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

C.Benham cbenham at adam.com.au
Sat Jun 29 07:22:50 PDT 2019

I share your lack of enthusiasm for plain Approval.  The ballot is 
insufficiently expressive.
There is defection incentive. Voters can be sucked in by a 
disinformation campaign that
some unacceptable horror candidate is really viable.

However at least "2-set sincerity" is guaranteed. We know that the voter 
sincerely prefers
all the candidates they approve to all the ones they don't.

The problem I'm addressing with the methods that I've proposed that use 
an explicit approval
cutoff is that Minimal Defense and Chicken Dilemma are incompatible.

So in Forest's scenario (1) the B voters' attitude is that they are 
mainly there to elect their favourite
but they are happy to help C pairwise beat A (and so maybe win by being 
the voted CW) if the C voters
will do the same for their candidate but not otherwise. They aren't 
there to be taken advantage of by
non-reciprocating ("defecting") truncators.

In his scenario (2) on the other hand the B voters are concerned enough 
about preventing the election
of A to be willing to risk being taken advantage of by the B voters' 
defection strategy.

The problem is that without the explicit approval cutoffs we have no way 
of knowing which it is. We can
only address the first one by having the method meet Chicken Dilemma or 
we can address the second
one by having the method meet Minimal Defense, but we can't do both.

The methods I suggested all fulfill Forest's requirements in his 3 
scenarios, and they all  guarantee that
the winner cannot be pairwise-beaten by a more (explicitly) approved 

BTW, what did you think of VIASME?  A simpler method with similar 
motivation would use ranked ballots
with explicit approval cutoffs. When only candidates that were 
originally approved on a ballot remain, the
ballot would be interpreted as disapproving the remaining candidates it 
ranks above none of the others.

Chris Benham

> *Forest Simmons* fsimmons at pcc.edu 
> <mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3CCAP29onet%2BO9hCZJ6hvNnnpUWNyrDkKa9xFXrX5P-RPoF6ndtfw%40mail.gmail.com%3E>
> /Thu May 30 /
>> In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.
>> 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)

On 29/06/2019 7:38 pm, Kristofer Munsterhjelm wrote:
> On 11/06/2019 00.23, C.Benham wrote:
>> On 8/06/2019 7:24 pm, Kristofer Munsterhjelm wrote:
>>>    ..I very much prefer methods that don't need Approval cutoffs.
>> Kristofer,
>> Why is that?
> My objection to (relying too much on) Approval cutoffs is similar to my
> objection to Approval itself. It's hard to determine where to put an
> explicit Approval cutoff, and an implicit Approval cutoff can limit the
> method too much. In either case, it becomes harder for a honest voter to
> fill in the ballot in a way that he won't regret later on.
> There are multiple sincere Approval ballots, so the honest voter doesn't
> know, ahead of time, which he should answer without using some
> heuristic. In contrast, ranking is easy: the voter can just start from
> the best and rank in order. Determining what that order is may require
> some thought, but there's less of a burden finding out just how that
> information should be rendered to the method itself.
> That wouldn't be so much a problem if the method is lenient with noisy
> input; if the ambiguity in where to put Approval cutoffs is like the
> ambiguity in where to equal rank. I think that's why a criterion like
> Plurality seems useful: it gives something extra if voters use
> heuristics close to some intuitive idea of what approving a number of
> candidates means, but doesn't get it wrong if the heuristics are
> slightly off. In contrast, Approval requires that honest voters get the
> distinction just right: if the voters put the cutoff too low, then an
> unwanted compromise wins, but if the voters put it too high, then the
> lack of compromise makes someone from the other side win.
> So to sum up, I guess a reason I don't like Approval is because it
> burdens a honest voter too much; and the reason I don't like Approval
> cutoffs is that, at least if implicit, they transport that burden over
> to the method in question.
> It's possible that a method may use Approval cutoffs yet be lenient
> enough (i.e. more like how the Plurality criterion behaves than how
> Approval itself behaves). In that case, I suppose they're okay. But it's
> not easy to know, from the ballot format itself, which it is.
> (Perhaps one indication of such is whether the method works if nobody
> uses the approval cutoff indicator, or everybody places it at the very
> top or very bottom. Methods that pass Plurality still work if every
> voter ranks every candidate, but Approval would give a perfect tie.)

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