I think the section "Pathologies of IRV" in the IRV article should be scrutinized and possibly corrected.  It says...

"Systems which fail Condorcet but pass mutual majority can exclude voters outside the mutual majority from the vote, essentially becoming an election between the mutual majority.[citation needed] IRV demonstrates this exclusion of up to 50 percent of voters, notably in the 2009 Burlington mayoral election where the later rounds became a runoff between the mutual majority of voters favouring Andy Montroll and Bob Kiss. This can recurse: if a mutual majority exists within the mutual majority, then the majority becomes a collegiate over the minority, and the inner mutual majority solely decides the votes of this collegiate."

Is the description about Burlington 2009 accurate?  I am not sure exactly what is meant by "mutual majority of voters".  The paragraph sounds very wonky.

--

r b-j . _ . _ . _ . _ rbj@audioimagination.com

"Imagination is more important than knowledge."

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On Sat, Mar 16, 2024 at 13:53 robert bristow-johnson <
rbj@audioimagination.com> wrote:

Mutual-Majority:

The majority-size set of voters who all prefer eachother’s single-favorites
to everyone else.

[end of Mutual Majority definition]

There can’t be more than one mutual-majority.

(…other than maybe one inside the other.)

There isn’t always one. Hare—due to its elimination of least favorite, &
its transfers, & its election of the 1st candidate to top a majority of
ballots—elects the favorite of the largest faction of a majority, which
might not always be mutual.

…but it can be said that if there’s a mutual-majority, then Hare will elect
the favorite of the largest faction of that mutual-majority.

I used to say that that means that Hare indeed gives a majority guarantee.
But that’s misleading, because the winner isn’t the favorite of the
mutual-majority, but only if its largest faction.

It has only a plurality among the mutual majority.

So the IRVists’ majority claim is deceptive (…as is their claim that your
ballot always helps your 2nd choice against your last choice)

As I said, I like Hare for parlor-elections for a pizza-topping or a movie,
but that’s all.

It has unnecessary, potentially-ruinous strategy-problems.

I used to point out that, when it eliminates a low-favoriteness CW, it
moves the win in the direction preferred by the median voters…i.e. in the
progressive direction… electing someone even more progressive.  Nothing
wrong with that, right?

But there are likely more than one other progressive candidate to whom the
CW’s voters can transfer…& then Hare’s favoritness standard can lead to a
silly flippant idiosyncratic choice.

Much better to just elect the CW, who pairbeats everyone, & who has stable
solid broad support.

…but for pizza-toppings or movies, Hare is great!!

On 2024-03-16 21:52, robert bristow-johnson wrote:

It's not just wonky; I think it's wrong and generalizing too much from IRV.

Methods that pass mutual majority elect from the smallest set of
candidates that a majority ranks ahead of the rest (not necessarily in
the same order). A method can pass MM independently of whether it passes
Condorcet.

What the author seems to be saying is that if a method passes MM but not
Condorcet, then it has center squeeze. I don't think that's a given;
center squeeze is more a feature of the non-Condorcet MM methods that
have been proposed (such as DAC/DSC and IRV).

It would be more accurate to say that IRV itself determines the
strongest wing of the strongest wing (recursively), and that's why it
gets center squeeze. IRV gets its later-no-help/harm properties by
successively shearing off information about candidates who are not part
of the current "strongest wing".

So the paragraph could probably be replaced with one that talks about
center squeeze itself: first, that it happens, and then why. Perhaps
draw some ideas from the following page, which likens the elimination
process to an "instant primary": https://betterchoices.vote/ConsensusVoting

-km

On 2024-03-16 20:45, Closed Limelike Curves wrote:

I haven't had much time to dedicate to Wikipedia of late, but here are
some comments and ideas about how the examples could be corrected.

The problem is that we can't have all of the criteria at once. That
doesn't mean that every method is equally good, but if the table is
meant to give an indication of which methods are better than others, it
would have to be reorganized.

I'm not sure how though? We could argue that elections with Condorcet
cycles are rare and thus Condorcet is important. Or reorder the columns
by how much Wikipedia traffic their respective articles get as a proxy
of how serious/interesting people think the criteria are?

Or have a section with arguments about what criteria are important.
IRVists would probably say LNH. Condorcet proponents would say
Condorcet. rb-j would say summability, approval and cardinal guys would
say weak FBC.

Maybe people can agree that clone independence is pretty important.
There might be a room for more general strategic nomination incentive,
too, and then we could link to Green-Armytage's results showing IRV to
have significant exit incentive despite its clone independence.

Ideally, we'd pick some sensible default ballot distribution and then
give information about how often failures occur. Impartial culture is a
useful "worst case" or pessimist distribution: if things can go wrong,
they likely will go wrong in IC, but it should be clear that that's what
it's used as a proxy for.

Spatial distributions are more realistic.

Then we could run simulators to get the failure probabilities and report
them. But as Wikipedia is not a place for OR, we would have to get them
published elsewhere first.

That ought to be the easiest one to fix. Make a reference to center
squeeze (see my reply to rb-j), one to monotonicity (IIRC there are
already references to sources about IRV nonmonotonicity), and one to
general exit incentive as indicating spoiler effects.

-km

These are great suggestions, thank you :)

For organizing the criteria, my proposal is to replace the current table
with maybe 5 numbers:

1. Condorcet efficiency
2. Social utility efficiency
3. Spoiler resistance (IIA compliance)
4. Participation satisfaction
5. Monotonicity satisfaction

(Is Jameson Quinn on this email list? I know he had some relevant
simulations.)

On Sun, Mar 17, 2024 at 4:39 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 2024-03-22 02:49, Closed Limelike Curves wrote:

IIA compliance might be less informative than you'd think, because every
Condorcet method has the same frequency of IIA failures: you can remove
a subset of non-winners to change the winner iff there is no Condorcet
winner. Non-Condorcet ranked methods are worse: they fail when there's a
cycle, and also whenever they fail to elect the CW.

So perhaps that should be replaced with a category listing, although it
would be interesting to see the actual IIA failure rate for Range with
automatic normalization (or above-mean approval strategy). Then again,
filling in numbers based on simulations from EM might be considered OR;
I don't know what the burden of proof/reliability rules of Wikipedia
would say.

Possible categories could be:
passes IIA (e.g. cardinal with an absolute scale, random pair)
LIIA (Ranked pairs, River)
ISDA (Smith//IRV)
Condorcet (Minmax)
None of the above (Plurality).

Alternatively having clone independence instead of IIA would be better
at differentiating between the methods. I would also suggest a strategy
resistance number, by James Green-Armytage's definition. And summability.

Although if you're doing clone independence, JGA's strategic exit/entry
might give a better idea of strategic nomination resistance, since some
nominally clone independent methods have incentive to enter or exit - in
particular IRV.

Jameson used to be on the list, but he hasn't posted since 2018.

-km

It's not OR if you put it on Arxiv first. ;)

IIA compliance might be less informative than you'd think, because every

Ooh, that's true. How about a spoiler index instead, then, going by the
winner's change in position? So, for example, if the runner-up is elected
after adding/removing a spoiler, that contributes 1 point; 2 points if it's
the third-place finisher, etc.

On Thu, Mar 28, 2024 at 3:08 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote: