# [EM] Deterministic Epsilon Consensus Idea stimulated by a question of Steve Bosworth

Forest Simmons forest.simmons21 at gmail.com
Thu Oct 7 15:50:41 PDT 2021

```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.

On the other hand, if epsilon were infinitesimal, the grades above "poor"
would serve merely as tie breakers ... not a bad idea for a general purpose
tie breaker method!

But as a stand alone method, it might be best to limit the choice of
epsilon to a value between zero and 1/6.

Why 1/6? Because of the six levels of grades, a five-sixths majority is a
reasonable partial consensus quota. In particular, an initial step that
disqualified every alternative pairwise defeated by more than a five-sixths
majority of the ballots could never disqualify all candidates when there
are only six levels.

[In general, if there are only k levels, there cannot be a beat cycle where
all of the winning votes consist of fractions greater than (1 - 1/k) of the
ballots.]

This and other considerations make me think that in general when there are
k levels of approval, 1/k might be  a good nominal value for epsilon.

This "method" is still in the  brainstorming stage, so all suggestions are
worth considering!

El mié., 6 de oct. de 2021 7:38 p. m., Forest Simmons <
forest.simmons21 at gmail.com> escribió:

> Steve's query about Chiastic Approval included the following ....
>
>  Also, correct me if I'm mistaken that XA does not guarantee that its
> winner will be elected with the support of a majority of all the votes
> (ballots) cast.
>
> The short answer is "no" ...  no method can guarantee majority voter
> support for its winner, unless they can guarantee that at least one
> candidate is ranked, rated, scored, or graded above bottom on more than
> half of the ballots submitted.
>
> The long answer is, "Why stop at half or two-thirds, as some methods
> require ... why not go for full 100% consensus?"
>
> But, you may object, full consensus is not always possible. Well, neither
> is forty percent support always possible, but that doesn't stop the
> Constitution from requiring two-thirds of the voters' support for certain
> kinds of amendments, etc.
>
> One expedient that has been suggested is the NOTA option for the case when
> the quota is not met.  This option gives new meaning to the word "approval"
> ... as Mike Ossipoff used to say, you approve a candidate if you would
> rather see her elected than have to come back next month to vote for
> someone else.
>
> I would like to suggest another option based on the standard MJ grade
> ballot ...
>
> Each candidate X gets a score that is given by the sum ..
>
> S(X) = Sum (over j from zero to five) of the product
>
> a(j)*epsilon^j,
>
> where epsilon is a value to be determined by the voters ... and the
> respective values of a(j), for j in {0, 1, 2, 3, 4} are the number of
> ballots on which candidate X is graded strictly above reject, poor,
> acceptable, good, or very good, respectively.
>
> Also each voter has the option of voting for a value of epsilon in the set
> {.01, .02, ... .99, 1.00}. The median of the distribution of these votes
> determines the value of epsilon.
>
> Elect the candidate X with the max value of S(X) (once the epsilon value
> has been determined).
>
> Note that if, for some j, the coefficient a(j) is the total number of
> ballots, then we can say candidate X is a full consensus candidate at level
> j.
>
> If there are several full consensus level j candidates, then the higher
> degree terms will determine the winner.
>
> Thanks!
>
> FWS
>
>
>>
>>
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