<div dir="auto">Or maybe it would be safer to say “…the member of the top-cycle who is pairwise-defeated by the candidate whose Borda [or implicit approval] is at or nearest to the middle.</div><div dir="auto"><br></div><div dir="auto">…even though it would sound counter-intuitive.</div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Nov 3, 2023 at 16:30 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">Because BF has one natural defeat & one natural victory. …& CW has two natural victories & one strategic lowering…& Bus has two natural defeats & one strategic raising…</div><div dir="auto"><br></div><div dir="auto">… then regardless of how we compare natural defeat or victory to strategic raising or lowering…</div><div dir="auto"><br></div><div dir="auto">…doesn’t that mean that BF is at the middle?</div><div dir="auto"><br></div><div dir="auto">Then say:</div><div dir="auto"><br></div><div dir="auto">Among the top-cycle, elect the nemesis of the nemesis is the candidate whose Borda [or implicit approval] is at or nearest to the middle [midrange, median or mean] ?</div><div dir="auto"><br></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Nov 2, 2023 at 23:50 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">I strongly agree with everything you said in this message ... including the importance of judicious use of truncations ... especially when approval cutoffs are not allowed.<div dir="auto"><br></div><div dir="auto">And most of the time no sincerity check is needed ... best policy is to elect the Smith candidate most likely to be the "bus" under whom the buriers threw the buried candidate to cause the cycle .... assuming that the most common cause of cycles is insincere order reversals.</div><div dir="auto"><br></div><div dir="auto">That's a controversial assumption, but I now believe that these insincere order reversals are much more common than inconsistent sincere preferences as a cause of these ballot cycles.</div><div dir="auto"><br></div><div dir="auto">Over the years I have contrived my share or scenarios that result in sincere Paper Rock Scissors cycles ... Paper sincerely covers Rock which sincerely smashes Scissors which cuts Paper ... and perfectly plausible issue space examples.</div><div dir="auto"><br></div><div dir="auto">But the insincere burials are easier to engineer ... even by accident ... just innocently pushing your second choice to the bottom of your ballot to give your favorite an edge ... perhaps assuming that as many people do that the same Borda Count used in Sports competitions had something to do with the tally of Condorcet methods like ... Black, Baldwin, and Nanson.</div><div dir="auto"><br></div><div dir="auto">Sincere pairwise beat cycles are not impossible .... but I believe that they are relatively much less likely .... based on the difficultly of them arising naturally as opposed to innocent opportunistic order reversals.</div><div dir="auto"><br></div><div dir="auto">It turns out that Condorcet wv is almost as easy to fool as Norda based Nanson ... two methods that almost always elect the Burier faction candidate as in your example below.</div><div dir="auto"><br></div><div dir="auto">We have devised methods that make burial backfire on the burial faction.</div><div dir="auto"><br></div><div dir="auto">That's good enough for me and you, but some people need more evidence ... and education ....including influential people like Foley and Maskin, who are proposing burial prone Baldwin in place of burial resistant IRV.</div><div dir="auto"><br></div><div dir="auto">I'm simply proposing a way of distinguishing statistically between the relative prevalence of sincere and imsincere pairbeaten cycles.</div><div dir="auto"><br></div><div dir="auto">Here's one test:</div><div dir="auto"><br></div><div dir="auto">As often as possible when an RP Condorcet rules election has no ballot CW ...</div><div dir="auto"><br></div><div dir="auto">Let W be the RP winner. And let X be the Smith candidate with the most losing votes against W. Finally, let Y be the Smith candidate with the fewest losing votes against X.</div><div dir="auto"><br></div><div dir="auto">Suppose the voters have agreed to a two stage runoff for Scientific purpose</div><div dir="auto"><br></div><div dir="auto">The first stage of the runoff is to decidenif there will be a second stage.</div><div dir="auto"><br></div><div dir="auto">If not W retainsbthe win .... and that's that. Otherwise, the final choice is between X and Y.</div><div dir="auto"><br></div><div dir="auto">If the ballots were sincere, then since they say X beats Y, the voters would expect X to win the secomd stage if it were held ... So if the ballot votes were sincere they would prefer not to have the second stage ... so W would retain her wim.</div><div dir="auto"><br></div><div dir="auto">But if X or Y were sincerely preferred over the other two participants in this new tangled runoffbthen the moderately well informed voters will be aware of that .... and the supporters of this "local CW" will willingly support having a second stage knowing that they can win it ... and thereby winvthe election.</div><div dir="auto"><br></div><div dir="auto">So in the long run if more of these RP winners are retained than not ..the null hypothesis of sincere cycle preponderance will be supported.</div><div dir="auto"><br></div><div dir="auto">fws</div></div><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>
<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>
<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>
<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>
<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>
<br>
Electing B here is completely unacceptable. 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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