[EM] Re: Woodall's "Descending Acquiescing Coalitions" method

[Kevin Venzke]

Chris,

 --- Chris Benham <chrisbenham at bigpond.com> a écrit :
> It has occurred to me that the method  might be improved by after the 
> first round of eliminations (determined
> by the second largest acquiescing coalition), then  ignore the 
> eliminated candidate(s) in determining the next
> largest acquiescing coalition; and after each subsequent round of 
> eliminations likewise ignore the eliminated
> candidates.

> Is there any problem with this idea?

I'm not sure I've understood your idea, but I'm sure such ideas are worth
exploring.  The most intuitive change, it seems to me, would be to actually
eliminate "eliminated" candidates (not just bar them from victory) and start
the process over.  Maybe you're saying that.  (But I also imagine there must
be a cost to altering the method in such ways.  I'm eyeing Participation, of
course.)

Another idea I haven't thought through would be to change the way the members
of an acquiescing coalition are counted.  For instance, in DAC, it bothers me
that an A>B>C=D voter contributes to set ABC as surely as A>B>C>D would.  
Might there be incentive to place a sure loser as strictly preferred to your 
least favorite candidates?

I'm willing to believe at this point that DAC meets Participation.  Borda
meets Participation, too, so that's two ranked methods which do.  What I would
like to do is consider three-candidate elections, and ask which candidates
can't be elected in given situations by a ranked method that meets Participation.
I'm not sure I'm up to this task, though.

> In his article, Woodall claims that Condocet is incompatible with 
> Participation, 4 out his 7 versions of
> Monotonicity, Later-no-harm and  Later-no-help.  For the Condorcet 
> die-hards,  would DAC  (either version)
> be a good Condorcet-completion method?

I'm not sure what you're thinking here.  Completing with DAC wouldn't permit
the method on the whole to meet Participation or later-no-help.  DAC's order-
reversal incentive would no doubt rub off to some extent, as well.
 
> You also wrote:
> In this paper, Woodall introduces the so-called
>  "plurality criterion":
>  
>  Plurality: If some candidate x has strictly fewer votes
>  in total than some other candidate y has first-preference
>  votes, then x should not have greater probability than y
>  of being elected.
> 
> "I do like this. It seems to acknowledge meaning in being ranked non-last."
> 
> CB: While I of course know what  "first-preference votes" are, I  am not 
> at all clear on exactly what the
> phrase "strictly fewer votes in total" means (in a ranked-ballot 
> context). What does it mean ?

For me, "votes in total" or "non-last votes," or "being voted preferable to at
least one candidate," means the number of ballots which acknowledge the candidate,
support him, in any way at all.  The other ballots, in my view, most likely
truncated the candidate.

So the criterion means that if X is mentioned on fewer ballots than Y received
first-place votes, we can't pick X.  It sounds like a good criterion to me,
because it seems unlikely that, in this case, we could possibly have a good
reason, sufficient information, to think that X is a better pick than Y.

But the main reason I noticed this criterion is because I think "number of
ballots which acknowledge the candidate in any way" can be useful information.


Kevin Venzke
stepjak at yahoo.fr


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