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Warren,<br>
<br>
<div class="subject root grey">Re: [EM] DH3 pathology, margins, and
winning votes </div>
<br>
<div class="msgarea">--- In <a
href="/group/RangeVoting/post?postID=lfm7r44oVHeqAwJVUzmNsGZyibO7IswY4QcxzZBUtvgkd0D15Y3bSXe8_t8GbESVUr3uA34RVtMu3KfNeWtKCcuh-v0hUw">RangeVoting@yahoogroups.com</a>,
Chris Benham <a class="moz-txt-link-rfc2396E" href="mailto:chrisjbenham@..."><chrisjbenham@...></a> wrote:<br>
><br>
> Warren,<br>
> I have two main points in reply to your "DH3 pathology"
anti-Condorcet<br>
> argument.<br>
><br>
> > DH3 scenario with strategic votes by the A- and B-voters.
#voters<br>
> > Their Vote<br>
> > 37 C>A,B>D<br>
> > 32 A>D>B,C<br>
> > 31 B>D>A,C<br>
> ><br>
> > Then the pairwise tallies are going to be:<br>
> ><br>
> > Definitely A,B > D > C<br>
> > Probably C > A,B<br>
> ><br>
> > In which case we (probably) have a Condorcet cycle scenario.
(It is<br>
> > actually two 3-cycles which share the common DC arc.) The
weakest<br>
> > defeats in these cycles are C>A,B which means, under both
every<br>
> > Condorcet rule I know of (since I think they all are
equivalent in the<br>
> > 3-cycle case) and Borda, that one of {A,B} is going to be the
winner.<br>
> ><br>
> > I verified that A wins in the 50-50 mixture case under
Tideman ranked<br>
> > pairs <RankedPairs.html>, Schulze beatpaths
<SchulzeComplic.html>, and<br>
> > basic Condorcet by using Eric Gorr's Condorcet calculator<br>
> > <<a href="http://www.ericgorr.net/condorcet/">http://www.ericgorr.net/condorcet/</a>>
using this input<br>
> ><br>
> >37:C>A>B>D<br>
> >37:C>B>A>D<br>
> >32:A>D>B>C<br>
> >32:A>D>C>B<br>
> >31:B>D>A>C<br>
> >31:B>D>C>A<br>
<br>
> The first is that those "defeat-dropper" style algorithms (like<br>
> Beatpath, Ranked Pairs, River,MinMax) that as you say are all
equivalent<br>
> in the 3-cycle case<br>
> are not my favourites. I prefer both DMC ('Definite Majority
Choice',<br>
> which allows voters to enter approval cutoffs) and Schwartz,IRV
(which<br>
> elects the<br>
> member of Schwartz set highest ordered by IRV on the original
ballots).<br>
<br>
--Can you go thru how those two new methods would work?<br>
<br>
CB: Certainly.<br>
<br>
Schwartz,IRV:<br>
"Identify the members of the Schwartz set, but drop no candidates from
the ballots.<br>
Commence a normal IRV count. When all but one Schwartz set member x has
been<br>
eliminated, elect x".<br>
<br>
For this method I favour allowing truncation, but not above bottom
equal-ranking.<br>
It is much better than Schwartz//IRV, which drops non-Schwartz set
members from<br>
the ballots before applying IRV. Of course Smith verus Schwartz isn't
a big deal.<br>
<br>
Definite Majority Choice.<br>
"Voters submit ranked ballots with approval cutoffs. Truncation and
equal-ranking allowed.<br>
Ballots with no approval cutoff specified are interpreted as approving
all candidates ranked <br>
above bottom or equal-bottom.<br>
Eliminate all candidates that are pairwise beaten by a more approved
candidate.<br>
Among the remaining candidates, one (x) will pairwise beat all the
others.<br>
Elect x."<br>
<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/DMC">http://wiki.electorama.com/wiki/DMC</a><br>
<br>
Several other algorithms are equivalent. Also quite good in my opinion
is the simple version with <br>
no approval cutoffs which just interprets all ranked (above
equal-bottom) candidates as approved .<br>
<br>
My current favourite method that uses high-intensity range ballots is
this "automated version":<br>
<br>
"Inferring ranking from ratings, eliminate all non-members of the
Schwartz set.<br>
Then interpret the ballots as approving those candidates that they rate
(among those remaining) <br>
above average (and half-approving those they rate exactly average).<br>
Based on these thus derived approvals, and again inferring ranking from
ratings, apply DMC."<br>
<br>
<br>
> My second point is that in your scenario the A and B supporters
seem<br>
> mainly concerned to elect their favourites, so in that case why
wouldn't<br>
> they simply be guided in their strategy by their favourite
candidates? Seeing how<br>
> they stand in the polls, it would be in the interests of both A
and B to<br>
> make a preference-swap deal at the expense of C. That way they
each increase<br>
> their chances of being elected form below 33% to about 50% without
anyone<br>
> having to flirt with the car-crash.<br>
<br>
--That sounds like naive bunk.<br>
The problem with that is, how the hell do voters "make a deal" with<br>
each other? This whole "deal" idea is a myth. It is unenforcable and<br>
votes are secret ballot and nobody can make a deal with a gazillion<br>
voters anyhow even if it were enforceable and verifiable.<br>
<br>
CB: "Naive bunk"? It is regular practice in Australian elections for
seats in Parliament.<br>
Admittedly this is helped a lot in most jurisdictions by truncation not
being allowed.<br>
The candidates are normally obliged to register "tickets" with the
electoral commission<br>
in advance of the election, partly so attempts to manipulate the result
by distributing bogus <br>
"how-to-vote" cards can be detected and stamped on.<br>
<br>
Unless there is automatic and/or long standing cooperation based on
ideological affinity<br>
the parties/candidates negotiate preference deals with each other.
Party volunteers on<br>
election day hand out how-to-vote cards to voters on their way in to
vote. Most voters<br>
take at least one and follow one of them.<br>
<br>
In your example, based on the sincere preferences, the candidates seem
to be about equidistant<br>
from each other on the "political spectrum". With a clear front-runner
(C) and the other two<br>
(A and B) too close to call, the A and B candidates both gain a lot
from swapping preferences.<br>
<br>
If the voters are so concerned to elect their favourite as to be
prepared, on their individual inititiative,<br>
to recklessly gamble with D, then I think enough of them would be happy
to instead just follow <br>
their favourite's how-to-vote card to prevent D from being elected.<br>
<br>
<blockquote type="cite">Heck, if that were your view, why not have them
all make a deal to vote honestly<br>
since we all know that generally results in better<br>
society-wide results? Well... sorry, not happening.<br>
<br>
</blockquote>
It is certainly possible for all the respectable viable candidates to
agree to put some pariah candidate bottom<br>
on their tickests. That has happened in Australia.<br>
<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
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