<div dir="auto">Colin, <div dir="auto"><br></div><div dir="auto">You just floated a bunch of methods that are way more complicated and objectively inferior in results compared to the specific method I suggested, as well as compared to many other methods of the same type:</div><div dir="auto"><br></div><div dir="auto">Absent a CW elect the candidate with the strongest defeat strength ... period.</div><div dir="auto"><br></div><div dir="auto">All of the other good methods that actually rival my suggestion in simplicity (by not introducing elimination steps, approval cutoffs, scores, equal-first rankings, etc.) are of this type ... I have wasted a lot of time time looking elsewhere.</div><div dir="auto"><br></div><div dir="auto">Here's a slightly less simple example of this promising type ...</div><div dir="auto"><br></div><div dir="auto">Absent a CW, elect the strongest defeat winner where strength of defeat is gauged by ... winning votes plus losing truncations.</div><div dir="auto"><br></div><div dir="auto">Each pairwise defeat has a winner and a loser ... winning votes (wv) means the pairwise support of the winner, i.e. the number of ballots on which the winner out ranks the loser.</div><div dir="auto"><br></div><div dir="auto">Losing truncations simply means the number of ballots on which the Loser is unranked.</div><div dir="auto"><br></div><div dir="auto">Let's look at our two previous examples in this light ...</div><div dir="auto"><br></div><div dir="auto">48 C</div><div dir="auto">28 A>B</div><div dir="auto">24 B</div><div dir="auto"><br></div><div dir="auto">A defeats B with strength 28 winning votes plus 48 losing truncations ... a total strength of 76.</div><div dir="auto"><br></div><div dir="auto">B beats C with 52 wv plus 52 losing truncations ... 104 total.</div><div dir="auto"><br></div><div dir="auto">C beats A with total strength 48 plus 72, or 120.</div><div dir="auto"><br></div><div dir="auto">So again, the Plurality winner C has the strongest defeat over any other candidate by this wv+losing truncations gauge.</div><div dir="auto"><br></div><div dir="auto">Example2:</div><div dir="auto"><br></div><div dir="auto">40 A>B</div><div dir="auto">35 B>C</div><div dir="auto">25 C</div><div dir="auto"><br></div><div dir="auto">A beats B with strength 40 wv plus 25 loser truncations... 65 total.</div><div dir="auto"><br></div><div dir="auto">B beats C with 75 wv plus 40 truncations ... a total strength of 115.</div><div dir="auto"><br></div><div dir="auto">C beats A with 60 wv plus 60 truncations. C wins. </div><div dir="auto"><br></div><div dir="auto">If the C faction truncated A in anticipation of the A faction's burial of C, it worked ... the defensive truncation saved the sincere CW.</div><div dir="auto"><br></div><div dir="auto">This is (arguably) a strategic improvement over our slightly simpler margins (wv minus lv) gauge that I am still recommending.</div><div dir="auto"><br></div><div dir="auto">It's like the difference between an error detecting code and an error correcting code.</div><div dir="auto"><br></div><div dir="auto">-Forest</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Feb 18, 2023, 9:54 AM Colin Champion <<a href="mailto:colin.champion@routemaster.app">colin.champion@routemaster.app</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<font face="Helvetica, Arial, sans-serif">Kristofer - firstly an
apology, I gave the result for Condorcet//fptp rather than
Condorcet,fptp. The correct results are: </font><font face="Helvetica, Arial, sans-serif"> minimax 64%, condorcet+fptp
59%, copeland,fptp 53% (vice 47%).<br>
As for other good, simple methods, I find it hard to say. Lots
of reasonably accurate methods are aesthetically objectionable for
a range of reasons; for instance I think that Condorcet+random is
at least as good as Condorcet+fptp (presumably because it's hard
to manipulate), but no one would be happy to see so prominent a
role given to chance. <br>
'Minisum' - which I think is the same as Tideman's "Simplified
Dodgson Rule" - is almost as good as minimax, but I can't see why
anyone would choose it in preference (it looks rather similar). It
has the drawback of having received little discussion in the
literature.<br>
Copeland,dblv is somewhat better than Copeland,fptp. The double
vote elects the candidate with the greatest sum of first and
second preferences. It's a lousy voting method but an effective
tie-break because it tends to blow up in the face of anyone who
attempts tactical voting. <br>
Copeland,minimax is very good, but again why bother? Its
resistance to tactical voting comes from minimax; Copeland's
method is little more than a sleeping partner. <br>
Copeland//Borda (which is one interpretation of
Dasgupta/Maskin) is probably slightly better than Copeland,fptp.<br>
Benham's method and Black's are both pretty good. So are some
of the more complicated methods such as RP.<br>
<br>
All this subject to the usual caveats about software reliablilty.
The results table is at
<a href="https://www.masterlyinactivity.com/condorcet/condorcet.html#results" target="_blank" rel="noreferrer">https://www.masterlyinactivity.com/condorcet/condorcet.html#results</a><br>
Colin<br>
</font><br>
<div>On 18/02/2023 11:47, Kristofer
Munsterhjelm wrote:<br>
</div>
<blockquote type="cite">On
2/18/23 10:42, Colin Champion wrote:
<br>
<br>
<blockquote type="cite"> But then I don't favour Kristofer's
proposal either. My evaluation suggests that burial is a
particular threat for Condorcet methods, and that in its
presence their accuracies are: minimax 64%, condorcet+fptp 59%,
copeland,fptp 48%. [Usual disclaimers apply.]
<br>
</blockquote>
<br>
That's fair; I was simply trying to find a minimal change to the
method that would at least grant Smith or something like it.
<br>
<br>
Really, what I'm concerned about is that there's such a, for lack
of a better term, steep cliff from the Condorcet domain down to
the Plurality domain. So everything's nice as long as you play on
top of the mountain, but if you misstep (i.e. produce a cycle),
then you don't gradually degrade, you fall directly into plain old
Plurality, with all of its vote splitting problems. The
discontinuity seems like something that's just asking to be
exploited.
<br>
<br>
Do you know of any alternate "bang for the buck" methods that
would be simple enough to be accepted?
<br>
<br>
-km
<br>
</blockquote>
<br>
</div>
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</blockquote></div>