<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
<p>Forest,<br>
<br>
<blockquote type="cite">If I had to narrow it down to three for
public proposal, I would probably choose the same three. DMC
would be right up there too ... in the form of approval based
Benham ... eliminate low approval candidates until an undefeated
candidate remains.
<div dir="auto"><br>
</div>
</blockquote>
I am very pleased that we are in such agreement. But I think
"DMC" is quite a bit worse than ASM and UncApproval. I thought
about it quite a bit a few years ago. <br>
<br>
Beyond being maybe a bit easier to explain and a bit more
appealing to those that love one-at-a-time eliminations, I can't
see any argument that it is better than Smith//Approval.<br>
<br>
I used to sometimes suggest a method that featured trying to help
voters by sometimes "moving" their approval cut-offs. For example
a version of Smith//Approval where ballots <br>
that make no approval distinction among the Smith set candidates
have their cut-offs moved the smallest distance so they do. (In
other words those that originally approved all of<br>
them would now approve all but those they rank above none of the
others and and those that originally originally approved none of
them would now approve those they rank below<br>
no others).<br>
<br>
But now I think (at least for ASM and UncApp) it is better for a
public proposal to pretend that "approval" is sincere and on some
absolute scale and not relative and tactical.<br>
<br>
Another idea I had was to use say 0-100 scoring ballots and
interpret a higher than average score (on the individual ballot)
as approval and an exactly average score as half-approval.<br>
<br>
But needless to say, that would slow down hand-counting a lot.
Also probably a bit too fancy for a public proposal.<br>
<br>
Chris B.<br>
<br>
<br>
</p>
<div class="moz-cite-prefix">On 9/08/2023 9:43 am, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfqRvyNp4xLPt6wAp7_PX41Ujvmxog3LHATckUsSF0OcBQ@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="auto">
<div>If I had to narrow it down to three for public proposal, I
would probably choose the same three. DMC would be right up
there too ... in the form of approval based Benham ...
eliminate low approval candidates until an undefeated
candidate remains.
<div dir="auto"><br>
</div>
<div dir="auto">We called the chain building method </div>
<div dir="auto">Uncovered Approval or unc(approval). Thanks
for dusting it off!</div>
<div dir="auto"><br>
</div>
<div dir="auto">For those not familiar with "chains" ...in the
election methods context a chain is a transitive beatpath
... so each member of the beatpath is beaten by each of its
predecessors ... not only by its immediate predecessor.</div>
<div dir="auto">
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
</div>
<br>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sun, Aug 6, 2023, 2:59
PM C.Benham <<a href="mailto:cbenham@adam.com.au"
target="_blank" rel="noreferrer" moz-do-not-send="true"
class="moz-txt-link-freetext">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"><br>
I think Condorcet methods that don't allow voters to enter
an approval <br>
threshold have to choose between trying to<br>
minimise Compromise incentive or trying to reduce
Defection incentive.<br>
<br>
The methods I like in this category allow voters to rank
however many <br>
candidates they like and also approve all but<br>
one or only one or any number in between of the candidates
(consistent <br>
with their rankings). Equal-ranking is allowed.<br>
<br>
Default approval goes only to candidates ranked below no
other candidate.<br>
<br>
I suggest that voters can just mark one of the candidates
as the lowest <br>
ranked one they approve (i.e. only that candidate<br>
and those ranked higher or equal to it are approved).<br>
<br>
But other ways of doing it could be fine.<br>
<br>
Regarding which algorithm, I very much like Forest's
Sorted Approval <br>
Margins.<br>
</blockquote>
</div>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">Or more commonly, "Approval Sorted Margins"</div>
<div dir="auto"><br>
</div>
<div dir="auto">[A rose by any other name ...]</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">
<br>
I also like another method of his, the exact name of which
I've <br>
forgotten (something about "Chain" building or climbing):<br>
<br>
*Begin the chain with the most approved candidate. Then
add the most <br>
approved candidate that covers that candidate.<br>
Then add the most approved candidate that covers all the
candidates <br>
already in the chain.<br>
<br>
Keep doing that as many times as possible, and then elect
the last added <br>
candidate*.<br>
<br>
I think nearly always this will elect the same candidate
as <br>
Smith//Approval, but is more elegant and ensures that the<br>
winner is Uncovered.<br>
<br>
For a practicable Condorcet method that uses plain ranked
ballots <br>
(equal-ranking and truncation allowed), I like<br>
Smith//Ranked below none minus ranked above none.<br>
<br>
*Eliminate all the candidates not in the Smith set. Give
each remaining <br>
candidate a score equal to the number of ballots<br>
on which it is ranked (among remaining candidates) below
no other <br>
candidate minus the number of ballots on which it<br>
is ranked (among remaining candidates) above no other
candidate.<br>
<br>
Elect the candidate with the highest score."<br>
<br>
Given how rare top cycles will likely be, I think this is
probably good <br>
enough.<br>
<br>
Obviously it meets Plurality. It fails both Minimal
Defense and Chicken <br>
Dilemma, but never both at once :)<br>
<br>
It looks fair and gives a pretty-enough winner. I'll be
back later with <br>
some examples.<br>
<br>
Chris Benham<br>
<br>
<br>
</blockquote>
</div>
</div>
</div>
</blockquote>
</body>
</html>