[EM] Arrow's theorem and cardinal voting systems (Juho Laatu)

[Kristofer Munsterhjelm]

On 30/01/2020 00.05, Forest Simmons wrote:
> Juho,
> 
> I always appreciate your comments, and I agree 100 percent with your
> point of view on this topic.
> 
> Unfortunately there are some Condorcet enthusiasts who believe that
> majority preference cycles can only occur from mistaken judgment among
> the voters or from insincere voting, so that the purpose of a Condorcet
> completion method is to find the most likely "true" social preference
> order. It's a fairly innocuous assumption and can serve as a heuristic
> for coming up with ideas for breaking cycles, but it is not a solid
> basis in itself for choosing between methods.
> 
> Also falsely assumed is that the CW's cannot be utility losers and that
> Condorcet Losers cannot be utility winners in any rational way.
> 
> These considerations make it clear that for optimal results relative to
> many applications the method must take into account preference
> intensities, which is why my favorite methods tend to be based on
> rankings with approval cutoffs if not outright score ballots.

Although I'm more of a Condorcetist myself, here's a thought.

As I said earlier on the list, if honesty consists of you normalizing
the worst candidate to 0 and the best candidate to 1, and then giving
every candidate in between a rating according to lottery equivalence
(and you're risk-neutral), then there is one and only one honest rated
ballot. Call that a semi-cardinal ballot.

For semi-cardinal ballots, IIA reappears (since you get majority rule
with two candidates), but that there is only one honest ballot should
make the externalization/manual DSV complaints go away to quite some degree.

How well can we do with such ballots? What kind of strategy resistance
and utility performance can a semi-cardinal method attain? It seems like
there's a strong limit to how well a method can deal with strategic
exaggeration, in particular, but it might still be interesting to look into.

(Of course, there's also the problem that ordinary voters would probably
not take the effort of being honest in the definition above. But I can't
see any other way of reducing the honesty ambiguity short of going
directly to rankings.)