[Election-Methods] A Better Version of IRV?

[Kristofer Munsterhjelm]

Chris Benham wrote:

> At one stage Woodall was looking for the method/s that meet as many of
> his "monotonicty properties" as possible while keeping  "Majority" 
> (equivalent to Majority for Solid Coalitions).  That is what led him to 
> Quota-Limited Trickle Down (QLTD) and  then Descending Acquiescing Coalitions (DAC).
>  
> But I wouldn't conclude from this that for public political elections he 
> currently prefers those methods (or DSC) to IRV.

I was going by his statement of DAC being "the first system I'm really
happy with" or something to that effect. It's true that he could have
changed his mind, and given your example below, he probably did.

> They  don't meet Mutual Dominant Third.
>  
> 49: A
> 48: B
> 03: C>B
>  
> The MDT winner is B, but DSC elects A.
>  
> 03: D
> 14: A
> 34: A>B
> 36: C>B
> 13: C
> The MDT winner is C, but DAC elects B.
>  
> This latter example (from Michael Harman, aka Auros) I think put
> Woodall off  DAC.  B is an absurd winner. Without the 3 ballots
> that ignore all the competitive candidates the majority favourite is C.

I agree that it is quite absurd.
In 2003, you referred to a method called "Descending Half-Solid
Coalitions", which, despite failing both LNHarm and LNHelp, "might be
preferrable to them". What is DHSC, and does it salvage DAC/DSC?

> But of course Smith implies MDT.

You said that Schwartz,IRV protects MDT candidates from being buried.
Does that hold for all Schwartz,X if X passes MDT? It would seem to do
so, since burial most often involves a cycle, and without a cycle the
Schwartz (and Smith) set is just a single candidate.

In that respect, Smith, or Schwartz,[something that passes MDT] is not
redundant, even if Smith itself implies MDT.

> DSC and DAC aren't just "monotonic" (meet mono-raise), they meet
> Participation (which of course is lost when combined with Smith/Schwartz
> because Participation and Condorcet are incompatible).
>  
> I think all methods that meet Condorcet are vulnerable to Burial. By 
> themselves
> DSC is certainly vulnerable to burial (and has a 0-info. random-fill 
> incentive) and
> DAC has strong truncation incentive.
> Your question about QLTD has been asked before:
> http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015367.html
>  
> http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015369.html

I see. If QLTD isn't cloneproof (and it isn't), then the result won't be
either, hence we could just as well go with first preference Copeland 
(unless that has a flaw I'm not seeing).