[EM] What are some simple methods that accomplish the following conditions?

[Kristofer Munsterhjelm]

On 11/06/2019 00.23, C.Benham wrote:
> 
> On 8/06/2019 7:24 pm, Kristofer Munsterhjelm wrote:
>>   ..I very much prefer methods that don't need Approval cutoffs.
> 
> Kristofer,
> 
> Why is that?

My objection to (relying too much on) Approval cutoffs is similar to my
objection to Approval itself. It's hard to determine where to put an
explicit Approval cutoff, and an implicit Approval cutoff can limit the
method too much. In either case, it becomes harder for a honest voter to
fill in the ballot in a way that he won't regret later on.

There are multiple sincere Approval ballots, so the honest voter doesn't
know, ahead of time, which he should answer without using some
heuristic. In contrast, ranking is easy: the voter can just start from
the best and rank in order. Determining what that order is may require
some thought, but there's less of a burden finding out just how that
information should be rendered to the method itself.

That wouldn't be so much a problem if the method is lenient with noisy
input; if the ambiguity in where to put Approval cutoffs is like the
ambiguity in where to equal rank. I think that's why a criterion like
Plurality seems useful: it gives something extra if voters use
heuristics close to some intuitive idea of what approving a number of
candidates means, but doesn't get it wrong if the heuristics are
slightly off. In contrast, Approval requires that honest voters get the
distinction just right: if the voters put the cutoff too low, then an
unwanted compromise wins, but if the voters put it too high, then the
lack of compromise makes someone from the other side win.

So to sum up, I guess a reason I don't like Approval is because it
burdens a honest voter too much; and the reason I don't like Approval
cutoffs is that, at least if implicit, they transport that burden over
to the method in question.

It's possible that a method may use Approval cutoffs yet be lenient
enough (i.e. more like how the Plurality criterion behaves than how
Approval itself behaves). In that case, I suppose they're okay. But it's
not easy to know, from the ballot format itself, which it is.

(Perhaps one indication of such is whether the method works if nobody
uses the approval cutoff indicator, or everybody places it at the very
top or very bottom. Methods that pass Plurality still work if every
voter ranks every candidate, but Approval would give a perfect tie.)