[EM] Universal Domain
Forest Simmons
forest.simmons21 at gmail.com
Sun Sep 12 07:29:41 PDT 2021
Excellent points and clarifications, Kristofer!
It is instructive to see how close the UD compliant FIASM comes to
resolving the dilemma ballot set we were talking about.
49 C
26 A>B
25 B
FIA's for A, B, and C, respectively are 26, 38, and 49. Candidate B's score
is closer to C's than to A's, so the list becomes
B>C>A with B's chicken gambit rewarded. However, one A>B voter truncating
B, moves B's score closer to A's resulting in the final order C>A>B.
If the faction sizes were 48 C, 28 A>B, and 24 B, the respective FIA scores
would be 28, 38, and 48, with B exactly halfway between A and C.
One A>B voter could tip the scale in favor of B or C by changing to A=B or
by truncating B, respectively. This shows that FIASM is as close as
possible to resolving the dilemma without violating Universal Domain. Pity
it cannot effectively satisfy clone dependence while clones straddle the
boundaries demarcating the three fractional approval zones ... which is one
important way to discern ranks within individual clone sets. Explicit
approvals would resolve that annoyance, but only by sacrificing Universal
Domain.
El dom., 12 de sep. de 2021 6:06 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:
> On 9/11/21 4:48 AM, Forest Simmons wrote:
> > Does Implicit Approval satisfy Universal Domain?
>
> As I understand it, universal domain means that the method should be
> able to provide an outcome for a set of untruncated ranked ballots, and
> do so for every possible set.
>
> Like Kevin says, implicit Approval should pass UD if the implied
> approval is defined for such untruncated elections. I think that most
> methods would consider every candidate to be approved in that case.
>
> There's a stronger sense where the only input allowed *is* untruncated
> ranked elections, but every method that allows for equal rank or
> truncation will fail that stronger version. This stronger sense is how
> Wikipedia defines it, here:
> https://en.wikipedia.org/wiki/Unrestricted_domain
>
> In addition, while IA methods may formally pass the (weaker) universal
> domain, they could very well still be awful methods under the restriction.
>
> Consider e.g. the following method: "Let the preliminary winner set be
> the set of candidates whose implicit approval score is maximum.
> Eliminate every candidate not in the set, then elect the Borda winner
> from the reduced election". If the election features no truncations at
> all, the method is just Borda, and Borda is not particularly good.
>
> And then there's the muddling of honesty and strategy that comes from
> rejecting universal domain, which gets worse the stronger the violation
> is. Maybe I should write a separate post on that :-)
>
> -km
>
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