[Election-Methods] A Better Version of IRV?

[Chris Benham]

> I think Smith (or Shwartz),IRV is quite a good  Condorcet method. It 
> completely fixes the failure of Condorcet while being more complicated
> (to explain and at least sometimes to count) than plain IRV, and a Mutual
> Dominant Third candidate can't be successfully buried.
> But it fails Later-no-Harm and Later-no-Help, is vulnerable to Burying 
> strategy, fails mono-add-top, and keeps  IRV's failure of  mono-raise 
> and (related) vulnerability to Pushover strategy.

Kristofer Munsterhjelm  wrote (Sunday, 13 July, 2008 ):

"At the risk of taking this thread away from its original topic, I wonder 
what you think of Smith,X or Schwartz,X where X is one of the methods 
Woodall says he prefers to IRV - namely QTLD, DAC, or DSC."

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.


"(Since QLTD is not an elimination method, it would go like this: first 
generate a social ordering. Then check if the ones ranked first to last 
have a Condorcet winner among themselves. If not, check if the ones 
ranked first to (last less one), and so on. As soon as there is a CW 
within the subset examined, he wins. Schwartz,QLTD would be the same but 
"has a Schwartz set of just one member" instead of "has a CW".)

DAC and DSC only satisfy one of LNHelp/LNHarm, but they're monotonic in 
return. According to Woodall, you can't have all of LNHelp, LNHarm, and 
monotonicity, so in that respect, it's as good as you're going to get. I 
don't know if those set methods are vulnerable to burying, though, or if 
they preserve Mutual Dominant Third."

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.

But of course Smith 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

Possibly more later,
Chris Benham


      Start at the new Yahoo!7 for a better online experience. www.yahoo7.com.au
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20080716/2cf88d44/attachment-0003.htm>