[EM] Smith+IRV//Approval

C.Benham cbenham at adam.com.au
Mon Sep 18 20:12:34 PDT 2023

It had crossed my mind that it might be possible to construct a 
(probably) complicated and implausible example where
the IRV winner wins but there is a more approved candidate that pairwise 
beats the IRV winner but is not in the Smith set.

That would be a very embarrassing failure of Double Defeat.

Your suggestion avoids that problem, but on the other hand to me it 
sounds a bit more arbitrary.

Why only "short" beatpaths?  Why not any beatpath?


On 19/09/2023 7:57 am, Forest Simmons wrote:
> How about simply restricting Approval to the candidates with short 
> beatpaths to the IRV winner (including the IRV winner itself)?
> The main advantage of this version is that it doesn't require any 
> explanation of Smith.
> fws
> On Sun, Sep 17, 2023, 8:52 AM C.Benham <cbenham at adam.com.au> wrote:
>     I've been thinking a bit why the Condorcet has so little popular
>     traction, why some quite intelligent people
>     are wary of it and prefer IRV.
>     Suppose we are talking about electing members of a parliament (or
>     legislature) in single-member seats.
>     Typically the two largest parties, say one centre-left and and one
>     centre-right, will between them win nearly
>     all the seats and with luck the one that is preferred by more voters
>     than the other will get more seats
>     (and so in a Parliamentary system will form a government with its
>     leader
>     becoming the Prime Minister).
>     So in this limited sense the result is very very roughly
>     "proportional".  Assuming the small wing parties'
>     supporters are normally spread out in lots of different districts,
>     they
>     will get no seats.
>     But suppose in a lot of the seats the contest looks like this:
>     47 A>>>C>B
>     43 B>>>C>A
>     10 C>A>>B
>     If this is IRV  or FPP then A easily wins, but the CW is C.
>     But A is clearly the highest "social utility" candidate, and assuming
>     that voting is voluntary and at
>     least somewhat inconvenient or costly, then C has only been voted
>     the CW
>     because both A and B
>     are on the ballot. If one of those candidates wasn't, then most of
>     his
>     or her supporters would stay
>     home and allow the other to easily beat C.
>     And if something similar (electing a weak centrist that most of the
>     voters don't like) happens in enough
>     seats it could result in the "weak centrist party" being grossly
>     over-represented in the legislature.
>     So to allay these fears I suggest this compromise with IRV:
>     Smith+IRV//Approval:
>     *Voters strictly rank from the top however many or few candidates
>     they
>     wish.  Default approval is only
>     for the top-ranked candidate, but voters can extend approval to
>     one or
>     more other candidates by marking
>     the lowest-ranked candidate they approve.
>     Elect the most approved candidate that is either in the Smith set
>     or is
>     the IRV winner.*
>     Allowing above-bottom equal-preferences (at least without a lot of
>     extra
>     complexity) makes Push-over strategising
>     easier.
>     So in the type of example I just discussed the IRV winner would
>     normally
>     have a much higher approval score
>     than the CW, but the supporters of the IRV runner-up could change
>     that
>     if they like by extending their approval
>     to the CW (who then might win, especially if the CW's supporters
>     refrain
>     from extending their approval to the IRV winner).
>     Chris B.
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