ("Dominant Mutual Third Burial Resistance"?)
would force the method to elect C.

Chris Benham



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