[EM] Re: 3-slot method
chrisbenham at bigpond.com
Thu Nov 25 05:52:51 PST 2004
In response to me posting this suggestion for a 3-slot single-winner method,
> (1) Voters put the candidates into one three slots, Preferred,
> Approved, or Disapproved. (Default is Disapproved).
> (2) If not all the candidates are rated as Disapproved by a majority,
> then eliminate those that are.
> (3) After the eliminations, candidates who are rated as Approved on
> ballots that rate no (remaining) candidate as Preferred
> are promoted on those ballots to Preferred.
> (4) Elect the winner of the pairwise comparison between the candidate
> who is (after steps 2 and 3) most Preferred and the
> candidate who is least Disapproved.
you offered these comments:
>First of all, it it not Condorcet, is it? It seems to me that in the
>following example, it will elect A though C is the CW:
>Defeats A>B(7:6), C>A(7:6), C>B(7:6), hence C is the CW. No candidate is
>disapproved by a majority (A:6, B:3, C:4). A is most preferred (6), B is
>least disapproved (3), hence A wins!
>Did you check any other criteria? I always try Condorcet and
>monotonicity first. I fear the latter is quite improbable because of the
> detail "If not all the candidates are rated as Disapproved by a
>majority..." and because of the IRV-like promotion in step (3).
Yes, in a very mild way, this method does fail Condorcet and
mono-raise (aka monotonicity).
Douglas Woodall gives this example:
>Total votes 21. No candidate is rated as Disapproved by more than
>half the voters, so a (being both most Preferred and least Disapproved)
>is elected. However, if one of the bca ballots is replaced by bac,
>then c is Disapproved by more than half the voters, and so is excluded.
>Then b is promoted to Preferred on the 3 cba ballots and so b will beat
>a by 11 votes to 10.
What I find surprising and remarkable in this 3-candidate example is
that a is both the most "Preferred" and the least
"Disapproved", and yet is not in the top cycle! (b>c 12-9, b>a 11-10).
In response to your other question, I did more-or-less satisfy myself
that it meets Minimal Defense, Trucation Resistance,
a kind of Mutual Majority (aka Majority for Solid Coalitions, aka
Majority), No Zero-Information Strategy (and therfore
the weaker Sincere Expectation Criterion).
This method was meant to be simple and (maybe) saleable. I am sure that
in public political elections it would work (99%)
as well as any other 3-slot method.
But on refllection, I now think the best 3-slot method is just:
"elect the least Disapproved member of the (3-slot) Schwartz set" !
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