[EM] Re: How to describe RAV/ARC

[Araucaria Araucana]

Substantial abbreviation of previous messages.

On 16 Mar 2005 at 15:54 PST, Forest Simmons wrote:
> On Wed, 16 Mar 2005, Araucaria Araucana wrote: 
>> On 15 Mar 2005 at 14:12 PST, Forest Simmons wrote:
>>> Here's my sales pitch (to EM members) for RAV/ARC:
>>>
>>> When candidate X beats Y in both approval and by head-to-head choice,
>>> let's say that X strongly beats Y.
>>>
>>> If X strongly beats Y then both approval and pairwise methods agree that Y
>>> should not win.
>>>
>>
>> - Pairwise, X>AW, but approval wise, Approval(AW)>Approval(X).
>>   Pairwise and Approval disagree.
>>   So X should be a member of your set P, but it isn't in ABS.
>
> But X is strongly beaten, so by definition of P, candidate X is not a
> member of P.

Ah, okay -- X is strongly beaten by Y and hence cannot be a member of
P.

And I see that A3, since defeated by A2 both via approval and
pairwise, likewise cannot be a member of P.

So P is the set of candidates not strongly beaten by any other
candidate.

>
> All I claimed above is that the set P is totally ordered in two 
> diametrically opposed ways.
>
> I made no claim about anything outside of P.
>
> I think you were mislead by the technical use of the word "total" 
> thinking, perhaps, that it referred to the totality of the original 
> candidates, which it did not.
>
>>  Do you want the least approved candidate, also not a member of the
>>  Smith Set, to be included in P?  Or is the higher-ranked approval
>>  Beatpath AW>Y>X considered a pairwise defeat?
>>
>> - Approval order above AW is not strictly increasing.
>
> There is no candidate with approval above that of the AW.

I meant in the Bubble Sorted ordering above AW.

>
>>
>> So is ABS equivalent to RAV/ARC as you and Jobst have asserted, or is it
>> slightly different?  Or is your pitch inaccurate?
>
> The RAV/ARC pitch is accurate, but in the section on lotteries after
> my RAV/ARC pitch, I made one mistake:
>
> I claimed in passing that if you didn't eliminate the strongly
> beaten candidates, the candidates that were as high or higher than
> the AW in the sorted list would constitute the set P.  But as your
> example shows, this set Q is sometimes a proper superset of P.
>
> Whether we should choose (by random ballot) from P or from Q
> deserves further study.

So in my reply comment just above, I meant the Bubble Sorted ordering
within Q.

Thanks for the clarification.  As we can see from this example, the
Smith Set {A1,A2,A3} can sometimes not include the approval winner,
and your set P of non-strongly-defeated candidates may not include
every member of the Smith set.

Here's an argument for Q vs. P.  A3 voters might move their approval
threshold above AW if they think they're being excluded unfairly from
the lottery.

Another thought -- what if CR-seeding is used instead of Approval?
Voters might prefer a sliding cutoff rather than an abrupt one.  The
boundary gets a little fuzzier doesn't it?

Digressing slightly -- I think a good general name for the bubble sort
methods would be "Pairwise Sorted <othermethod>".  For example,
Pairwise Sorted Approval (PSA), Pairwise Sorted Cardinal Ratings
(PSCR), etc.  In other words, pairwise sorting (bubble sorting should
be understood) of some other method's ranking.

Your random ballot method could be called something like Random Ballot
Resolution (Pairwise/<other method>), since it is intended to resolve
the disagreement between Pairwise comparisons and whatever other
method you are using as a hybrid.

For example, RBR(pairwise/approval) or RBR(pairwise/CR).

Now, can you figure out a good way to pitch this to the masses?  PSA
or PSCR might be within grasp, but if even I have trouble with it, the
strong defeat concept in RBR(P/A) could be very tricky to explain.

Ted
-- 
araucaria dot araucana at gmail dot com