<div dir="ltr"><br><div class="gmail_extra"><br><br><div class="gmail_quote">On Thu, Apr 24, 2014 at 5:15 AM, C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">
<div>Forest,<br>
<br>
Just because you can contrive some example </div></div></blockquote><div><br></div><div>Actually it was a range of examples. where the only requirement was that the sincere Condorcet preference have the smallest first place support.<br>
</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><div> where method X
appears to resist Burial strategy better than method Y<br>
is no (or a very very weak) reason to suppose that one couldn't
just as easily contrive a converse example (i.e. where method Y resists Burial strategy better than method X.)<br></div></div></blockquote><div><br></div><div>I didn't claim that TACC was uniformly better with respect to burial. I only said that my examples showed that Woodall/Benham was not uniformly better than TACC.<br>
</div><div><br></div><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><div>
<br>
This is especially the case without some sensible
burial-resistance criterion that you can show is met by X or not
Y, or failing that<br>
perhaps some computer simulation that shows that method Y rewards
Burial strategists significantly more often than method X.<br>
<br>
Also, while you are comparing TACC with Benham/Woodall and IRV I
think should also be benchmarking it against the other two<br>
methods that combine pairwise and approval information,
Smith//Approval (almost the same thing as another method you
promoted<br>
as "Majority Enhanced Approval", where you descend a chain
starting with the most approved candidate, only adding candidates
that<br>
covers all the already added candidates and then elect the last
added candidate) and Schulze Approval Margins (the same thing, at
least<br>
with 3 candidates, as Approval Margins Sort).<br></div></div></blockquote><div><br></div><div>Yes, I was thinking that these other methods would require more thought about where to put the approval cutoff, but your encouragement makes me want to examine them again with respect to the Chicken Dilemma. As you say Smith//Approval is inadequate but I need to consider the approval margins idea, and the descending covering idea, which has the advantage over TACC of being Independent of Pareto Dominated Alternatives. <br>
</div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><div>
<br>
Those other methods also deny the buriers in your example, without
electing a candidate X that is both pairwise-beaten and
positionally<br>
dominated by some candidate Y. (Of course Smith//Approval fails
Chicken Dilemma, so we can leave that aside if you like.)<br>
<br>
An example that highlights TACC problems:<br>
<br>
25 A>B (sincere may be A or A>C)<br>
06 A>C<br>
32 B>C<br>
27 C>A<br>
10 C<br>
<br>
C>A>B>C, Approvals C75 > A58 > B57 (Top Ratings
C37 > B32 > A31)<br>
<br>
TACC rewards the A>B maybe buriers by electing A, even though
C positionally dominates and pairwise beats A. AM/AMS very
comfortably elects C.<br>
<br>
If say, 2 of the 10 C voters change to B ( a Push-over strategy)
then the TACC winner changes from A to C.<br></div></div></blockquote><div><br></div><div>I'll look at this example later, but it may be moot now that I am starting to look at approval margins, etc.<br><br></div>
<div>Thanks for your insights.<br><br></div><div>Forest <br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><div>
<br>
Chris Benham<div class=""><br>
<br>
<br>
<br>
On 4/24/2014 5:17 AM, Forest Simmons wrote:<br>
</div></div>
<blockquote type="cite"><div class="">
<div>Chris,</div>
<div> </div>
<div>What you say below makes perfect sense in a zero information
election.</div>
<div> </div>
<div>Now suppose the actual ballot set is </div>
<div> </div>
<div>35 A>C</div>
<div>40 B>C</div>
<div>25 C>A</div>
<div> </div>
</div><div>Then IRV elects A while Woodall/Benham and TACC elect C.</div>
<div> </div>
<div>Four years later the polls confirm that public opinion has
not changed at all from the above ballot set, so candidate
A convinces her supporters to bury C. The ballot set becomes</div><div><div class="h5">
<div> </div>
<div>35 A>B</div>
<div>40 B>C</div>
<div>25 C>A</div>
<div> </div>
<div>Neither IRV nor TACC is affected by this burial, but
Benham&Woodall reward the A faction for their strategic
order reversal.</div>
<div> </div>
<div>It appears that IRV (in general) and TACC (at least in this
case) are less vulnerable to burial strategy
than Benham/Woodall.</div>
<div> </div>
<div>But let's take this case a little further. Since the B
supporters prefer C over A, they have a strong incentive to
protect C from this obvious threat. What can they do under IRV
or Benham/Woodall? They can betray their favorite B and vote 40
C>B, which does get C re-elected, thus rewarding their order
reversal.</div>
<div> </div>
<div>Forest</div>
<div> </div>
<div class="gmail_quote">On Wed, Apr 23, 2014 at 7:44 AM, C.Benham
<span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>
wrote:<br>
<blockquote style="BORDER-LEFT:#ccc 1px solid;MARGIN:0px 0px 0px 0.8ex;PADDING-LEFT:1ex" class="gmail_quote">
<div bgcolor="#FFFFFF" text="#000000">
<div>Forest,
<div><br>
<br>
<blockquote type="cite">
<div class="gmail_extra">40 A>B>C<br>
</div>
<div class="gmail_extra">35 B>C>A<br>
</div>
25 C>A>B</blockquote>
<br>
</div>
In this example ballot set of yours (which you say is the
result of the A faction burying against the sincere
Condorcet Winner C) there is no reason<br>
to suppose that any of the ballots are more likely to be
insincere than any of the others.<br>
<br>
In this sort of situation (with 3 candidates in a cycle
and all the ballots containing the same amount of
information) we should avoid electing a candidate<br>
X that is positionally dominated, especially by a
candidate that pairwise beats X. In this case that just
says "not C".<br>
<br>
<blockquote type="cite">
<div class="gmail_extra">35 A>B>C <br>
</div>
<div>
<div class="gmail_extra">40 B>C>A<br>
</div>
25 C>A>B</div>
</blockquote>
<br>
In this ballot set (which again you say is the result of
the A faction burying against C) TACC elects C. But
again there isn't any information on the ballots<br>
that suggests that some ballots are more likely to be
insincere than any others.<br>
<br>
So the result must be justifiable on the assumption that
all the votes are sincere. On these ballots C is
positionally dominated and pairwise beaten by B.<br>
B also positionally dominates A.<br>
<br>
Approval Margins, Approval Margins Sort, IRV, Benham,
Woodall and all other good (and/or sane) methods elect B.<br>
<br>
Chris Benham
<div>
<div><br>
<br>
<br>
<br>
<br>
On 4/23/2014 7:29 AM, Forest Simmons wrote:<br>
</div>
</div>
</div>
<div>
<div>
<blockquote type="cite">
<div dir="ltr"><br>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote"><br>
<blockquote style="BORDER-LEFT:rgb(204,204,204) 1px solid;MARGIN:0px 0px 0px 0.8ex;PADDING-LEFT:1ex" class="gmail_quote">
<div>On 04/21/2014 11:39 PM, C.Benham wrote:<br>
<blockquote style="BORDER-LEFT:rgb(204,204,204) 1px solid;MARGIN:0px 0px 0px 0.8ex;PADDING-LEFT:1ex" class="gmail_quote">Forest,<br>
<br>
<blockquote style="BORDER-LEFT:rgb(204,204,204) 1px solid;MARGIN:0px 0px 0px 0.8ex;PADDING-LEFT:1ex" class="gmail_quote">48 C<br>
27 A>B<br>
25 B<br>
</blockquote>
<br>
<blockquote style="BORDER-LEFT:rgb(204,204,204) 1px solid;MARGIN:0px 0px 0px 0.8ex;PADDING-LEFT:1ex" class="gmail_quote">Borda, TACC, and IRV
based methods like Woodall and Benham
elect C.<br>
<br>
But Borda is clone dependent, and the
IRV style elimination based<br>
methods fail monotonicity. So TACC is a
leading contender if we<br>
really take the Chicken Dilemma
seriously.<br>
</blockquote>
<br>
Benham and Woodall are a lot more
resistant to Burial than TACC (and<br>
other Condorcet methods that meet
mono-raise, aka monotonicity) because<br>
they meet<br>
"Unburiable Mutual Dominant Third"<br>
</blockquote>
</div>
</blockquote>
</div>
<br>
</div>
<div class="gmail_extra">How about the following set
of sincere preferences?<br>
<br>
</div>
<div class="gmail_extra">40 A>C>B<br>
</div>
<div class="gmail_extra">35 B>C>A<br>
</div>
<div class="gmail_extra">25 C>A>B<br>
<br>
</div>
<div class="gmail_extra">Candidate C is the sincere
winner under Benham, Woodall, TACC, or any other
method meeting the Condorcet Criterion.<br>
<br>
</div>
<div class="gmail_extra">Suppose that the A faction
decides to bury C:<br>
<br>
<div class="gmail_extra">40 A>B>C<br>
</div>
<div class="gmail_extra">35 B>C>A<br>
</div>
25 C>A>B<br>
<br>
</div>
<div class="gmail_extra">Woodall, Benham, Condorcet
(both wv and margins) reward this subterfuge by
electing A, whereas under TACC the tactic
backfires by getting B elected.<br>
<br>
</div>
<div class="gmail_extra">Under Condorcet (wv) the C
faction can defend itself by truncating to 25 C.
This wouldn't help under Woodall/Benham: <br>
</div>
<div class="gmail_extra"><br>
You get the same result if you replace the
respective faction sizes 40, 35, 25 with any three
positive numbers a, b, c that satisfy both
a>b>c and b+c>a.<br>
<br>
</div>
<div class="gmail_extra">Now consider the following
example where b>a>c:<br>
<br>
<div class="gmail_extra">35 A>B>C (sincere
A>C>B)<br>
</div>
<div class="gmail_extra">40 B>C>A<br>
</div>
25 C>A>B<br>
<br>
</div>
<div class="gmail_extra">Woodall/Benham still
rewards the burial. TACC elects C without any
defensive move. Condorcet elects B without any
defensive move.<br>
<br>
</div>
<div class="gmail_extra">Under TACC or Condorcet it
never hurts and sometimes helps for the CW
supporters to truncate the rest of the candidates.
But as you can see in the cases we are dealing
with here, only much more drastic defensive action
can save the CW under Woodall/Benham.<br>
<br>
</div>
<div class="gmail_extra">Conclusion: although in
some cases the UMDT confers a superior defense
against burial, that doesn't make Woodall and
Benham uniformly more burial resistant than TACC.<br>
<br>
</div>
<div class="gmail_extra">Forest<br>
</div>
</div>
</blockquote>
<br>
</div>
</div>
</div>
</blockquote>
</div>
<br>
</div></div></blockquote>
<br>
</div>
</blockquote></div><br></div></div>