[EM] Universal Domain

[Forest Simmons]

universal domain

In social choice, the requirement that a procedure should be able to
produce a definite outcome for every logically possible input of individual
preference orderings.

So, all ranked equal is a "logically possible preference ordering."

The main thing I'm wondering is how to modify ASM (Approval Sorted Margins)
to make it more broadly acceptable ... and to perhaps comply with Universal
Domain as a bonus.

Here's my best attempt so far:

FIASM Fractional Implicit Approval Sorted Margins: Ballots are ranked
preference style with equal rankings and truncations allowed. Each
candidate's fractional implicit approval score is the number of ballots on
which it is ranked equal top plus half the number of ballots on which it is
ranked above at least one candidate, but not ranked top.

The candidates are listed in fractional implicit approval order. While
there is any adjacent pair where the fractional implicit approval order
contradicts the pairwise (head-to-head) win order, transpose the members of
the out-of-order pair with the smallest absolute discrepancy in fractional
implicit approval.

The resulting list is a social order that satisfies a reverse symmetry
property ... reversing all of the ballot ranking inputs (so that equal top
becomes equal bottom [or truncated] and vice versa) reverses the social
order output.

Does this method satisfy Universal Domain?

Now, what if optional explicit cutoff marks were allowed to demarcate the
three levels (0, 1/2, or 1) of fractional approval. Would that violate
Universal Domain?

If so, then the Oxford definition quoted above is inadequate, since it does
not logically rule out optional marks when the lack of any optional mark
defaults to a standard ranking, and the only stated requirement is that no
standard ranking be unusable.

Thoughts?

El vie., 10 de sep. de 2021 10:56 p. m., Kevin Venzke <stepjak at yahoo.fr>
escribió:

> To my mind Implicit Approval (as a method in itself) only satisfies it if
> you can define the ballot format while discussing only relative rankings.
> So, for example, if the voter ranks all candidates totally equal to each
> other (no matter whether they are explicitly so ranked, or the ballot is
> submitted with all preferences truncated), this can only be allowed to mean
> that all are approved or that none are approved, since there is no way to
> differentiate these two stances using relative rankings only.
>
> Kevin
>
>
> Le vendredi 10 septembre 2021, 21:49:14 UTC−5, Forest Simmons <
> forest.simmons21 at gmail.com> a écrit :
>
>
> Does Implicit Approval satisfy Universal Domain?
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> Election-Methods mailing list - see https://electorama.com/em for list
> info
>

El 10 sep. 2021 10:56 p. m., "Kevin Venzke" <stepjak at yahoo.fr> escribió:

To my mind Implicit Approval (as a method in itself) only satisfies it if
you can define the ballot format while discussing only relative rankings.
So, for example, if the voter ranks all candidates totally equal to each
other (no matter whether they are explicitly so ranked, or the ballot is
submitted with all preferences truncated), this can only be allowed to mean
that all are approved or that none are approved, since there is no way to
differentiate these two stances using relative rankings only.

Kevin


Le vendredi 10 septembre 2021, 21:49:14 UTC−5, Forest Simmons <
forest.simmons21 at gmail.com> a écrit :


Does Implicit Approval satisfy Universal Domain?
----
Election-Methods mailing list - see https://electorama.com/em for list info
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