[EM] Universal Domain

[Forest Simmons]

Evidently, at some point it became apparent that complete rankings (or
symmetrically completed partial rankings) were inadequate for defense
against certain kinds of offensive maneuvers ... we needed to have partial
rankings to distinguish between winning votes and margins to measure defeat
strength, etc.

But, it seems to me that we have to go further if we want a method that can
reasonably defend against both Burial and Chicken attacks.

The classic ballot profile

49 C
26 A>B
25 B

is well known as a Chicken attack against the sincere Condorcet candidate A
by the B faction when it's honest preferences were 25 B>A. So this ballot
set must elect C or reward the delinquent faction B, or fail Plurality by
electing A.

But the same profile could arise just as well from a truncation attack
against the sincere Condorcet candidate B by the C faction when its honest
preferences were 49 C>B. So this ballot set must not elect C if it is to
disappoint its naughty gambit.

In summary, to satisfy Plurality, we cannot elect A. To deter Chicken
attacks on a possible sincere CW we cannot elect B, and to deter
truncation/burial attacks on a possible sincere CW we cannot elect C.

But Universal Domain says our method has to pick one of the three
candidates.

What would IRV do?

It would happily eliminate B and then elect C, the same as it would do if
the true preferences were 49 C>B: defeat of the CW by truncation or burial
is not a problem for IRV: it never made any promises about Condorcet.

However the 51 IRVvoters that preferred B over C would be highly
disappointed by this outcome ... in fact, it is quite likely that some of
the A>B faction would forestall it by insincerely reversing their
preference to B>A.

How could relaxing Universal Domain slightly get us out of this dilemma?

I think the answer is to use the traditional Sequential Pairwise
Elimination factorization of a Condorcet method into two parts ... one part
for setting an  agenda ... and the other part for sorting the agenda
pairwise (always giving priority to rectifying the order of the
out-of-order pair nearest the least promising end of the agenda).

It is only the agenda setting part that requires going slightly beyond
"Universal" in Universal Domain. For example, setting the agenda by some
kind of approval, implicit or otherwise.

The other factor, the Pairwise win/loss/tie matrix is completely determined
by the ordinal information in the ballots.

In our example, what if the A faction could distinguish the Chicken attack
from the other scenario by use of an explicit approval cutoff: 26 A>>B ?

This is enough to change the SPE (Sequential Pairwise Elimination) agenda
so that B with the least approval is pitted against A and so is eliminated
first and does not get rewarded for the attack.

In the second scenario the default/implicit approval cutoff (truncation) is
assumed which gives B the greatest approval ... pitting A against C, and
then C against B, making the sincere Condorcet candidate B the winner.

It seems to me that this factorization idea is the safest and most
transparent way of resolving this dilemma. Since it (SPE) is an ancient
method with lots of pragmatic use in all sorts or traditional "deliberative
assemblies" (Robert's Rules terminology) we should not feel too timid in
proposing it for public elections.

What say ye?

El sáb., 11 de sep. de 2021 9:01 p. m., Kevin Venzke <stepjak at yahoo.fr>
escribió:

> All options being ranked equal is certainly allowed, what I'm saying is
> that it can only have one meaning.
>
> I think your first method satisfies UD but the second doesn't. I wouldn't
> agree that this makes the definition inadequate. It doesn't only say that
> every possible ordering has to be admissible, it says that the method's
> result should be "definite" for any set of these orderings. If you may need
> to know other information from the ballots, then the result isn't defined
> for the orderings alone.
>
> I guess that the point of UD is to set a baseline for how (quite a lot of
> very reasonable) election methods work, so that certain proofs will
> succeed, which depend only on preference orderings... It explains formally
> how we can set aside objections like "my method doesn't allow this kind of
> preference order, so the proof fails" or "my method can't be resolved with
> only this information, so the proof fails" etc.
>
> Kevin
>
>
>
> Le samedi 11 septembre 2021, 21:14:03 UTC−5, Forest Simmons <
> forest.simmons21 at gmail.com> a écrit :
>
>
> 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?
> ----
> 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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