[EM] Universal Domain

[Kristofer Munsterhjelm]

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