[EM] Smith+IRV//Approval

Forest Simmons forest.simmons21 at gmail.com
Mon Sep 18 23:08:43 PDT 2023

No difference in practice, because when Smith has only three members, all
three have short beatpaths to every candidate.

Simpler to omit the word "short" and not worry anybody about it.

So whichever is easier to

On Mon, Sep 18, 2023, 8:12 PM C.Benham <cbenham at adam.com.au> wrote:

> 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?
> Chris
> 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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