[EM] Steve's reply:: Deterministic Epsilon Consensus Idea stimulated by a question of Steve Bosworth
Forest Simmons
forest.simmons21 at gmail.com
Fri Oct 8 16:50:50 PDT 2021
Good points! Evidently I misunderstood what Steve was getting at. In that
light I'm embarrassed to say that my reply seems quite condescending.Thanks
for restoring to Steve the credit that he deserves!
That said, if the naive voter can vote a sincere ballot solely on the basis
of the commonly understood meanings of the descriptions excellent(ideal),
very good, good, acceptable, poor, and reject .... then that ballot can be
used equally well for MJ, Super MJ, and Epsilon Consensus, whether for
macro or micro values of epsilon.
If epsilon is positive but less than 1/N^6, where N is the number of
ballots, then the order of scores for the respective alternatives is the
lexicographical order of 6-tuples of the form (a0, a1, a2, a3, a4, a5)
where the alpha numerics a0, a1, a2, a3, a4, and a5 represent the
respective numbers of ballots on which the alternative under consideration
is graded better than or equal to reject, poor, acceptable, good, very
good, or excellent, respectively.
My original intention for Epsilon Consensus was as a tie breaker (with
infinitesimal epsilon) for Super Majority Judgment ... but it is much
simpler to just allow epsilon to assume standard (but appropriately small)
values to supply a stand-alone method.
As long as epsilon is small enough, this method gives no more incentive for
grade inflation than MJ does, which its proponents aver to be more or less
negligible, depending on the voter levels of naïveté.
The contemplated Super MJ is no easier or harder than MJ, but if the voters
will vote sincerely, i.e. with the same naivete as MJ voters (thereby
producing identical ballot sets for both MJ&SMJ) super majority
alternatives will be more favored under SMJ talley rules, which makes a
higher degree of consensus likely for SMJ:
For a given alternative j and grade g in the ordered set [reject, ...,
excellent], let F(j, g) be the number of ballots on which alternative j is
graded at or better than g.
Note that for every j, the ballot number F(j, reject) has the same value N,
the total number of ballots submitted.
Let g(j) be the max value of g such that F(j, g) is greater than or equal
to (5/6)N.
The SMJ winner is chosen from argmax g(j) by use of any previously agreed
upon tie breaker method ... I suggest Epsilon Consensus with the value of
epsilon set at 1/N^6 .
FWS
El vie., 8 de oct. de 2021 12:46 p. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:
> On 08.10.2021 07:25, Forest Simmons wrote:
> > The verbiage is intended for developers, not users. Programmers have to
> > convert everything to numbers via ASCII codes, etc. All of this must be
> > out of sight to keep the users from pointless worry. The design stage is
> > for the EM scientists to work out the nitty gritty details. Yes, it's
> > fun for us, but it is also necessary... for us, but not for Joe Q
> > Public. You are not a programmer, but you are a promoter, so you need to
> > know more than the user, but not as much as a software engineer. Does
> > that help?
>
> Let me try to make what might be Steve's implicit argument a little
> stronger.
>
> With MJ, it's true that if you want to assign numerical values to the
> grades, the exact numbers you use don't matter as long as they're
> monotone in the grades themselves: the number assigned to Poor should be
> less than the number assigned to Acceptable, and so on.
>
> Is that true of the epsilon method? If not, it requires more information
> than MJ. If I recall correctly, by B&L's model, the grades are not
> supposed to exist on any given numerical scale, but the society that
> uses MJ should have a common idea of what "Excellent" means relative to
> "Poor".
>
> I have only cursorily read the method proposal, but you said:
>
> > Note that if epsilon is one, the method is just Range Voting on a
> > scale of zero to five ... which gives a clear incentive for
> > concentrating ratings to the extremes of zero and five, or the extremes
> > of "reject" and "excellent" in the MJ terminology.
>
> That suggests that the epsilon method has a more demanding
> interpretation of the grades - that a common language of what
> "Excellent" means is not enough, since it implicitly assigns each grade
> a definite score if epsilon happens to be chosen to be one.
>
> -km
>
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