[EM] Approval-enhanced IRV (take 2)

C.Benham cbenham at adam.com.au
Wed Sep 13 00:03:31 PDT 2023

It is very difficult (if not impossible)  to modify IRV without causing 
it to lose some criterion compliance
that a lot of its supporters like.  This is part of the case that it is 
in its way a good method, certainly compared
to STAR.

49 A 24 B 27 C>B| Here, with the C>B voters extending their approval to 
B, the winner in this suggested "approval-enhanced" method is B. But 
plain IRV meets Later-no-Harm, which a lot of people like. In this 
example if the 24 B voters change to B>C (even without approving C) then 
the winner would change from B to C, breaking LNHarm.

49 A 24 B>C 27 C>B|

Now the new IRV winner is C and C  also now pairwise beats both the 
other candidates.

I am sure that a more complicated example could be found that 
demonstrates that it also fails Later-no-Help, so maybe Toby
was right in calling this a "kludge" after all.

Chris Benham

>   [EM] Approval-enhanced IRV (take 2)
> *C.Benham*cbenham at adam.com.au 
> <mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Approval-enhanced%20IRV%20%28take%202%29&In-Reply-To=%3C9fed1bfa-1ee8-cb6c-8e85-e394d3eb898f%40adam.com.au%3E>
> /Mon Aug 21 09:36:20 PDT 2023/
>  *
> ------------------------------------------------------------------------
> This is I think more appealing and streamlined than my earlier 
> version. *Voter strictly rank from the top however many candidates 
> they wish. Also they can mark one candidate as the highest ranked 
> candidate they approve. Default approval is only for the top-ranked 
> candidate. Determine the IRV winner. On ballots that approve the IRV 
> winner, approval for any candidate or candidates ranked below the IRV 
> winner is withdrawn. Elect the pairwise winner between the (thus 
> modified) approval winner and the IRV winner.* This works fine in the 
> same way as the earlier version in the example given to talk about 
> Minimal Defense and Chicken Dilemma. It is more Condorcet efficient 
> than normal IRV, and meets (or comes close enough to meeting) 
> appropriately modified versions of the LNHs and Minimal Defense and 
> Chicken Dilemma. 49 A  (sincere might be A>B) 24 B   (sincere might be 
> B>C) 27 C>B If the C voters B>A preference is strong they can by 
> approving B avoid regret for not Compromising. Then the final pairwise 
> comparison will be between B and A and B will win. Chris Benham

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