[Election-Methods] A Better Version of IRV?

[Chris Benham]

Kristofer,

"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?"
 Quoting Woodall:
Here are three ways of assigning scores to sets of candidates. Recall that a voter
is 
in solidly committed to a set X of candidates if the voter puts the candidatesX as the top jXj candidates on their ballot. A voter acquiesces to a set Xof candidates if they do not indicate a preference for any candidate outside Xover any candidate in 
they vote just for a proper subset of the candidates in 
outside 
are solidly committed to X; i.e., either they are solidly committed to X, or elseX (and for no candidateX). The solid coalition S(X) in support of X consists of all voters whoX. The acquiescing coalition A(X) in support of Xconsists of all voters who acquiesce to X. The half-solid coalition H(X) insupport of 
with weight 1, together with all voters in the acquiescing coalition but not
in the solid coalition, each counted with weight 
2 
2 X consists of all voters in the solid coalition for X, each counted1; so jH(X)j = 1(jS(X)j +jA(X)j).

<end quote>
 
That means "each counted with weight of  half". The 3 rules/methods are
equivilalent if  no voters truncate. Above-bottom equal-ranking is assumed
to be not allowed.
 
I consider it desirable that LNHarm and LNHelp should be in at least 
probabilistic balance, so that 0-info. voters don't have strong incentive
to either truncate or random-fill.
 
But DHSC still fails MDT, giving the same result as DSC in the 
49A, 48B, 3C>B example. And it should be DACish enough to still
fail Independence from Irrelelevant Ballots (IIB), so the short answer
to your question is no.
 
"You said that Schwartz,IRV protects MDT candidates from being buried.
Does that hold for all Schwartz,X if X passes MDT?"
 
Yes.

"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)."

What is supposed to be the attraction of  "first preference Copeland"?
And how do you define it exactly? 
 
Chris Benham
 



Kristofer Munsterhjelm  wrote (Friday, 18 July, 2008 ):

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).



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