[EM] What are some simple methods that accomplish the following conditions?

Forest Simmons fsimmons at pcc.edu
Mon Jun 3 13:31:24 PDT 2019


Yes, we did, and I still do believe that Approval Sorted Margins is a
superior method to DMC.  In fact, Approval sorted Margins and Covering
Enhanced Approval are my two favorite Condorcet compliant methods. However,
the order for ease of explaining and selling to the public seems to be the
opposite of my preference order in the case of these three methods.  I
could be wrong on this point.

BTW, I like the recent tweaks you are making to IBIFA.

I don't consider Asset Voting a settled deterministic method, since the are
no agreed upon constraints about how the candidates are allowed to use
their "assets."

Here's a version that I would support:  A base election method is
established well before voting takes place. Voters submit as much ranking
or rating information (relevant to the base method) as they like, and if
not sure where to place the approval cutoff (for example) they can indicate
both an upper and lower limit for the approval cutoff, and (by some code)
request their favorite to choose where in that interval to mark the cutoff.
At the other extreme of voter trust of favorite, voters may simply indicate
that they would like their ballot to be an exact replica of their
favorite's. In any case, the voter specifies how much discretionary "power
of attorney" so to speak gets delegated to their indicated proxy.

Once the candidate proxies have made their requested amendments to the
ballots, then the election is decided by those ballots in the previously
agreed upon base method.

If the voter has n candidates tied for favorite and cannot make up her mind
among them, then she can submit the entire set of n favorites, in which
case each of those favorites gets a copy of her ballot to amend,, and each
of those amended ballots gets a weight of 1/n in the election.

Can you think of anything closer to Strong FBC compliance than this
candidate proxy enhancement of any good base method?

What voters want more than anything else is Strong FBC compliance.  They
know that Approval does not satisfy the Strong FBC, and they (wrongly)
believe that IRV does satisfy it. That's the main reason they think IRV is
better than Approval. The other reason they prefer IRV is that they don't
feel confident about deciding on approval cutoff's.

Candidate Proxy Ballot Enhancement (CPBE?) takes care of their approval
cutoff indecision, and gives them (the closest possible thing to) true
compliance with the Strong FBC.

I would suggest Approval Sorted Margins for the base method, since that
method (by adjusting approval cutoffs) takes care of Chicken Defense and
other basic defensive strategy requirements. Voters submit rankings or
ratings with upper and lower limits for the approval cutoff (when in
doubt), etc.(as indicated above).


On Sun, Jun 2, 2019 at 3:34 PM C.Benham <cbenham at adam.com.au> wrote:

> Forest (and interested others),
> I (or maybe we) discovered/decided some years ago that  Approval Sorted
> Margins is definitely better than DMC.
> Regarding alternatives to IRV that lay claim to be at least as good, two
> of my strong standards are that the method must meet
> one of Condorcet and FBC  and that it must meet one of (at least in the
> case of methods that don't allow an explicit approval
> cut-off in the rankings)  Minimal Defense (and maybe some yet-to-coined
> irrelevant-ballot independent version of it) and Chicken
> Dilemma.   (I say "one of" in both cases because we know that two of isn't
> possible).
> The main other ways I categorise methods is according to types of ballots
> used and relatively simple (to explain and sell and use)
> versus less so.
> I am negative on both "Asset" voting and weakening  the Plurality
> criterion.
> Chris Benham
> On 2/06/2019 8:01 am, Forest Simmons wrote:
> just one other tweak to MDDA:  Kevin's official version of MDDA says that
> in the case of two of more candidates surviving the disqualification test,
> in that case the most approved candidate should be elected.  My tweak is to
> elect from among the undisqualified candidates the one furthest from being
> disqualified; no need to switch horses in this case.
> On Sat, Jun 1, 2019 at 2:41 PM Forest Simmons <fsimmons at pcc.edu> wrote:
>> Kevin, Chris, and Kristofer:
>> Great ideas!.
>> DMC (explicit approval version) also comes to mind as fairly simple to
>> describe:
>> *Remove candidates from the bottom of the approval list until there is a
>> ballot pairwise beats-all candidate among the remaining candidates (to
>> elect). *
>> And analogous to Chris's equivalence between Approval Sorted Margins and
>> Condorcet(approval margins), we have the equivalence between DMC and
>> Condorcet(winning approval).
>> Of course we are talking explicit approval every time we say approval in
>> this context.
>> We know that none of these Condorcet efficient methods satisfies the FBC,
>> but how about MDDA with explicit approval instead of its implicit approval
>> default?
>> This has the problem that Chris has pointed out in MJ and other Bucklin
>> versions where addition of irrelevant ballots can change a majority of
>> ballots into a minority.
>> So here's my idea: do MDDA with explicit approval AND symmetric
>> completion of all of the ballots except for the Top Rank.  By excusing the
>> top rank from symmetric completion, we preserve the FBC, but we lose the
>> Condorcet Criterion.
>> [This shows how close we can get to both the CC and the FBC, if we do a
>> full symmetric completion including the top rank, then this version of MDDA
>> satisfies the CC but not the FBC. We can toggle back and forth.
>> Suppose that we balance on the edge (of symmetric completion in the top
>> rank or not) with asset voting so the proxies could finesse this
>> difference. The unsophisticated voters could just vote their favorites,
>> etc. Would this come even closer to satisfying both the CC and the FBC? In
>> other words mightn't this expedient externalize the strategizing enough to
>> satisfy both FBC and CC for all practical purposes?]
>> I think that the FBC is more important in this context, so suggest that
>> we exempt at least the top rank from symmetric completion if not all of the
>> approved ranks.
>> Now what about the irrelevant ballots problem?  I think that symmetric
>> completion, if only for the truncated candidates, would suffice.  If X and
>> Y are both truncated on N new ballots then N/2 of them count for X>Y and
>> N/2 of them count for Y>X so a majority defeat between X and Y is preserved.
>> Note that symmetric completion among only the truncated candidates is the
>> same as "half power truncation."
>> This brings me to another question.  Suppose that voters knew that
>> candidate B became a plurality loser because of insincere truncation.
>> Would they feel so bad it B won anyway?
>> This leads to a weak form of Plurality:  If a candidate fails Plurality,
>> even after the ballots have been symmetrically completed, then that
>> candidate must not be elected.
>> Would this weak form be adequate?
>> Thanks for your great ideas and interest in these questions!
>> Forest
>> On Sat, Jun 1, 2019 at 12:49 PM Kevin Venzke <stepjak at yahoo.fr> wrote:
>>> Hi Forest,
>>> I had two ideas.
>>> Idea 1:
>>> 1. If there is a CW using all rankings, elect the CW.
>>> 2. Otherwise flatten/discard all disapproved rankings.
>>> 3. Use any method that would elect C in scenario 2. (Approval, Bucklin,
>>> MinMax(WV).)
>>> So scenario 1 has no CW. The disapproved C>A rankings are dropped. A
>>> wins any method.
>>> In scenario 2 there is no CW but nothing is dropped, so use a method
>>> that picks C.
>>> In both versions of scenario 3 there is a CW, B.
>>> If step 3 is Approval then of course step 2 is unnecessary.
>>> In place of step 1 you could find and apply the majority-strength solid
>>> coalitions (using all rankings)
>>> to disqualify A, instead of acting based on B being a CW. I'm not sure
>>> if there's another elegant way
>>> to identify the majority coalition.
>>> Idea 2:
>>> 1. Using all rankings, find the strength of everyone's worst WV defeat.
>>> (A CW scores 0.)
>>> 2. Say that candidate X has a "double beatpath" to Y if X has a standard
>>> beatpath to Y regardless
>>> of whether the disapproved rankings are counted. (I don't know if it
>>> needs to be the *same* beatpath,
>>> but it shouldn't come into play with these scenarios.)
>>> 3. Disqualify from winning any candidate who is not in the Schwartz set
>>> calculated using double
>>> beatpaths. In other words, for every candidate Y where there exists a
>>> candidate X such that X has a
>>> double beatpath to Y and Y does not have a double beatpath to X, then Y
>>> is disqualified.
>>> 4. Elect the remaining candidate with the mildest WV defeat calculated
>>> earlier.
>>> So in scenario 1, A always has a beatpath to the other candidates, no
>>> matter whether disapproved
>>> rankings are counted. The other candidates only have a beatpath to A
>>> when the C>A win exists. So
>>> A has a double beatpath to B and C, and they have no path back. This
>>> leaves A as the only candidate
>>> not disqualified.
>>> In scenario 2, the defeat scores from weakest to strongest are B>C, A>B,
>>> C>A. Every candidate has
>>> a beatpath to every other candidate no matter whether the (nonexistent)
>>> disapproved rankings are
>>> counted. So no candidate is disqualified. C has the best defeat score
>>> and wins.
>>> In scenario 3, the first version: B has no losses. C's loss to B is
>>> weaker than both of A's losses. B
>>> beats C pairwise no matter what, so B has a double beatpath to C.
>>> However C has no such beatpath
>>> to A, nor has A one to B, nor has B one to A. The resulting Schwartz set
>>> disqualifies only C. (C needs
>>> to return B's double beatpath but can't, and neither A nor B has a
>>> double beatpath to the other.)
>>> Between A and B, B's score (as CW) is 0, so he wins.
>>> Scenario 3, second version: B again has no losses, and also has double
>>> beatpaths to both of A and
>>> C, neither of whom have double beatpaths back. So A and C are
>>> disqualified and B wins.
>>> I must note that this is actually a Condorcet method, since a CW could
>>> never get disqualified and
>>> would always have the best worst defeat. That observation would simplify
>>> the explanation of
>>> scenario 3.
>>> I needed the defeat strength rule because I had no way to give the win
>>> to B over A in scenario 3
>>> version 1. But I guess if it's a Condorcet rule in any case, we can just
>>> add that as a rule, and greatly
>>> simplify it to the point where it's going to look very much like idea 1.
>>> I guess all my ideas lead me to
>>> the same place with this question.
>>> Oh well, I think the ideas are interesting enough to post.
>>> Kevin
>>> >Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu>
>>> a écrit :
>>> >
>>> >In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One
>>> consequence of these constraints is that in all three profiles below the
>>> cycle >A>B>C>A will obtain.
>>> >
>>> >I am interested in simple methods that always ...
>>> >
>>> >(1) elect candidate A given the following profile:
>>> >
>>> >P: A
>>> >Q: B>>C
>>> >R: C,
>>> >and
>>> >(2) elect candidate C given
>>> >P: A
>>> >Q: B>C>>
>>> >R: C,
>>> >and
>>> >(3) elect candidate B given
>>> >
>>> >P: A
>>> >Q: B>>C  (or B>C)
>>> >R: C>>B. (or C>B)
>>> >
>>> >I have two such methods in mind, and I'll tell you one of them below,
>>> but I don't want to prejudice your creative efforts with too many ideas.
>>> >
>>> >Here's the rationale for the requirements:
>>> >
>>> >Condition (1) is needed so that when the sincere preferences are
>>> >
>>> >P: A
>>> >Q: B>C
>>> >R: C>B,
>>> >the B faction (by merely disapproving C without truncation) can defend
>>> itself against a "chicken" attack (truncation of B) from the C faction.
>>> >
>>> >Condition (3) is needed so that when the C faction realizes that the
>>> game of Chicken is not going to work for them, the sincere CW is elected.
>>> >
>>> >Condition (2) is needed so that when  sincere preferences are
>>> >
>>> >P: A>C
>>> >Q: B>C
>>> >R: C>A,
>>> >then the C faction (by proactively truncating A) can defend the CW
>>> against the A faction's potential truncation attack.
>>> >
>>> >Like I said, I have a couple of fairly simple methods in mind. The most
>>> obvious one is Smith\\Approval where the voters have
>>> >control over their own approval cutoffs (as opposed to implicit
>>> approval) with default approval as top rank only. The other
>>> >method I have in mind is not quite as
>>> >simple, but it has the added advantage of satisfying the FBC, while
>>> almost always electing from Smith.
>>> ----
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