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<div class="moz-cite-prefix">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 class="moz-cite-prefix">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 class="moz-cite-prefix">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 class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">from</div>
<div class="moz-cite-prefix">Richard Lung.<br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">On 15/01/2020 20:57, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAP29ondZVZJoURj6O5CrgCfgV+3ojSUofx80PXg+vns5ev+NBw@mail.gmail.com">
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<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"
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>
</div>
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