[EM] Universal Domain
Kevin Venzke
stepjak at yahoo.fr
Sat Sep 11 21:00:33 PDT 2021
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?----
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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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