<div dir="auto">So that suggests that, for SP, agenda-ordered by Borda or implicit approval, would, in the strategic top-cycle, start by comparing CW & BF.</div><div dir="auto"><br></div><div dir="auto">BF wins that comparison, & goes against Bus. </div><div dir="auto"><br></div><div dir="auto">Bus wins.</div><div dir="auto"><br></div><div dir="auto">The burial is penalized.</div><div dir="auto"><br></div><div dir="auto">The familiar, widely used & precedented SP is autodeterrent.</div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, Nov 4, 2023 at 10:20 Michael Ossipoff <<a href="mailto:email9648742@gmail.com">email9648742@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto">Referring to what I was saying about the order of the 3 too-cycle candidates’ Borda or implicit approval:</div><div dir="auto"><br></div><div dir="auto">I told why I claim that BF is the most likely one to be middle. </div><div dir="auto"><br></div><div dir="auto">So what’s the most likely order for the top & bottom of that ordering?</div><div dir="auto"><br></div><div dir="auto">Well, top & bottom are the most extreme difference in the ordering “. So, isn’t that difference more likely to not contradict a pairwise defeat?</div><div dir="auto"><br></div><div dir="auto">Together, those two facts suggest that the most likely order for the 3 candidates’ Borda or implicit approval is:</div><div dir="auto"><br></div><div dir="auto">Bus>BF>CW.</div><div dir="auto"><br></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Nov 3, 2023 at 06:35 Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" target="_blank">forest.simmons21@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto"><div><br><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Oct 30, 2023, 6:21 PM C.Benham <<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><u></u>
<div>
<p><br>
Why do we support the Condorcet criterion? For me there are three
reasons:<br>
<br>
(1) Failure to elect a voted CW can give the voters who voted the
CW over the actual winner<br>
a potentially very strong, difficult (if not impossible ) to
answer complaint.<br>
<br>
And those voters could be more than half the total.<br>
<br>
(2) Always electing a voted CW is (among methods that fail
Favorite Betrayal) is the best way to minimise<br>
Compromise incentive.<br>
<br>
(3) Limited to the information we can glean for pure ranked
ballots (especially if we decide to only refer<br>
to the pairwise matrix), the voted CW is the most likely utility
maximiser.<br>
<br>
If there is no voted CW , then the winner should come from the
Smith set. Condorcet is just the logical<br>
consequence of Smith and Clone Independence (specifically
Clone-Winner).<br>
<br>
Some methods are able to meet Condorcet but not Smith, but
hopefully they get something in return.<br>
(For example I think Min Max Margins gets Mono-add-Top and maybe
something else).<br>
<br>
So coming to the question of which individual member of the Smith
set should we elect, I don't see that a<br>
supposed, guessed-at "sincere CW" has an especially strong claim,
certainly nothing compared to an actual<br>
voted CW.<br>
<br>
Suppose sincere looks like:<br>
<br>
49 A>>>C>B<br>
48 B>>>C>A<br>
03 C>A>>>B<br></p></div></blockquote></div></div><div dir="auto">My favorite burial proof method is to elect the nemesis of the nemesis of the (repeated) Submidway Approval Elimination winner.</div><div dir="auto"><br></div><div dir="auto">Max Approval is 52</div><div dir="auto">Min Approval is 3</div><div dir="auto">Midway is 27.5</div><div dir="auto"><br></div><div dir="auto">So we eliminate C.</div><div dir="auto"><br></div><div dir="auto">Updating approvals we have 52 for A and 48 for B. Midway is 50. B is the only Sub Midway candidate so A is the SubMidway Approval winner.</div><div dir="auto"><br></div><div dir="auto">The nemesis of A is C, and C has no nemesis because it not pairbeaten. We respect the Condorcet Criterion and elect C, a very weak CW.</div><div dir="auto"><br></div><div dir="auto">There is no way out of it if we want a Condorcet Criterion Compliant method.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><p>
<br>
Suppose that all voters get about the same utility from electing
their favourites. In that case A is the big utility<br>
maximiser.<br>
<br>
Now suppose that this is say the first post-FPP election, and the
voters are all exhorted to express their full<br>
rankings, no matter how weak or uncertain some of their
preferences may be, because we don't want anything <br>
that looks like the (shudder) "minority rule" we had under FPP.<br></p></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">This reminds me of the practice omanipulative judges in the US warning jurors to ignore their sacred right of "Jury Nullification" (inherited from English Common Law).</div><div dir="auto"><br></div><div dir="auto">Those lying (by intimidation) judges are a disgrace to their office ... and should be stripped of their holy robes ... imho.</div><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><p>
<br>
So they vote:<br>
<br>
49 A>C<br>
48 B>C<br>
03 C>A<br>
<br>
C is the voted CW. For some pro-Condorcet zealots, this is ideal.
No sincere preferences were reversed or <br>
"concealed", resulting in the election of the "sincere CW".<br>
<br>
(In passing I note that in most places if the non-Condorcet method
IRV/RCV were used, A would be uncontroversially<br>
elected probably without anyone even noticing that C is the CW.)<br>
<br>
Backing up a bit, suppose that instead of the voters being
exhorted to fully rank no-matter-what, they are given the<br>
message "this election is for a serious powerful office, so we
don't want anything like GIGO ("garbage in, garbage out")<br>
so if some of your preferences are weak or uncertain it is quite
ok to keep them to yourself via truncation or equal-ranking."<br></p></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">That warning should be mandatory ... as should an honest effort to "fully inform" a jury of their most sacred rights predatimg even the Magna Carta.</div><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><p>
<br>
So they vote:<br>
<br>
49 A<br>
48 B<br>
03 C>A<br>
<br>
Now the voted CW is A. Should anyone be seriously concerned
that, due to so many voters truncating, that some other<br>
candidate might actually be the "sincere CW"?<br></p></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Your example shows the wisdom of electing the ballot CW when there is one.</div><div dir="auto"><br></div><div dir="auto">In fact, all of our burial resistant methods elect the voted CW when one exists. But when one does not exist we suspiciously suspect that its absence was most likely caused by subversion of a CW, since that is by far the easiest way to create a beat cycle ... whether innocently or with "malice aforethought."</div><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><p>
<br>
For me, if voters have the freedom to fully rank but for whatever
reason choose to truncate (and/or equal-rank, assuming that<br>
is allowed) a lot of that is fine and the voting method should
prefer not to know about weak and uncertain preferences.<br>
<br>
The type of insincere voting that most concerns me is that which
produces outrageous failure of Later-no-Help, achieving by
order-reversal<br>
Burial what could not have been done by simple truncation.<br>
<br>
46 A<br>
44 B>C (sincere is B or B>A)<br>
10 C<br></p></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Let's see what our Sub Midway Approval Elimination burial resistant method does here:</div><div dir="auto"><br></div><div dir="auto">The respective max and min implicit approval scores are 54 for C and 44 for B. So Midway is 49. Both A and B have Sub Midway Approval leaving C as the candidate whose nemesis's nemesis we should elect.</div><div dir="auto"><br></div><div dir="auto">C's nemesis is B, and B's nemesis is A.</div><div dir="auto"><br></div><div dir="auto">So A is the winner of our burial resistant method.</div><div dir="auto"><br></div><div dir="auto">How does this work?</div><div dir="auto"><br></div><div dir="auto">Well, Nanson is very good at fingering the Burial Faction Favorite, but Poor man's Nanson aka SubMidApproval Elimination is even better at electing the BFF than ordinary Nanson or RP wv, although they are both pretty good at it as this example shows.</div><div dir="auto"><br></div><div dir="auto">Once you have the likely BFF you can follow the cycle forward one or backward two candidates to the "bus" under which the buried candidate was buried. </div><div dir="auto"><br></div><div dir="auto">[Electing this "bus" is what makes the method backfire on the burying faction ... so electing the strongest bus (their could be a clone set of them) is the proper aim of a good burial proof method designer ... to completely deter potential subverters from even flirting with the idea.]</div><div dir="auto"><br></div><div dir="auto">Like I said you can go in either direction around the cycle to get to a "bus" from the BFF candidate .... but it's better psychologically to elect the syrongest wv defeater of the strongest wv defeater of the Nanson winner .... as opposed to saying "Elect the candidate with the most losing votes against the Nanson winner" .. they are almost always the same candidate even when Smith has more than three members.</div><div dir="auto"><br></div><div dir="auto">Like I say, SubMidAolroval Elimination is more reliable than even ordinary Nanson or RP wv at finding the BFF candidate. But for the curjous, you can always do a sincere runoff between the likely strongest Bus (the nemesis of the nemesis of the likely BFF), and the Smith candidate with the fewest losing votes against it (i.e.against the bus) the same as the weakest Smith weakest Smith candidate to defeat the BFF.</div><div dir="auto"><br></div><div dir="auto">[It is easy to show that a subverted CW always defeats the BFF, which beats the bus that beat the buried candidate that precipitated the insincere cycle resulting from the burial.]</div><div dir="auto"><br></div><div dir="auto">In this example the sincere runoff (were that option to be taken) would be between the Bus A and the Smith candidate B with the fewest losing votes to it A.</div><div dir="auto"><br></div><div dir="auto">For the sincere winner of this runoff we have to go clear back to the original scenario. And it turns out that A is the sincere winner of the runoff, because C, the sincere CW was acting more like a BFF ... so not a finalist in the runoff!</div><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><p>
<br>
Electing B here is completely unacceptable. </p></div></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Right, and now we have a method designed to automatically avoid that kind of mistake.</div></div><div dir="auto"><div dir="auto"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><p>Regardless of whether
or not the B>C voters are sincere, there isn't any case that B
has a stronger<br>
claim than A.<br>
<br>
I don't like (but it can sometimes be justified) a larger faction
being stung by a successful truncation Defection strategy of a
smaller one, but apart<br>
from that I consider a lot of truncation to be normal, natural and
mostly desirable.<br>
<br>
More later.</p>
<p>Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
</p><blockquote type="cite"><b style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial">Forest
Simmons</b><span style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline!important;float:none"><span> </span></span><a href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Benefit%20of%20a%20doubt%20runoff%20challenge&In-Reply-To=%3CCANUDvfru_xs%2BEE6kd7Xbb4p%2Bsh3Zijqy-yCmBwNPOdwLP1emgQ%40mail.gmail.com%3E" title="[EM] Benefit of a doubt runoff challenge" style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal" rel="noreferrer" target="_blank">forest.simmons21
at gmail.com</a><br style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial">
<i style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial">Sun
Oct 29 21:30:58 PDT 2023</i>
<hr style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;text-decoration-style:initial;text-decoration-color:initial">
<pre style="white-space:pre-wrap;color:rgb(0,0,0);font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;text-decoration-style:initial;text-decoration-color:initial">Are the beatcycles that sometimes arise from expressed ballot preferences
... are these cycles more likely to arise from occasional inevitable
inconsistencies inherent in sincerely voted ballots? ... or from ballots
that reflect exaggerated preferences from attempts to improve the election
outcome over the one likely to result from honest, unexagerated ballots (?)
Should Condorcet methods be designed on the assumption that most ballot
cycles are sincere? .... or on the assumption that most are the result of
insincere ballots (?)
Some people think that the question is irrelevant ... that no matter the
answer, the best result will be obtained by assuming the sincerity of the
voted ballots. Others think healthy skepticism is necessary for optimal
results. What do you think?</pre>
</blockquote>
<br>
<p></p>
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