[EM] three-slot methods

[Forest Simmons]

Let's try your MAR method on the "unreliable poll" example that I consider
to be Approval's achilles heel:

First Table:

60 A>B>C
25 C>B>A
15 B>C>A

Second Table:

40 A>B>C
35 C>B>A
25 B>C>A

Let's suppose that the first table gives true preferences, and that the
second table gives the results of an unreliable poll.

It seems to me that on the basis of this poll the ABC voters would vote
sincerely, not having much hope for A, therefore wanting B to be approved
over C in the likely even that A wasn't around for the second round.

No matter what the other voters did, A would survive to the second round
and C would be eliminated.

So in the second round the 60 AB ballots would approve only A, giving the
win to A, according to MAR (Majority Approval Runoff).

As I remember, it was likely that MCA would also give the win to A, but
not so clear cut.

Now let's change the tables by letting the first set of preferences be the
fake poll results and the second set the true preferences.

The ABC voters would see nothing to lose in voting A>B>C, since according
to the polls B, the only other candidate with a chance of surviving the
first round, would be easily eliminated in the second round.

The CBA voters would not bury B, since according to the polls B is
their only hope of surviving the first round.

So all three factions would see nothing to lose in voting sincerely.

Sincere votes would result in B and C surviving to the second round, with
B, the sincere CW, winning.

This does seem to be better than MCA.

Concerning unreliable polls, there is a good article on this in the
October issue of Z Magazine.

Forest


On Thu, 9 Oct 2003, [iso-8859-1] Kevin Venzke wrote:

>  --- Forest Simmons <fsimmons at pcc.edu> a écrit :
> > However, among three slot methods MCA might be easier to sell.
> >
> > I will gladly go with the one that is most acceptable to the public.
> >
> > Forest
>
> Here's an idea for a three-slot method which increases somewhat the "strategic
> distance" (if that's a term) between the first two slots.  It's not summable,
> but doesn't require a pairwise matrix:
>
> The voter places each candidate in one of three slots.
> The ballots are counted such that each voter gives a vote to every candidate
> placed in either the first or second slot.
> If no more than one candidate has votes from a majority, the candidate with the
> most votes wins.
> Otherwise, eliminate the candidates who don't have votes from a majority, and
> recount the votes in the same way as before, except ballots which place none of
> the remaining candidates in the third slot, only give a vote to candidates placed
> in the first slot.  The candidate with the most votes wins.
>
> I call this method "MAR" for "Majority Approval Runoff," although it doesn't really
> end with a runoff.  In the case where two candidates have a majority, it's the same
> as finishing with a pairwise comparison, however.  I don't recommend having more
> than two counts, since it's not clear how to count ballots which rank all remaining
> candidates equally, and consequently not clear how to eliminate more candidates.
>
> The mentality is that the measure of a candidate's suitability for election is
> his approval (or "support," to use a less loaded term), but once candidates
> have majority approval, another measure is needed.  We could put a lot of things
> here instead, such as electing the finalist with the most first-slot votes.
>
> The "strategic distance" between the first two slots is increased from MCA.  That is,
> in MCA, it is a bit strange to use the middle slot: If you put A in first and B in
> the middle, it means you think A and B might be contenders for Majority Favorite,
> but if A doesn't win that way, you think, to some extent, that A isn't a contender
> anymore, even by having greatest approval.  Put differently, why would you try to
> break an A-B tie for majority favorite, but not for greatest approval?  (Maybe if
> one suspects that Worst is a contender by greatest approval, but not by majority
> favorite?)
>
> I suspect if, in deciding on MCA strategy, we take it as granted that the odds of
> a candidate winning by majority favorite are proportional (or somehow tied) to
> his odds of winning by greatest approval, we might find that the middle slot is
> pretty useless.  Worth thinking about.
>
> In MAR, the "distance" between the first two slots is the chance that some candidate
> in each slot will have majority approval; the distinction is useful if you want
> to approve two very viable candidates.  In MCA that distance is the chance that
> such candidates will tie for majority *favorite*, which is much less likely, I
> think.
>
> I thought that perhaps MAR would meet Participation, but it doesn't: It's possible
> for you to give the election to a middle-slot candidate when a first-slot candidate
> would have won, in the case where, without your vote, only Favorite has majority
> approval, but with your vote, Compromise also has a majority, and beats Favorite
> pairwise (i.e. in the fake runoff).  However, unlike MCA, I can't come up with
> any scenario where your vote causes Worst (a third-slot candidate) to win.
>
> I'm not so pleased with the arbitrary nature of a majority cutoff...  It would be
> nice if an Approval-type method could be devised which satisfies later-no-harm;
> that is, the voter would be able to "withdraw" approval from Compromise if it
> would make Favorite win, and not just if some majority rule can be invoked.
>
>
> Kevin Venzke
> stepjak at yahoo.fr
>
>
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