[EM] Universal Domain
Kristofer Munsterhjelm
km_elmet at t-online.de
Sun Sep 12 06:06:06 PDT 2021
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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