[EM] Chain Climbing

[Forest Simmons]

Date: Wed, 23 Apr 2014 16:47:01 -0400
> From: Jameson Quinn <jameson.quinn at gmail.com>
> To: election-methods <election-methods at electorama.com>
> Subject: [EM] Fwd:  TACC (total approval chain climbing) example
> Message-ID:
>         <
> CAO82iZwN-bEURnbYUzz6qZuswNucYkUr2vYdJnqWoaSv_bOThQ at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Oops; I mis-replied individually, instead of to the list. Here's what I
> said:
> ----
> This thread is interesting. However, it's also very heavy on the acronyms.
> Can I ask that when you use an acronym, you make sure it's explained
> adequately on the electorama wiki? At a quick check,
> http://wiki.electorama.com/wiki/TACC is inadequate and
> http://wiki.electorama.com/wiki/MAM is nonexistent.
>
> As to the discussion: this is really the heart of the chicken dilemma. I
> don't think there's any way to look at a set of ballots like
>
> 40 C
> 35 A>B
> 25 B
>
> ... and get an answer that's not going to be wrong some of the time. If
> these ballots are honest, then B should win. If the B voters are truncating
> an honest A second preference, than A would be the ideal winner, but
> perhaps the system should choose C in order to discourage that strategy.
> And if enough of the B voters are truncating C, you could make an argument
> that C is the best winner.
>

Jameson,


You are absolutely right about the heart of the Chicken Dilemma; there is
no way to tell from the above ballot set alone who the real winner should
be, because different sincere scenarios  lead to the same set of ballots.  As
you mentioned it could well be that A is the sincere Condorcet candidate,
and that the ballots reflect a chicken challenge by the B faction.  Also it
is entirely possible that B is the sincere Condorcet candidate
corresponding to sincere preferences


40 C>B, 35 A>B,  25 B>C,


and the voted ballot set represents a defense by the B faction against a
potential attack by the A faction.


One way out of this predicament is an interactive method like SODA.  But
until the electorate is educated and familiar with proxy methods like SODA,
what can we do?


Another way to solve this dilemma is to make sure that raising B to equal
top by the A faction makes a difference in the winner.  This raising of B
makes B the ballot CW, so all of the methods seriously considered by this
EM list elect B in this case.  So if we want this move to make a
difference, A or C should be the winner for the original ballot set,
repeated here for convenience:


40 C
35 A>B
25 B



Condorcet(margins) elects A, and so fails the Plurality Criterion, while
the rest of the methods taken seriously on this EM list elect B or C.  The
ones that elect B, including Condorcet(wv), do not distinguish adequately
between the two cases.


But Woodall, Benham, Implicit Approval Chain Climbing, and Chris's new
method MaxLV(equal rank whole)Margins all elect C from the original ballot
set.


Another way out of this dilemma is to give the voters an explicit approval
cutoff option.  Then the method should elect respectively B or C according
to the strength of the preference expressed on the A faction ballots: 35
A>B, or 35 A>>B, respectively .


Some methods that work this way are Condorcet(approval margins),
Condorcet(winning approval), Smith//Approval, and Majority Enhanced
Approval.


Another name for Condorcet(winning approval) is Democratic Majority Choice.
Among all candidates that are not pairwise beaten by any candidate with
greater approval, it elects the one that beats all of the others.


In this example with the A>>B ballots instead of the A>B ballots, the
approval order is C>A>B, which is in line with the pairwise beat cycle of
C>A>B>C, so C is the only candidate not beaten by an higher approval
candidate.  So candidate C is the DMC winner.


 From the Condorcet(winning approval) point of view, the defeat where the
approval of the winner is smallest is the one in which B defeats C, since B
has the smallest approval of any of the three candidates.  So this is the
defeat that is the weak link in the cycle.


In general, a defeat of a candidate by an higher approval candidate will
never be the weakest link in a cycle, whether defeat strength is measured
by winning approval or by approval margins.

If there are two defeats directed toward higher approval, winning approval
gives more strength to the one with the higher source, while approval
margins gives more strength to the one with the smallest increase in
approval from source to target.


In summary, explicit approval cutoffs and measurement of defeat strength by
winning approval or by approval margins, turns River, Beatpath (Schulze),
and Ranked Pairs into Chicken Proof methods.


The winning approval strength versions are familiar to some of us as DMC.  The
methods Smith//Approval and DMC are analogous to Benham and Woodall, except
you replace IRV with Approval and you replace the IRV elimination order
with the approval order (from lowest to highest).  If you eliminate
candidates from the bottom of the approval list until there is a candidate
that beats all of the rest pairwise, that candidate is the DMC winner.


Majority Enhanced Approval (MEA) is practically the same as
Smith//Approval, but is a more seamless way of arriving at the winner.  In
the rare cases where they differ, the MEA winner will be an uncovered
candidate that covers the Smith//Approval winner.


Here's the definition of MEA: initialize a list with (the name of) the
candidate at the top of the approval list.  Then while all of the listed
candidates are covered add to the list the name of the highest approval
candidate that covers all of the other candidates on the list.  Elect the
candidate whose name was added to the list last.


This MEA winner is a member of Landau, hence Smith.  In addition (like
Smith//Approval) the method MEA satisfies Independence from Pareto
Dominated Alternatives, along with monotonicity, and clone independence
(whenever clones are adjacent in the approval order).


Because of these nice properties I prefer the use of explicit approval
cutoffs.  If any voters do not specify an explicit approval cutoff, then
their truncations should by default be taken as disapproval,


The approval cutoffs allow voters greater ability to make their will
known.  In some cases they help to discern strong preferences among ranked
clones that would otherwise be impossible to express on mere ordinal
ballots.  Which is a stronger refutation of putative clone status?  A new
candidate D being ranked between C and C' on a few ballots. or an approval
cutoff being placed between them on the same ballots?


Where do we go from here?


Forest
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