[EM] Smith+IRV//Approval

[Richard Lung]

Some "quite intelligent" people were wary of Condorcet pairing over two centuries ago, namely Pierre-Simon Laplace because Condorcet pairing treats different orders of preference as of equal value.
Laplace, by the way, was rated one of historys half-dozen greatest mathematicians. He offers what JFS Ross called a rather "elliptical" proof for his belief.
He was inclined to say that was too obvious for a proof. When his American translator of Mechanique Celeste, saw that remark, he said he knew he was in for a hard nights work.
An order of choice recognises some choices have priority over others. Condorcet pairing does not, which is reason to be wary of it.
Order (in the vote) and proportion (in the count) are prerequisites of mathematics and of civilization in general, tho politicians demur.

Richard Lung.



On 17 Sep 2023, at 4:52 pm, 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
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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