<div><br></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Jun 21, 2024 at 17:22 Chris Benham <<a href="mailto:cbenhamau@yahoo.com.au">cbenhamau@yahoo.com.au</a>> .</div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto">
<br>
I can understand voted Smith-set fundamentalism, and that is
expensive enough.</div></blockquote><div dir="auto"><br></div><div dir="auto">It a avoids the possible embarrassment of electing a Condorcet loser, with the likely resulting repeal. Maybe some additional desired criteria are gained too.</div><div dir="auto"><br></div><div dir="auto">RP(wv) & Schulze do even better, with their clone-independence, & probably various other criterion-gains.</div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto"> But if there is a top cycle I don't share the
mind-set "Probably there is a sincere CW (concealed by strategic
truncation or order-reversal) and our top priority should be to
infer or guess who that is and elect him/her." There may well be no
sincere CW or a higher SU candidate. So quite nice, but mainly just
a marketing benefit.</div></blockquote><div dir="auto"><br></div><div dir="auto">No. Available evidence, including thousands of CIVS polls, indicates that sincerely-voted top-cycles are rare. It isn’t speculation. It’s experience.</div><div dir="auto"><br></div><div dir="auto"> Because any top-cycle is almost surely strategic, & because allowing offensive strategy to defeat a sincere CW (with the consequent defensive-strategy-need) results in big problematic defensive-strategy-need…</div><div dir="auto"><br></div><div dir="auto">…& because it doesn’t make a whole hell of a lot of difference who wins in a sincerely-voted circular-tie…</div><div dir="auto"><br></div><div dir="auto">…then yes, what matters is, as well as possible, preventing offensive-strategy from talking the win away from a sincere-CW.</div><div dir="auto"><br></div><div dir="auto">The wv Condorcet methods excellently achieve that….resulting in a fully strategy-free method</div><div dir="auto"><br></div><div dir="auto">…by which I mean, a method with which no defensive-strategy is needed. </div><div dir="auto"><br></div><div dir="auto">…the achievement of the Condorcet ideal.</div><div dir="auto"><br></div><div dir="auto">…&, in general, the ideal goal of voting system reform.</div><div dir="auto"><br></div><div dir="auto">The best wv Condorcet methods that I’ve heard of are:</div><div dir="auto"><br></div><div dir="auto">RP(wv)</div><div dir="auto">Schulze</div><div dir="auto">MinMax(wv)</div><div dir="auto">Smith//MinMax(wv)</div><div dir="auto"><br></div><div dir="auto">RP(wv) Schulze meet the most criteria.</div><div dir="auto"><br></div><div dir="auto">Those methods achieve the ideal by two properties.</div><div dir="auto"><br></div><div dir="auto">1. Minimal-Defence Criterion compliance </div><div dir="auto"><br></div><div dir="auto">2. Autodeterence</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto"><br>
<br>
Of course I agree with the value of "reduced strategic incentives".<br>
<br>
<blockquote type="cite">
<pre>In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there.</pre>
</blockquote>
They "won't" because it isn't even possible to imagine any "other
considerations".<br>
<br>
In reference to my example showing MDDA 2 failing Mono-add-Plump:<br>
<br>
<blockquote type="cite">
<pre>The voters' behavior had a side effect of strengthening B.</pre>
</blockquote>
No, it just had the "side effect" of exposing the method's perverse
stupidity.<br>
<br>
<blockquote type="cite">
<pre>All sorts of monotonicity failures take such an appearance.
</pre>
</blockquote>
None anything like as starkly. And without some excuse we avoid
them. IRV used to be ridiculed for failing mono-raise (then just
called "Monotonicity"), but we know that it isn't possible to fix
that without losing other criterion compliances that some people
like.<br>
But again, I can't believe that we have to put up with failure of
Mono-add-Plump in order to get anything desirable.<br>
<br>
<blockquote type="cite">
<blockquote type="cite">
<pre>In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
</pre>
</blockquote>
<pre>But given their compatibility, isn't that a strange thing to say?
</pre>
</blockquote>
Not really. The criterion can have nothing to say against candidate
X in some ballot profile but then if we modify that profile by just
adding ballots the plump for X it can decide that X is no longer
acceptable. That is what I meant by the "concept". The two criteria
are compatible because there are other candidates and GMC doesn't
say that X has to win in the original profile. Purely
strengthening X (by stuffing extra X-plumping ballots into the
ballot box) can, according to the criterion. change X from a
candidate that is not disqualified into one that is. That makes the
criterion silly and unacceptable. <br>
<br>
Because of mutual criteria incompatibilities, we can sometimes make
a case for a (at least in some way) silly method. But there is no
need or excuse for a silly criterion.<br>
<br>
<blockquote type="cite">
<blockquote type="cite">
<pre>I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
*Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.*
</pre>
</blockquote>
<pre>It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
</pre>
</blockquote>
I see. Then substitute the Strong Defensive Strategy Criterion for
SFC. <br>
<br>
<a href="https://electowiki.org/wiki/Strategy-free_criterion" target="_blank">https://electowiki.org/wiki/Strategy-free_criterion</a><br>
<br>
<blockquote type="cite"><span style="color:rgb(32,33,34);font-family:sans-serif;font-size:14px;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(249,249,249);text-decoration-style:initial;text-decoration-color:initial;display:inline!important;float:none">If
a Condorcet candidate exists, and if a majority prefers this
candidate to another candidate, then the other candidate should
not win if that majority votes sincerely and no other voter
falsifies any preferences.</span></blockquote>
<br>
I think that is very similar to the Generalised Majority Criterion,
enough for me to reject it on the same grounds. And even if I didn't
have that criticism, I don't see why it's something we should care
much about. It looks like something contrived just to serve as
ammunition against Hare and Margins. (And possibly the similar GMC
was contrived just to help promote the Schulze method.)<br>
<br>
Putting back my "celebrated" example from December 2008:<br>
<br>
<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">25: A>B
26: B>C
23: C>A
04: C
78 ballots (majority threshold = 40)
B>C 51-27, C>A 53-25, A>B 48-26. Implicit Approval scores: C 53, B 51, A 48.
All the candidates have a majority-strength defeat, so none are eliminated and the most approved candidate, C, wins.
Say we now add 22 ballots that all plump (i.e. bullet vote) for C:
25: A>B
26: B>C
23: C>A
26: C
100 ballots (majority threshold = 51)
B>C 51-49, C>A 75-25, A>B 48-26. Implicit Approval scores: C 75, B 51, A 48.
Now only B is without a "majority-strength defeat", so the winner changes from C to B.
Of course the method also fails Irrelevant Ballots Independence. If we now add 3 ballots that plump for X, the majority threshold rises to 52 and so C's majority-strength defeat goes away and C wins again by being the most approved candidate.</pre>
As I also wrote then:<br>
<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"><blockquote type="cite"><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">As I hope some may have guessed from the spectacular failure of Mono-add-Plump, the GMC
concept is grossly unfair to truncators. And Winning Votes (as a GMC complying method) is
unfair to truncators.
Say the 26C "we're just here to elect C and don't care about any other candidate" voters use a
random-fill strategy, each tossing a fair coin to decide between voting C>B or C>A; then even if as
few as 4 of them vote C>A they will elect C. Their chance making C the decisive winner is 99.9956%
(according to an online calculator).
I have some sympathy with the idea of giving up something so as to counter order-reversing buriers,
but not with the idea that electing a CW is obviously so wonderful that when there is no voted CW
we must guess that there is a "sincere CW" and if we can infer that that can only (assuming no voters
are order-reversing) be X then we must elect X.</pre>
</blockquote>All that also applies to MDDA 2 and SFC. Take the case where of the original 26 C plumbers, 4 vote C>A and the rest vote C>B.
25: A>B
26: B>C
27: C>A
22: C>B
100 ballots (majority threshold = 51)
B>C 51-49, C>A 75-25, A>B 52-48. Implicit Approval scores: C 75, B 51, A 52.
No candidate has sub-majority approval and no candidate has a majority-strength defeat so the MDDA 2 winner is the most approved candidate, C.
Chris B.
</pre>
<br>
<div>On 21/06/2024 9:32 pm, Kevin Venzke
wrote:<br>
</div>
<blockquote type="cite">
<pre>Hi Chris,
</pre>
<blockquote type="cite">
<pre>On Mono-add-Plump as a weak version of Participation:
</pre>
<blockquote type="cite">
<pre>Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking.
</pre>
</blockquote>
<pre>
What sort of "trouble"? I don't see how your conclusion follows from
your premise. Why do "almost all proposals fail Participation"? It
isn't because there is anything inherently wrong with "that kind of
thinking". It is because it just happens that Participation is very
expensive (in terms of other desirable criterion compliances, such as
Condorcet). But in that way Mono-add-Plump is very very cheap (if not
free), and some of us are currently "in trouble" due to disregarding
"this kind of thinking".
</pre>
</blockquote>
<pre>What I'm saying is that if we pursue criteria in the vein of Participation (or
monotonicity), we cut down the list of methods we can consider, and we aren't
necessarily getting anything of value except that fewer people can call the method
absurd. What I call inherently of value would be things like sincere Condorcet
efficiency or reduced strategic incentives.
</pre>
<blockquote type="cite">
<pre>Suppose a mini-bus with a driver is contracted to pick up a group of
people and take then on a trip to one of X, Y or Z after polling the
passengers on their ranking-preferences among these alternative
destinations. After the bus is nearly full it is mistakenly assumed that
there will be no more passengers and the driver applies some algorithm
to the rankings of those present and announces that winning alternative
is X.
Then it is learned that there are two more passengers to come to fill up
the bus. They do so and the driver says to them "I've polled all the
other passengers and at the moment the winning destination is X. Where
would you like to go?" and they reply "X is our first preference and Y
wouldn't be too bad and we are very glad we aren't gong to Z".
The driver replies "You prefer Y to Z? In that case the new winning
alternative is Y". Now if these two voters (and perhaps others whose
first preference was X) were enlightened election-method experts, they
might think "Obviously this fellow's election-method algorithm fails
Participation (and presumably Later-no-Harm). Perhaps it meets
Condorcet, which we know is incompatible with both Participation and
Later-no-Harm. Perhaps before we showed up there was a top cycle and our
Y>Z preferences turned Y into the Condorcet winner.
But we know that Condorcet is also incompatible with Later-no-Help so us
revealing our second preferences could have just as likely helped us, so
I suppose we were just unlucky."
Or if they were not experts but charitably minded they might think "I
suppose it is possible that this fellow made an honest mistake due to
him being thick and us confusing him with too much information".
Now replay this scenario except this time the new passengers just say
"Great! We just really want to go to X and we don't know or care about
any other destination." And then the driver says "In that case the
winning alternative changes from X to Y".
The response could only be that the destination-decider (supposedly
purely based on the passengers' stated preferences) is insane (or
malevolent, in any case illegitimate) and that Y is obviously an
illegitimate winner.
Did you notice a very different vibe from the first case, which was a
failure of Participation and Mono-add-Top but not Mono-add-Plump?
</pre>
</blockquote>
<pre>The difference in vibe is quite similar to your own difference in vibe when you
compare these situations.
In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there. And that's
fine, that is their right.
</pre>
<blockquote type="cite">
<pre>In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
</pre>
</blockquote>
<pre>But given their compatibility, isn't that a strange thing to say?
</pre>
<blockquote type="cite">
<pre>Your new MDDA 2 method fails the example I gave:
25 A>B
26 B>C
23 C>A
04 C
(78 ballots, majority threshold = 40)
Implicit approval scores: C 53, B 51, A 48. No candidate is
disqualified due to sub-majority approval.
B>C 51-27, C>A 53-25, A>B 48-26. All candidates have a
"majority" strength defeat, so it "isn't possible" to disqualify any
candidate on that basis. So, according to the rules of MDDA 2, we elect
the most approved candidate, C.
Now say we add 22 ballots that plump for C to give:
25 A>B
26 B>C
23 C>A
26 C
(100 ballots, majority threshold = 51)
Implicit approval scores: C 75, B 51, A 48. Now A has sub-majority
approval and so is disqualified.
B>C 51-49, C>A 75-25, A>B 48-26. Now C and A have
majority-strength defeats and B doesn't, so (according to the rules of
MDDA 2), A (again) and C are disqualified leaving B as the new winner.
The contention that C is the right winner when there were just 78
ballots but when we add 22 ballots that plump (bullet vote) for C the
right winner is no longer C is .... completely crazy.
</pre>
</blockquote>
<pre>The voters' behavior had a side effect of strengthening B. All sorts of monotonicity
failures take such an appearance.
And again, there could be differences in severity, e.g. what percent of voters think
a given phenomenon is absurd. But I don't find that very interesting because it
doesn't tell us about the merits of the method. It's basically marketability.
</pre>
<blockquote type="cite">
<blockquote type="cite">
<pre>Well, in an environment where the concept of "median voter" is likely
to be meaningful,...
</pre>
</blockquote>
<pre>
What "environment" is that? And why is that the environment the one we
should primarily focus on?
</pre>
</blockquote>
<pre>One where voter and candidate preferences can be explained by an underlying issue
space. In this case if you could project everyone onto a plane or spectrum it would
be a bit easy to find the median voter and their preferred candidate.
I think this usually describes public elections, but it probably wouldn't cover a
vote on what color is the best, or a vote on what cuisine to have delivered. So I
think we should probably have IIB for those cases.
</pre>
<blockquote type="cite">
<pre>I think that is the sort of thinking that
leads some people to support Median Ratings methods, which we know are
garbage because they fail Dominant Candidate and Irrelevant Ballots
Independence, and the voters have a strong incentive to just submit
approval ballots (giving the same result as Approval). And it has led
you to the absurdity of suggesting a method that fails Mono-add-Plump.
</pre>
</blockquote>
<pre>Not at all, median rating methods aren't motivated by the notion of a single median
voter. There are multiple median voters on different posed questions, and that's
true on a pairwise matrix as well.
</pre>
<blockquote type="cite">
<pre>I think for the purposes of properly analysing single-winner election
methods and inspiring the invention of new ones, we can and should do
without criteria that refer to irrelevant ballots dependent "majority"
thresholds or pairwise defeats. Those have almost no positive point
aside from marketing.
</pre>
</blockquote>
<pre>You're saying that criteria directly specifying "majority" and not something else
is what lacks positive points aside from marketing? That could be true.
</pre>
<blockquote type="cite">
<pre>My suggestion for something as close as possible to Minimal Defense:
*If the number of ballots that vote X above bottom and Y no higher than
equal-bottom is greater than Y's maximum pairwise support, then Y can't
win.*
</pre>
</blockquote>
<pre>I don't hate that. I don't know what you gain from using "max pairwise support"
instead of "votes in total."
</pre>
<blockquote type="cite">
<pre>I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
*Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.*
</pre>
</blockquote>
<pre>It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
</pre>
<blockquote type="cite">
<pre>That already inspires a simple method suggestion: DDI,MMM: *Elect the
candidate not disqualified by Double-Defeat (Implicit) that is highest
ordered by MinMax(Margins).*
What do you think of that?
</pre>
</blockquote>
<pre>I don't like it but it might be fine.
</pre>
<blockquote type="cite">
<pre>And what is wrong with your "Improved
Condorcet Approval" method ? I think it would be good using
unrestricted ranking ballots with an explicit approval cutoff.
</pre>
</blockquote>
<pre>ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my recent simulations
on frontrunner truncation strategy, C//A is among the best Condorcet methods. In
random elections I am disturbed that ICA and C//A are worse than WV methods at
strong FBC (i.e. what I call compromise incentive).
You've asked me many times about C//A(explicit) and I still think it's bad. The
entire notion of C//A(implicit) being good at deterring burial is based on the
fact that if you use burial to prevent there from being a Condorcet winner, then in
the "cycle resolution" you cannot prefer any candidate to the one you raised
insincerely.
In C//A(explicit), burial only backfires if it actually creates a fake CW. Creating
a fake cycle is never bad for your favorite.
Kevin
<a href="http://votingmethods.net" target="_blank">votingmethods.net</a>
</pre>
</blockquote>
</div>
</blockquote></div></div>