[EM] Re: How to describe RAV/ARC

[Araucaria Araucana]

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.
>
> What happens if we eliminate all of the candidates that are strongly 
> beaten?
>
> The remaining candidates form a set P that are totally ordered by the 
> ordinary pairwise beat relation.
>
> The top of this totally ordered chain is the RAV/ARC winner.
>
> That ends my EM sales pitch for RAV/ARC. [I would use a different pitch 
> for the general public.]

[First post using gmail address instead of mailinator]

Hi Forest,

According to this sales pitch, RAV/ARC does not have quite the same effect as
Approval-seeded Bubble Sort [aka Total Approval Ranked Pairs, Tournament
Voting (approval-seeded)].

Using ABS, it is possible that a candidate X could end up ranked below the
Approval Winner AW, but because a higher-seeded candidate Y defeats X but is
defeated by AW, X cannot end up in your set P.

Consider the following situation with the following RP (wv) ordering:

   A1>A2
   A2>A3
   A3>A1
   A1>AW, A1>X, A1>Y
   A2>AW, A2>X, A2>Y
   A3>AW, A3>X, A3>Y
   AW>Y
   Y>X
   X>AW

Seeding by descending order of approval, we start with

     AW A2 A1 A3 Y X

There are two cycles:  A1>A2>A3>A1, AW>Y>X>AW.

ABS ends up with the following social ordering:

   A1>A2>A3>AW>Y>X

A1 wins, and also wins via other strong wv methods.  Now consider the three
interesting situations here:

- The approval winner is not in the Smith Set.

- 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.
  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.

So is ABS equivalent to RAV/ARC as you and Jobst have asserted, or is it
slightly different?  Or is your pitch inaccurate?

Ted (aka Monkey Puzzle)
-- 
araucaria dot araucana at gmail dot com