<div dir="ltr"><div>I've suggested larger electoral systems for this.</div><div><br></div><div>If you use Single Transferable Vote for a nonpartisan blanket Primary Election to get down to somewhere between 5 and 9 (I think 7 may be better than 5), then Tideman's Alternative as a Condorcet system, you get a pretty reliable result.</div><div><br></div><div>Consider the two-party oligarchy problem: 30% of voters vote D, 24% vote C, the parties are {A,B} and {C,D}. If A>B>C>D for an {A} voter, then C is your Condorcet winner:<br><br>30%: D>C>B>A</div><div>24%: C>D>B>A</div><div>46%: {A,B}>C>D</div><div><br></div><div>24% + 46% consider C>D. There's no marginal utility for C voters to vote D>C as a way to band together and prevent a loss.</div><div><br></div><div>Now, the 30% can vote D>A>C>B, under the theory that A is the Condorcet loser. A few outcomes:</div><div><br></div><div>1. An A vs. C pair where A defeats C creates a full cycle (A>C>{D,B}, D>A, Smith set is all candidates). We're looking at 23% give or take for each of A and B, so the cycle will break in the runoff iteration, and C still wins even with all 30% voting D>C.</div><div>2. If 32% and 22% instead of 30% and 24% for {C,D} voters, then this huge 32% plurality can indeed defeat C. If just 4% of C voters defect and decide that D is f*$%ing crazy and their vote is C>B>D>A (because A is worse, to them)—and this is highly-likely, as we all well know and have seen in real elections—then D voters just elected B, who is worse from their perspective.</div><div><br></div><div>This tampering doesn't likely elect D, but rather pushes the winner farther toward A. The distortion from the other side also doesn't work, although it might be possible for 21% A>B>C>D voters to rank A>D>B>C and elect D (also a worse outcome).</div><div><br></div><div>Pretty much only D and A have any utility voting as such. C and B voters would be best off voting honestly, e.g. C>D>B or C>B>D. Changing your first choice is always weakening your first choice.</div><div><br></div><div>With a span of 7, you have {A,B,C,D,E,F,G} at roughly 14% of the vote. The impact of these groups and the usefulness or utility of tactical voting falls away, so these failures simply stop happening. Don't use group voting tickets.</div><div><br></div><div>This proportional NPBP, Condorcet Election has a few other interesting properties, notably due to vote impact.</div><div><br></div><div>Imagine of the 7, {C,D,E} being centered around {D} (the natural Condorcet candidate), D defeats all other candidates, while E defeats all candidates except D. E loses to D by 10%. If E can get out 10% more voters—out of the whole election, not just 10% more E voters—then E can win. That's pretty heavy.</div><div><br></div><div>Likewise, social media propaganda has to make some major shifts. It can't change the winner to A or G or even E. The change in ballots is immense and complex and nonsense. This system resists such propaganda.</div><div><br></div><div>On the other hand, CHANGING a vote is two votes. If D offends A voters who vote A>B>C>D>E, then A voters will change their vote to A>B>C>E>D. That's -1 D, +1 E—it's 2 votes. Just a 5% movement here will switch the winner from D to the substantially-similar E, even though the only people who switched their votes were fringe voters who are nowhere near the base for D and E.</div><div><br></div><div>This is more-sensitive with 7 candidates. It does require voters to rank so many candidates, and voters typically rank to six in practice (according to Fair Vote). If they tend to rank to three, then e.g. B>C>D and F>E>D votes form the edges, and we have likely enough of those (A and G voters are 2/7, then half of B and F voters makes 3/7, leaving 71% of voters who likely explicitly rank the Condorcet candidate) to accurately locate the Condorcet candidate. I worry about 9 or 11 or 15 because it'll break.</div><div><br></div><div>Think in terms of larger electoral systems. Think in terms of how many candidates and the distribution of first-choice voters, and in terms of engineering an election cycle to create the conditions which protect your election from such failures. You will not find one voting rule to rule them all: when 9 people show up from one party, 5 show up from another, 3 small parties send a candidate, and you have 2 independents, any single-winner method will bluntly fail. You need a primary election.</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Jun 9, 2019 at 10:20 PM C.Benham <<a href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<p>Kevin,<br>
<br>
So to be clear the possible "complaint" some voters might have
(and you think we should take seriously) is "We lied and the
voting method<br>
(instead of somehow reading our minds) believed us".<br>
<br>
So therefore it is good to have a less expressive ballot because
that reduces the voter's opportunities to tell stupid lies and if
the method<br>
is simple enough then maybe also the temptation for them to do so.<br>
<br>
To me that is absurd. If I agreed with that idea I would forget
about the Condorcet criterion and instead demand a method that
meets <br>
Later-no-Help, such as IRV or Bucklin or Approval.<br>
<br>
But I've thought of a patch to address your issue. We could have
a rule which says that if the winner's approval score is below
some fixed <br>
fraction of that of the most approved candidate, then a
second-round runoff is triggered between those two candidates.
What do you<br>
think of that? What do you think that fraction should be?<br>
<br>
Chris <br>
<br>
<br>
</p>
<div class="gmail-m_-2507526158578233008moz-cite-prefix">On 10/06/2019 9:57 am, Kevin Venzke
wrote:<br>
</div>
<blockquote type="cite">
<div class="gmail-m_-2507526158578233008ydp8f615ceyahoo-style-wrap" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px">
<div>Hi Chris,</div>
<div><br>
</div>
<div>
<div>
<div>
<blockquote type="cite" style="margin:0px;padding:8px;color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>>I don't think
it's ideal if burying X under Y (both disapproved) can
only backfire when Y is made the CW.
<div>>></div>
</blockquote>
<span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>Why
is that? </span></div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
</span></div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Because I
think if voters decide to attempt to prevent another
candidate from being CW, via insincerity, there should
be risks to doing that. Of course there is already some
risk. But if you "knew" that a given candidate had no
chance of being CW then there would be nothing to lose
in using that candidate in a burial strategy.</span></div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
</span></div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>The
post-election complaint (by any of the voters) would be
.. what?</span></div>
<div><br>
</div>
<div>For either a successful burial strategy, or one that
backfires and elects an arbitrary candidate, I think the
possible complaints are clear. Maybe someone would argue
that a backfiring strategy proves the method's incentives
are just fine. But that wouldn't be how I see it. I think
if, in actual practice, it ever happens that voters
calculate that a strategy is worthwhile, and it completely
backfires to the point that everyone would like the
results discarded, then that method will probably get
repealed.</div>
<div><br>
</div>
<div>><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
<span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>If
you don't allow voters to rank among their unapproved
candidates then arguably you are not even trying to
elect the sincere CW.</span><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
<span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>Instead
you are just modifying Approval to make it a lot more
Condorcet-ish. </span></div>
<div><br>
</div>
<div>Not an unfair statement. If you require voters to have
that much expressiveness then you can't use implicit.</div>
<div><br>
</div>
<div>To me, the motivation for three-slot C//A(implicit) is
partly about burial, partly about method simplicity,
partly about ballot simplicity. C//A(explicit) retains 1
of 3. (Arguably slightly less for the Smith version.)
Possibly it has its own merits, but they will largely be
different ones.</div>
<div><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
<span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>A lot
of voters like relatively expressive ballots. I think
that is one of the reasons why Approval seems to be a
lot less popular than IRV.</span><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
</div>
</div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
</span></div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">I have no
*inherent* complaints about the ballot format of explicit
approval plus full ranking.</span></div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
</span></div>
<div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Kevin</span></div>
<br>
</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
</div>
<div id="gmail-m_-2507526158578233008ydpb6a32dd9yahoo_quoted_0445501564" class="gmail-m_-2507526158578233008ydpb6a32dd9yahoo_quoted">
<div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;color:rgb(38,40,42)">
<div> Le jeudi 6 juin 2019 à 21:03:19 UTC−5, C.Benham
<a class="gmail-m_-2507526158578233008moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au" target="_blank"><cbenham@adam.com.au></a> a écrit : </div>
<div><br>
</div>
<div><br>
</div>
<div>
<div id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751">
<div>
<p>Kevin,<br clear="none">
</p>
<blockquote type="cite">Specifically should "positional
dominance" have the same meaning whether or not the
method has approval in it?</blockquote>
<br clear="none">
If the voters all choose to approve all the candidates
they rank, then yes. (For a while I was wrongly
assuming that Forest's suggested<br clear="none">
default approval was for all ranked-above-bottom
candidates, but then I noticed that he specified that it
was only for top voted candidates).<br clear="none">
<br clear="none">
One of my tired examples:<br clear="none">
<br clear="none">
25: A>B<br clear="none">
26: B>C<br clear="none">
23: C>A<br clear="none">
26: C<br clear="none">
<br clear="none">
Assuming all the ranked candidates are approved, C is by
far the most approved and the most top-voted candidate.
<br clear="none">
Normal Winning Votes (and your idea 2 in this example)
elect B.<br clear="none">
<br clear="none">
<blockquote type="cite">I will go easy on these methods
over failing MD, because it happens when some of the
majority don't approve their common candidate.</blockquote>
<br clear="none">
For me this this type of ballot avoids the Minimal
Defense versus Chicken Dilemma dilemma, rendering those
criteria inapplicable.<br clear="none">
<p>48: A<br clear="none">
27: B>C<br clear="none">
25: C<br clear="none">
<br clear="none">
The problem has been that we don't know whether the
B>C voters are thinking "I am ranking C because
above all I don't want that evil A<br clear="none">
to win" or "My C>A preference isn't all that
strong, and I think that my favourite could well be
the sincere CW, and if C's supporters rank<br clear="none">
B above A then B has a good chance to win. But if they
if they create a cycle by truncating I'm not having
them steal it".<br clear="none">
<br clear="none">
With the voters able to express explicit approval we
no longer have to guess which it is.<br clear="none">
<br clear="none">
</p>
<blockquote type="cite"> I don't think it's ideal if
burying X under Y (both disapproved) can only backfire
when Y is made the CW.
<div><br clear="none">
</div>
</blockquote>
Why is that? The post-election complaint (by any of the
voters) would be .. what?<br clear="none">
<br clear="none">
If you don't allow voters to rank among their unapproved
candidates then arguably you are not even trying to
elect the sincere CW.<br clear="none">
Instead you are just modifying Approval to make it a lot
more Condorcet-ish. <br clear="none">
<br clear="none">
A lot of voters like relatively expressive ballots. I
think that is one of the reasons why Approval seems to
be a lot less popular than IRV.<br clear="none">
<br clear="none">
Chris Benham<br clear="none">
<br clear="none">
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt8593146214" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt96283">
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751moz-cite-prefix">On
6/06/2019 5:34 pm, Kevin Venzke wrote:<br clear="none">
</div>
<blockquote type="cite"> </blockquote>
</div>
</div>
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt8593146214" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt32286">
<div>
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydpe4c7db39yahoo-style-wrap" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px">
<div>Hi Chris,</div>
<div><br clear="none">
</div>
<div>I've been short on time so I don't actually
have much thought on any of the methods, even my
own.</div>
<div><br clear="none">
</div>
<div>I suppose Idea 2 is the same as
Schwartz-limited MinMax(WV) if nobody submits
disapproved rankings. I'm not sure if it makes
sense to reject the method over that. Specifically
should "positional dominance" have the same
meaning whether or not the method has approval in
it? As a comparison, I will go easy on these
methods over failing MD, because it happens when
some of the majority don't approve their common
candidate.</div>
<div><br clear="none">
</div>
<div>I would have liked to simplify Idea 2, but
actually Forest's eventual proposal wasn't all
that simple either. As I wrote, if you add "elect
a CW if there is one" it can become much simpler,
so that it isn't really distinct from Idea 1. I
actually tried pretty hard to present three
"Ideas" in that post, but kept having that
problem.</div>
<div><br clear="none">
</div>
<div>I posted those ideas because I thought Forest
posed an interesting challenge, and I thought I
perceived that he was trying to fix a problem with
CD. That said, I am not a fan of
Smith//Approval(explicit). If all these methods
are basically the same then I probably won't end
up liking any of them. I don't think it's ideal if
burying X under Y (both disapproved) can only
backfire when Y is made the CW.</div>
<div><br clear="none">
</div>
<div>Kevin</div>
<div><br clear="none">
</div>
<div><br clear="none">
</div>
</div>
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yahoo_quoted" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yahoo_quoted_0454840046">
<div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;color:rgb(38,40,42)">
<div> Le mercredi 5 juin 2019 à 21:26:23 UTC−5,
C.Benham <a shape="rect" class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au" rel="nofollow" target="_blank"><cbenham@adam.com.au></a>
a écrit : </div>
<div><br clear="none">
</div>
<div>Kevin,<br clear="none">
</div>
<div>
<div id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920">
<div>
<p>I didn't comment earlier on your "idea
2". <br clear="none">
<br clear="none">
If there no "disapproved rankings" (i.e.
if the voters all approve the candidates
they rank above bottom),<br clear="none">
then your suggested method is simply
normal Winning Votes, which I don't like
because the winner can<br clear="none">
be uncovered and positionally dominant or
pairwise-beaten and positionally dominated
by a single other<br clear="none">
candidate.<br clear="none">
<br clear="none">
On top of that I don't think it really
fills the bill as "simple". Approval
Margins (using Sort or Smith//MinMax<br clear="none">
or equivalent or almost equivalent
algorithm) would be no more complex and in
my opinion would be better.<br clear="none">
<br clear="none">
I would also prefer the still more simple
Smith//Approval.<br clear="none">
<br clear="none">
What did you think of my suggestion for a
way to implement your idea 1? </p>
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqt3873327189" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqtfd25173"><br clear="none">
Chris <br clear="none">
</div>
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqt3873327189" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqtfd71007">
<div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920moz-forward-container"><br clear="none">
<br clear="none">
<br clear="none">
<blockquote type="cite">
<p><b>Kevin Venzke</b> <a shape="rect" title="[EM] What are
some simple methods that
accomplish the following
conditions?" href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3C1931864740.14928463.1559418507456%40mail.yahoo.com%3E" rel="nofollow" target="_blank">stepjak at
yahoo.fr </a><br clear="none">
Sat Jun 1 12:48:27 PDT 2019 </p>
<p><br clear="none">
Hi Forest,<br clear="none">
<br clear="none">
I had two ideas.<br clear="none">
<br clear="none">
Idea 1:<br clear="none">
1. If there is a CW using all
rankings, elect the CW.<br clear="none">
2. Otherwise flatten/discard all
disapproved rankings.<br clear="none">
3. Use any method that would elect C
in scenario 2. (Approval, Bucklin,
MinMax(WV).)<br clear="none">
<br clear="none">
So scenario 1 has no CW. The
disapproved C>A rankings are
dropped. A wins any method.<br clear="none">
In scenario 2 there is no CW but
nothing is dropped, so use a method
that picks C.<br clear="none">
In both versions of scenario 3 there
is a CW, B.<br clear="none">
<br clear="none">
If step 3 is Approval then of course
step 2 is unnecessary.<br clear="none">
<br clear="none">
In place of step 1 you could find
and apply the majority-strength
solid coalitions (using all
rankings)<br clear="none">
to disqualify A, instead of acting
based on B being a CW. I'm not sure
if there's another elegant way<br clear="none">
to identify the majority coalition.<br clear="none">
<br clear="none">
Idea 2:<br clear="none">
1. Using all rankings, find the
strength of everyone's worst WV
defeat. (A CW scores 0.)<br clear="none">
2. Say that candidate X has a
"double beatpath" to Y if X has a
standard beatpath to Y regardless<br clear="none">
of whether the disapproved rankings
are counted. (I don't know if it
needs to be the *same* beatpath,<br clear="none">
but it shouldn't come into play with
these scenarios.)<br clear="none">
3. Disqualify from winning any
candidate who is not in the Schwartz
set calculated using double<br clear="none">
beatpaths. In other words, for every
candidate Y where there exists a
candidate X such that X has a<br clear="none">
double beatpath to Y and Y does not
have a double beatpath to X, then Y
is disqualified.<br clear="none">
4. Elect the remaining candidate
with the mildest WV defeat
calculated earlier.<br clear="none">
<br clear="none">
So in scenario 1, A always has a
beatpath to the other candidates, no
matter whether disapproved<br clear="none">
rankings are counted. The other
candidates only have a beatpath to A
when the C>A win exists. So<br clear="none">
A has a double beatpath to B and C,
and they have no path butt. This
leaves A as the only candidate<br clear="none">
not disqualified.<br clear="none">
<br clear="none">
In scenario 2, the defeat scores
from weakest to strongest are
B>C, A>B, C>A. Every
candidate has<br clear="none">
a beatpath to every other candidate
no matter whether the (nonexistent)
disapproved rankings are<br clear="none">
counted. So no candidate is
disqualified. C has the best defeat
score and wins.<br clear="none">
<br clear="none">
In scenario 3, the first version: B
has no losses. C's loss to B is
weaker than both of A's losses. B<br clear="none">
beats C pairwise no matter what, so
B has a double beatpath to C.
However C has no such beatpath<br clear="none">
to A, nor has A one to B, nor has B
one to A. The resulting Schwartz set
disqualifies only C. (C needs<br clear="none">
to return B's double beatpath but
can't, and neither A nor B has a
double beatpath to the other.)<br clear="none">
Between A and B, B's score (as CW)
is 0, so he wins. <br clear="none">
<br clear="none">
Scenario 3, second version: B again
has no losses, and also has double
beatpaths to both of A and<br clear="none">
C, neither of whom have double
beatpaths butt. So A and C are
disqualified and B wins.<br clear="none">
<br clear="none">
I must note that this is actually a
Condorcet method, since a CW could
never get disqualified and<br clear="none">
would always have the best worst
defeat. That observation would
simplify the explanation of<br clear="none">
scenario 3.<br clear="none">
<br clear="none">
I needed the defeat strength rule
because I had no way to give the win
to B over A in scenario 3<br clear="none">
version 1. But I guess if it's a
Condorcet rule in any case, we can
just add that as a rule, and greatly<br clear="none">
simplify it to the point where it's
going to look very much like idea 1.
I guess all my ideas lead me to<br clear="none">
the same place with this question.<br clear="none">
<br clear="none">
Oh well, I think the ideas are
interesting enough to post.<br clear="none">
<br clear="none">
Kevin<br clear="none">
<br clear="none">
>Le jeudi 30 mai 2019 à 17:32:42
UTC−5, Forest Simmons <fsimmons
at <a href="http://pcc.edu" target="_blank">pcc.edu</a>> a écrit : <br clear="none">
><br clear="none">
>In the example profiles below
100 = P+Q+R, and
50>P>Q>R>0. One
consequence of these constraints is
that in all three profiles below the
cycle >A>B>C>A will
obtain.<br clear="none">
><br clear="none">
>I am interested in simple
methods that always ...<br clear="none">
><br clear="none">
>(1) elect candidate A given the
following profile:<br clear="none">
><br clear="none">
>P: A<br clear="none">
>Q: B>>C<br clear="none">
>R: C,<br clear="none">
>and <br clear="none">
>(2) elect candidate C given<br clear="none">
>P: A<br clear="none">
>Q: B>C>><br clear="none">
>R: C,<br clear="none">
>and <br clear="none">
>(3) elect candidate B given<br clear="none">
<br clear="none">
><br clear="none">
>P: A<br clear="none">
>Q: B>>C (or B>C)<br clear="none">
>R: C>>B. (or C>B)<br clear="none">
><br clear="none">
>I have two such methods in mind,
and I'll tell you one of them below,
but I don't want to prejudice your
creative efforts with too many
ideas.<br clear="none">
><br clear="none">
>Here's the rationale for the
requirements:<br clear="none">
><br clear="none">
>Condition (1) is needed so that
when the sincere preferences are<br clear="none">
<br clear="none">
><br clear="none">
>P: A<br clear="none">
>Q: B>C<br clear="none">
>R: C>B,<br clear="none">
>the B faction (by merely
disapproving C without truncation)
can defend itself against a
"chicken" attack (truncation of B)
from the C faction.<br clear="none">
><br clear="none">
>Condition (3) is needed so that
when the C faction realizes that the
game of Chicken is not going to work
for them, the sincere CW is elected.<br clear="none">
><br clear="none">
>Condition (2) is needed so that
when sincere preferences are<br clear="none">
<br clear="none">
><br clear="none">
>P: A>C<br clear="none">
>Q: B>C<br clear="none">
>R: C>A,<br clear="none">
>then the C faction (by
proactively truncating A) can defend
the CW against the A faction's
potential truncation attack.<br clear="none">
><br clear="none">
>Like I said, I have a couple of
fairly simple methods in mind. The
most obvious one is Smith\\Approval
where the voters have <br clear="none">
>control over their own approval
cutoffs (as opposed to implicit
approval) with default approval as
top rank only. The other <br clear="none">
>method I have in mind is not
quite as <br clear="none">
>simple, but it has the added
advantage of satisfying the FBC,
while almost always electing from
Smith.<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
<br clear="none">
</p>
</blockquote>
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