[EM] DH3 pathology, margins, and winning votes

[Chris Benham]

Warren,

Re: [EM] DH3 pathology, margins, and winning votes

--- In RangeVoting at yahoogroups.com 
</group/RangeVoting/post?postID=lfm7r44oVHeqAwJVUzmNsGZyibO7IswY4QcxzZBUtvgkd0D15Y3bSXe8_t8GbESVUr3uA34RVtMu3KfNeWtKCcuh-v0hUw>, 
Chris Benham <chrisjbenham at ...> wrote:
 >
 > Warren,
 > I have two main points in reply to your "DH3 pathology" anti-Condorcet
 > argument.
 >
 > > DH3 scenario with strategic votes by the A- and B-voters. #voters
 > > Their Vote
 > > 37 C>A,B>D
 > > 32 A>D>B,C
 > > 31 B>D>A,C
 > >
 > > Then the pairwise tallies are going to be:
 > >
 > > Definitely A,B > D > C
 > > Probably C > A,B
 > >
 > > In which case we (probably) have a Condorcet cycle scenario. (It is
 > > actually two 3-cycles which share the common DC arc.) The weakest
 > > defeats in these cycles are C>A,B which means, under both every
 > > Condorcet rule I know of (since I think they all are equivalent in the
 > > 3-cycle case) and Borda, that one of {A,B} is going to be the winner.
 > >
 > > I verified that A wins in the 50-50 mixture case under Tideman ranked
 > > pairs <RankedPairs.html>, Schulze beatpaths <SchulzeComplic.html>, and
 > > basic Condorcet by using Eric Gorr's Condorcet calculator
 > > <http://www.ericgorr.net/condorcet/> using this input
 > >
 > >37:C>A>B>D
 > >37:C>B>A>D
 > >32:A>D>B>C
 > >32:A>D>C>B
 > >31:B>D>A>C
 > >31:B>D>C>A

 > The first is that those "defeat-dropper" style algorithms (like
 > Beatpath, Ranked Pairs, River,MinMax) that as you say are all equivalent
 > in the 3-cycle case
 > are not my favourites. I prefer both DMC ('Definite Majority Choice',
 > which allows voters to enter approval cutoffs) and Schwartz,IRV (which
 > elects the
 > member of Schwartz set highest ordered by IRV on the original ballots).

--Can you go thru how those two new methods would work?

CB: Certainly.

Schwartz,IRV:
"Identify the members of the Schwartz set, but drop no candidates from 
the ballots.
Commence a normal IRV count. When all but one Schwartz set member x has been
eliminated, elect x".

For this method I favour allowing truncation, but not above bottom 
equal-ranking.
It is much better than Schwartz//IRV, which drops non-Schwartz set 
members from
the ballots before applying IRV.  Of  course Smith verus Schwartz isn't 
a big deal.

Definite Majority Choice.
"Voters submit ranked ballots with approval cutoffs. Truncation and 
equal-ranking allowed.
Ballots with no approval cutoff specified are interpreted as approving 
all candidates ranked
above bottom or equal-bottom.
Eliminate all candidates that are pairwise beaten by a more approved 
candidate.
Among the remaining candidates, one (x) will pairwise beat all the others.
Elect x."

http://wiki.electorama.com/wiki/DMC

Several other algorithms are equivalent.  Also quite good in my opinion 
is the simple version with
no approval cutoffs which just interprets all ranked (above 
equal-bottom) candidates as approved .

My current favourite method that uses high-intensity range ballots is 
this "automated version":

"Inferring ranking from ratings, eliminate all non-members of the 
Schwartz set.
Then interpret the ballots as approving those candidates that they rate 
(among those remaining)
above average (and half-approving those they rate exactly average).
Based on these thus derived approvals, and again inferring ranking from 
ratings, apply DMC."


 > My second point is that in your scenario the A and B supporters seem
 > mainly concerned to elect their favourites, so in that case why wouldn't
 > they simply be guided in their strategy by their favourite 
candidates? Seeing how
 > they stand in the polls, it would be in the interests of both A and B to
 > make a preference-swap deal at the expense of C. That way they each 
increase
 > their chances of being elected form below 33% to about 50% without anyone
 > having to flirt with the car-crash.

--That sounds like naive bunk.
The problem with that is, how the hell do voters "make a deal" with
each other? This whole "deal" idea is a myth. It is unenforcable and
votes are secret ballot and nobody can make a deal with a gazillion
voters anyhow even if it were enforceable and verifiable.

CB: "Naive bunk"? It is regular practice in Australian elections for 
seats in Parliament.
Admittedly this is helped a lot in most jurisdictions by truncation not 
being allowed.
The candidates are normally obliged to register "tickets" with the 
electoral commission
in advance of the election, partly so attempts to manipulate the result 
by distributing bogus
"how-to-vote" cards can be detected and stamped on.

Unless there is automatic and/or long standing cooperation based on 
ideological affinity
the parties/candidates negotiate preference deals with each other. Party 
volunteers on
election day hand out how-to-vote cards to voters on their way in to 
vote. Most voters
take at least one and follow one of them.

In your example, based on the sincere preferences, the candidates seem 
to be about equidistant
from each other on the "political spectrum". With a clear front-runner 
(C) and the other two
(A and B) too close to call, the A and B candidates both gain a lot from 
swapping preferences.

If the voters are so concerned to elect their favourite as to be 
prepared, on their individual inititiative,
to recklessly gamble with D, then I think enough of them would be happy 
to instead just follow
their favourite's how-to-vote card  to prevent  D from being elected.

> Heck, if that were your view, why not have them all make a deal to 
> vote honestly
> since we all know that generally results in better
> society-wide results? Well... sorry, not happening.
>
It is certainly possible for all the respectable viable candidates to 
agree to put some pariah candidate bottom
on their tickests. That has happened in Australia.


Chris Benham





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