[EM] Universal Domain
Forest Simmons
forest.simmons21 at gmail.com
Sun Sep 12 06:43:00 PDT 2021
Kevin, thanks for your clarifications about Universal Domain; they
confirmed my worst fears ... that all of my favorite methods violate it,
and that it is likely impossible (as Kristofer has helped me understand) to
make a clone proof, monotone agenda based Banks or Landau method without
violating it.
In particular, all of the good approval variants ... chiastic approval,
midrange approval, etc violate Universal Domain or, like fractional
implicit approval (FIA), are not truly compatible with both monotonicity
and clone independence. Agendas based on the pairwise matrix, seem to
always fail mono raise because raising x from below to above y always
entails lowering y from above to below x ... increasing an entry in x's row
decreases an entry in y's row.
For ordinary round robin team tournaments, this no problem ... team x can
get another point against team y without y decreasing its entry in column
x, and the clone dependence of Borda doesn't seem to matter ... mostly
because there are no ballots to worry about in this sports tournament
context. So the agenda is set by the total number of points scored by a
team in the entire tournament minus the total points scored against it. The
logical way to bring this agenda into pairwise conformity is by Borda
Sorted Margins ... try to beat that with Kemeny-Young! You get Borda from
the pairwise matrix (row sum minus column sum), but how do you get K-Y?
Anyway if in general we are to separate the strategic burden into the
formation of the agenda, and have nearly complete rankings for the
formation of a truly faithful pairwise matrix, we either need two sets of
rankings, or one set of rankings annotated by approval cutoffs, ratings,
or other markings not permitted by Universal Domain.
Until academicians get a better appreciation of the importance of defensive
levers against offensive attacks like Chicken and Burial, I'm afraid we can
expect our non-Universal Domain innovations to be marginalized by academia.
It may be a long row to hoe!
Other such innovations are proxy methods, including Asset Voting, lottery
methods, oracles, voting for a public ranking, use of ballot space and
candidate space metrics, binary decision tree ballots, etc. And of course
multi-winner PR methods ... all are wide open!
El sáb., 11 de sep. de 2021 11:51 p. m., Forest Simmons <
forest.simmons21 at gmail.com> escribió:
> 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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