[EM] Approval-enhanced IRV

[C.Benham]

49 A (sincere might be A>B)
24 B
27 C>B

This is the classic example used by fans of the Minimal Defense 
criterion to attack any method that elects A here, like IRV and Margins.

More than half the voters rank B above A and A no higher than 
equal-bottom, and yet (failing MD) A wins.

A big point for it is that the 27 C>B voters have reason to regret not 
compromising and voting B>C.

With this method, if their main concern is to defeat A they can mark B 
as approved and achieve that goal without having to insincerely
order-reverse.

A is the IRV winner.  B will be the candidate with the most approval 
opposition to A.  B pairwise beats A. All the ballots that rank B already
truncate just below B, so B wins.

The MD criterion has gone a bit out of fashion because it directly 
contradicts the Chicken Dilemma criterion.

49 A
24 B (sincere is B>C)
27 C>B

That says that the B faction should not be able to steal the election 
from B by this defection (insincere truncation against a faction that is 
giving
yours its second-preference votes). Normal IRV  meets CD.

  Here if the C>B voters have maybe not such a strong B>A preference and 
want to guard against being stung by Defection, then they can not
mark B as approved.  Then C will be the candidate with the most approval 
opposition to the IRV winner A.  A wins that pairwise comparison and
so is elected.

The reason for the last part of the method in the full version is that 
without it I fear that some voters might be able to rank one or more extra
candidates that changes the IRV winner from one that wins the pairwise 
comparison against a candidate they prefer to one that loses it,
thereby breaking LNHelp.

Chris B.



On 6/08/2023 1:37 pm, Forest Simmons wrote:
> For us old lazy guys who sometimes need help seeing the obvious ... 
> how about a couple of pertinent examples with their most pertinent 
> features high lighted?
>
> On Sat, Aug 5, 2023, 8:29 PM C.Benham <cbenham at adam.com.au> wrote:
>
>     This idea is inspired by our recent and ongoing "war on Burial".
>
>     Approval-enhanced IRV
>
>     *Voters strictly rank from the top however many candidates they
>     choose
>     and have the option of
>     marking their highest-ranked approved candidate. Default approval
>     is to
>     only the candidate ranked
>     above all others.
>
>     Find the winner of the pairwise comparison between the IRV winner and
>     the candidate X with the most
>     approval opposition to the IRV winner.
>
>     The IRV winner is elected if it wins (or say if ties) that pairwise
>     comparison.
>
>     If X wins it, then do the whole thing again as if all ballots
>     truncate
>     just below X.
>
>     If that doesn't produce a new winner, then elect X.
>
>     If it does, then elect the original IRV winner.*
>
>     This should hang on to LNHelp while meeting modified versions of
>     LNHarm
>     and Minimal Defense.
>
>     Here is a  maybe-good-enough-most-of-the-time shorter prettier
>     variation:
>
>     *Voters strictly rank from the top however many candidates they
>     choose
>     and have the option of
>     marking their highest-ranked approved candidate. Default approval
>     is to
>     only the candidate ranked
>     above all others.
>
>     If the IRV winner is also the most approved candidate then it is
>     elected.
>
>     Otherwise elect the winner of the pairwise comparison between the IRV
>     winner and the candidate
>     with the most approval opposition to the IRV winner.*
>
>     Not a Condorcet method and probably nothing like a practical proposal.
>
>     Chris Benham
>
>
>
>
>
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