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<div class="moz-cite-prefix">Thankyou Forest Simmons. It is
appreciated.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">The link is:</div>
<div class="moz-cite-prefix"><a
href="https://www.smashwords.com/books/view/997528">https://www.smashwords.com/books/view/997528</a></div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Richard Lung.</div>
<div class="moz-cite-prefix"><br>
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<div class="moz-cite-prefix">On 19/01/2020 22:30, Forest Simmons
wrote:<br>
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<blockquote type="cite"
cite="mid:CAP29oncXVeQW-F0+5jr716YDjhXvUCoh18e+TgMVbCg_vmoRRQ@mail.gmail.com">
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<div>Fascinating! We need people like you to knock us out of
complacency ... out of the comfortable ruts that we inhabit.</div>
<div><br>
</div>
<div>I look forward to following the link you gave me!<br>
</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, Jan 16, 2020 at 10:25
AM Richard Lung <<a href="mailto:voting@ukscientists.com"
moz-do-not-send="true">voting@ukscientists.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<div>This is obviously a very learned summary that would
require considerable study to do justice to, much more
than my old head is capable of, quite apart from severe
personal distresses, that have been over-whelming our
lives.</div>
<div>Yet, just the other day, after a half century of
amateur study, to my surprise, my naive physicists
mathematical text crawled across the finishing line of
publication. Only the last chapter is of direct interest
to electoral mathematicians. It contains an explanation of
how to conduct a two-dimensional election: FAB STV 2D. <br>
</div>
<div>The two dimensions are Representation and Arbitration.
The latter graphs at 90 degrees (neutrally) to the former,
and the count is conducted without disturbing the normal
one-dimensional count that is FAB STV. But taken together
as a complex variable the count is according to the rules
of complex variables.</div>
<div><br>
</div>
<div>from</div>
<div>Richard Lung.<br>
</div>
<div><br>
</div>
<div><br>
</div>
<div>On 15/01/2020 20:57, Forest Simmons wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">
<div>Just a couple of additional thoughts:</div>
<div><br>
</div>
<div>Besides Arrow and Gibbard-Sattherwaite we have lots
of criterion incompatibility results from Woodall, and
defensive strategy criteria from Mike Ossipoff, Steve
Eppley, et. al.. In particular we never worried about
Later No Help and later No Harm until Woodall came
along. Venzke and Benham picked up the torch and
brought Woodall into the EM Listserv discussion.<br>
</div>
<div><br>
</div>
<div>Many EM contributors have clarified which
combinations of various criteria of more practical
than academic stripe are compatible or not:
Participation, FBC, Precinct Summability, Chicken,
etc. <br>
</div>
<div><br>
</div>
<div>In particular, we now know through the work of
Ossipoff, Venzke, Benham, and others that the Chicken
Defense and Burial Defense (against CW burial) are
incompatible in the presence of Plurality and the the
FBC, unless we allow an explicit approval cutoff or
some other strategic switch on the ballots. Standard
ordinal ballots are not adequate for this even when
truncation and equal rankings (including equal top)
are allowed. A non-standard ballot that allows us to
get compatibility to all of these except the CC is
MDDA(sc) which is Majority Defeat Disqualification
Approval with symmetric completion below the approval
cutoff. This method also satisfies other basic
criteria such as Participation, Clone Independence,
Mono-Raise, Mono-Add, and IDPA, for example.</div>
<div><br>
</div>
<div>In the context of the current discussion, the
approval cutoff or some equivalent strategic switch is
essential for the compatibility of chicken resistance
and burial resistance.. No strategy, no
compatibility. So basically there is no decent method
that is resistant to both Burial of the CW and Chicken
offensives. (IRV is chicken resistant and has a form
of burial resistance, but routinely buries the CW
unless voters strategically betray their favorite to
save the CW. Furthermore, it fails mono-raise.)</div>
<div><br>
</div>
<div>Before collaborative efforts of EM List members
there was no known clone independent, monotonic method
for electing from the uncovered set. The closest
thing was Copeland, which is clone dependent.</div>
<div><br>
</div>
<div>Again the main point is that Arrow, and
Gibbard-Satterthwaite are not the "end of history" for
election methods, just like the collapse of the USSR
was not the end of history as Fukuyama once proclaimed
or Thatcher's famous TINA "there is no alternative"
(to capitalism). Arrow and G-S give very valuable
insights and help us avoid cul-de-sacs, but they are
not the last word in election methods progress. The
"end of history" and TINA slogans are an excuse for
giving up prematurely for lack of imagination. We
cannot allow Arrow and G-S to become excuses for lack
of imagination in Election Methods. What if Yee had
given up before inventing the beautiful Yee diagrams
that constitute an Electo-Kaleidoscope for the study
of election methods analogous to the telesope and the
electron microscope in astronomy as instruments in
other branches of knowledge?<br>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Mon, Jan 13, 2020
at 3:32 PM Forest Simmons <<a
href="mailto:fsimmons@pcc.edu" target="_blank"
moz-do-not-send="true">fsimmons@pcc.edu</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px
0px 0.8ex;border-left:1px solid
rgb(204,204,204);padding-left:1ex">
<div dir="ltr">
<div>Rob,</div>
<div><br>
</div>
<div>Thanks for starting this great thread!</div>
<div><br>
</div>
<div>The "no perfect car" analogy is good. More
definite is the "no 100 percent efficient
internal combustion engine" analogy that follows
from the second law of thermodynamics. It
applies to all kinds of engines, but that
doesn't mean that internal combustion is as good
as it gets.</div>
<div><br>
</div>
<div>If Gibbard-Satterthwaite tells us that we
cannot have all of the nice properties we want
in one election method, that doesn't mean that
one method is as good as the next.</div>
<div><br>
</div>
<div>It follows from Arrow that we cannot have the
Majority Criterion and the IIAC at the same
time, but there are many decent methods (like
River) that do satisfy the MC, and a bunch of
other nice properties, like Monotonicity, Clone
Independence, the Condorcet Criterion, and
Independence from Pareto Dominated Alternatives,
as well as the basic Neutrality and Anonymity
fairness criteria.</div>
<div><br>
</div>
<div>The way to think of Arrow's "Dictator"
theorem is that it is extremely hard to get a
rankings based method with even minimal decency
conditions (like non-dictatorship) without
scuttling the IIAC.</div>
<div><br>
</div>
<div>In other words, no decent ordinal based
method can satisfy the IIAC, which is the same
point of view that Toby and Eppley expressed.
It comes down to the mere existence of a
Condorcet Cycle. Here's the subtle part that
most people don't understand. Condorcet Cycles
can exist in the preference schedules of an
election even if the election method makes no
mention of Condorcet, for example even in
IRV/Hare/STV/RCV elections:</div>
<div><br>
</div>
<div>45 A>B>C</div>
<div>20 B>C>A</div>
<div>35 C>A>B</div>
<div><br>
</div>
<div>There exists a majority preference cycle
A>B>C>A even though it causes no
problem for IRV, since B is eliminated and then
C is the majority winner between the two
remaining candidates.</div>
<div><br>
</div>
<div>Now let's check the IIAC. Suppose that A,
one of the losers withdraws from the race. Then
the winner changes from C to B, since B beats C
by a majority. This shows that IRV does not
satisfy the IIAC, because removing a loser from
the ballot changes the winner.</div>
<div><br>
</div>
<div>But this is not just a problem for IRV, it's
a problem for any method that respects the
Majority Criterion; if the method makes A the
winner, then removing B changes the winner. If
it makes B the winner, then removing C changes
the winner. If it makes C the winner, then (as
we saw in the case of IRV above) removing A
changes the winner. to B.</div>
<div><br>
</div>
<div>So Arrow's "paradox" can be considered as
forcing us to realize that the IIAC is not a
realistic possibility in the presence of ordinal
ballots because such ballots allow us to detect
oairwise (head-to-head) preferences, and when it
comes down to a single pair of candidates the
Majority Criterion says the pairwise winner must
be chosen,<br>
</div>
<div><br>
</div>
<div>However, as someone mentioned, Approval
Voting avoids this "paradox" once the ballots
have been submitted, since the Approval winner A
is always the "ballot CW," and in two different
ways:(1) For any other candidate X, candidate A
will be rated above X on more ballots than not,
and (2) A's approval score will be higher than
the sore of any other candidate. From either
point of view, if we remove a loser Y from the
ballots, then A will still be the winner
according to the same ballots with Y crossed
out.</div>
<div><br>
</div>
<div>That's at the ballot level. But if Y
withdrew before the ballots were filled out, it
could change the winner, because if Y were the
only approved candidate for a certain voter
before the withdrawal, that voter might decide
to lower her personal approval cutoff before
submitting her ballot. Or she could raise the
cutoff if Y had been the only disapproved
candidate.<br>
</div>
<div><br>
</div>
<div>As others have mentioned in this discussion,
Approval Voting externalizes the problem of the
IIAC from being a decision problem for the
method itself to a strategical decision problem
for the voter. A voter might think of that as an
unfair burden.</div>
<div><br>
</div>
<div>One answer to this problem could be DSV
(Designated Strategy Voting): You submit your
sincere ratings, and the DSV machine applies a
strategy of your choice or a default strategy to
transform the ballots into approval style
ballots. Rob LeGrand explored some of the
possibilities and limitations of this approach
in his master's thesis. He doesn't claim to
have exhausted the possibilities. (I also have
some ideas in this vein that still need
exploring.)</div>
<div><br>
</div>
<div>What constitutes a "sincere rating." One
approach to that has already been mentioned in
the ice-cream flavor context in this thread.
Another is to use as a rating for candidate X
your subjective probability that on a typical
issue of any significance candidate X would
support the same side you support.<br>
</div>
<div><br>
</div>
<div>It's not just Approval that requires some
hard thinking in conjunction with filling out
the ballots. Ranking many candidates (think
about the number of candidates in the election
that propelled Schwarznegger into office) may be
just as burdensome as trying to decide exactly
which candidates to mark as approved. In
Australia you can get around this difficulty by
copying "candidate cards" or by voting the party
line. Presumably these experts are reflecting
state of the art strategy in their rankings ...
the strategy that is indispensable for optimum
results according to Gibbard-Satterthwaite.
This is not just a problem of Approval, though
it may seem worse in Approval. In actuality,
aoproval and score/range are the only commonly
used methods where optimal strategy never
requires you to "betray " your favorite.<br>
</div>
<div><br>
</div>
<div>To cut the Gordian knot of this complexity
Charles Dodgson (aka Lewis Carroll) suggested
what we now call Asset Voting. Each Voter
delegates her vote to the candidate she trusts
the most to rep[resent her in the decision
process. Since write-ins are allowed, she can
write in herself if she doesn't trust anybody
else to be her proxy. These proxies get
together with their "assets" (delegated votes)
and choose a winner by use of some version of
Robert's Rules of Order.</div>
<div><br>
</div>
<div>Which criteria are satisfied by this method?
Does Gibbard Satthethwaite have anything to say
about it? How about Arrow? For that matter does
first past the post plurality satisfy the IIAC?
(No more or less than Approval in reality.)<br>
</div>
<div><br>
</div>
<div>Let's talk about Gibbard-Satterthwaite. Is
there any incentive for a person to delegate as
proxy someone other than her favorite? <br>
</div>
<div><br>
</div>
<div>If we are talking representative democracy,
then why would you want to delegate your vote to
candidate B when candidate A was the one you
trusted most to represent you in making
important decisions once in office?</div>
<div><br>
</div>
<div>All of the "problems" with the method are
essentially externalized to the deliberations
governed by"Robert's Rules of Order" in the
smoke filled room.<br>
</div>
<div><br>
</div>
<div>Gibbard-Satterthwaite is taken to say that it
is impossible to obtain sincere preferences or
sincere utilities from voters in the context of
full information (or disinformation) elections.
Yet it turns out to be relatively easy; you just
need to separate the ballot into two parts. The
first part requires strategic voting to pick the
two alternatives as finalists. The second part
is used solely to choose between these two
options. (In the case of cardinal ballots the
finalists are lotteries.) A version of the
uncertainty principle obtains here: if you use
the sincere ballots for any other instrumental
purpose than to choose between the two
finalists, then you almost certainly destroy
their sincerity.</div>
<div><br>
</div>
<div>However there would be no problem comparing
tthe sincere part with the strategical part to
get statistics about voters' willingness to vote
insincerely in choosing the finalists. <br>
</div>
<div><br>
</div>
<div>Another avenue that has been barely explored
is the use of chance to incentivize consensus
when there is a potential for it.</div>
<div><br>
</div>
<div>For example, suppose that preferences are</div>
<div><br>
</div>
<div>60 A>C>>>>B</div>
<div>40 B>C>>>>A</div>
<div><br>
</div>
<div>Under approval voting the A faction has a
strong incentive to downgrade C and vote 60
A>>>>>C>B making A the
(insincere) approval winner as
Gibbard-satterthwaite would predict.</div>
<div><br>
</div>
<div>However, if the rules said that in the
absence of a full consensus approval winner, the
winner would be chosen by random ballot, then
(assuming rational voters voting in their own
interest) C would be the sure outcome; no
rational voter in either faction would prefer
random ballot expectations over a sure deal on
C.</div>
<div><br>
</div>
<div>Jobst Heitzig is the pioneer in this area.</div>
<div><br>
</div>
<div>In sum, Arrow, <a href="http://et.al"
target="_blank" moz-do-not-send="true">et.al</a>.
should not constitute a nail in the coffin of
creative progress in Election Methods. IMHO
that is an important message we need to send if
we want to attract new talent.</div>
<div><br>
</div>
<div>Forest<br>
</div>
<div><br>
</div>
<div><br>
</div>
<br>
<div class="gmail_quote"><br>
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