[EM] Smith+IRV//Approval

C.Benham cbenham at adam.com.au
Sun Sep 17 08:52:17 PDT 2023

I've been thinking a bit why the Condorcet has so little popular 
traction, why some quite intelligent
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: 

*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

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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