---------------------------- Original Message ----------------------------

Subject: [EM] Minmax ranked method

From: "Kristofer Munsterhjelm" km_elmet@t-online.de

Date: Sun, November 5, 2017 3:24 am

To: "EM" election-methods@lists.electorama.com

�
i'm still parsing this phrase.

--
r b-j � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."

On 11/05/2017 08:08 PM, robert bristow-johnson wrote:

Whoops, yeah, I saw that could be a bit confusing just after I posted :-)

For each potential council, there's a voter that's most displeased with
having that council elected. A minmax method minimizes how displeased
this most displeased voter is (which may be a different voter for
different proposals).

In veto situations, if a minority can say "nope", it's more important
that no such minority can be annoyed enough that they do so than just
how annoyed the rest of the voters get.

�

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Subject: Re: [EM] Minmax ranked method

From: "Kristofer Munsterhjelm" km_elmet@t-online.de

Date: Sun, November 5, 2017 3:39 pm

To: rbj@audioimagination.com

"EM" election-methods@lists.electorama.com

and, for a Smith set of size 3, Minmax picks the same candidate as does Ranked-Pairs (margins) as does Schulze (margins), right?� i just wanna make sure i got that right.

so how is the rule worded differently for these three methods in this context of 3 candidates?

--
r b-j � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."

On 11/06/2017 08:02 AM, robert bristow-johnson wrote:

That's because the word "minmax" is used in two different contexts. In
the Minmax Condorcet method, what you're taking the minimum of the
maximum of is the Condorcet matrix. The Minmax method chooses the
candidate with the weakest (minimal) greatest (maximal) defeat, i.e. the
candidate who loses the least one-on-one to the candidate he loses the
most to. When there's a Condorcet winner, that CW doesn't lose to
anybody, and so he's the winner of the Minmax method since you can't do
better than not losing at all.

In Minmax Approval, what you're minmaxing over is the voters'
preferences. It chooses the council that is minimally unrepresentative
to the voter to which it is maximally unrepresentative. E.g. consider an
Approval system like this:

100: A B
10: C D

Any proportional representation system would choose A and B for a
two-seat election. Minmax Approval would choose one of A and B for the
first seat and one of C and D for the second. This is because it's much
worse to leave the worst voter (one of the ten) not represented at all,
than it is to leave both only slightly represented.

In veto terms, if the 10 voters can say "nope", it doesn't matter how
well represented the 100 voters are by {A, B}. Either C or D must be on
the council because otherwise, it will be rejected. (By the same logic,
the method can't elect both C and D because then the majority of 100
would go nope).

Sometimes it isn't possible to please everybody, e.g.

100: A B
10: C D
5: E F

(two to elect)

but then it would try to come closest to actually pleasing everybody.
Most likely it would have the same outcome as the last example because
there's a greater chance that a minority of 10 can block the process
than that a minority of 5 can do so.

---------------------------- Original Message ----------------------------

Subject: Re: [EM] Minmax ranked method

From: "Kristofer Munsterhjelm" km_elmet@t-online.de

Date: Mon, November 6, 2017 7:36 am

To: rbj@audioimagination.com

"EM" election-methods@lists.electorama.com

From: "Kristofer Munsterhjelm" km_elmet@t-online.de

i understand that now.� but i mean in the ranked-ballot context.� (sorry to poke in this question out of context.)

and that is the same candidate who is chosen by� RP (margins) and by Schulze (margins).

i understand there is no issue (with any of those 3 methods: Minmax, RP, Schulze) when there is a CW.� my specific question was about the case that there is no CW and a Smith set of 3 candidates, which i think is the Rock-Paper-Scissors scenario.

--
r b-j � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."

On 11/07/2017 03:55 AM, robert bristow-johnson wrote:

To reduce the confusion, let's call the method Simpson (which is another
name for Minmax Condorcet), and call the other types of methods
"veto-friendly" (from the example I gave).

Only for three candidates. For instance, Schulze and RP are cloneproof,
but Simpson is not; e.g.
https://en.wikipedia.org/wiki/Independence_of_clones_criterion#Minimax

When there are only three candidates, then RP and Schulze give the same
result as Simpson. When there are more candidates but a Smith set of
three, then RP and Schulze might give a different result from Simpson.
In Wikipedia's clone example above, the Smith set is {B1, B2, B3} (three
candidates), but Simpson elects A.

Also, Simpson probably isn't a good candidate for a veto-friendly method
since it's more majoritarian than even a proportional method. E.g.

51: A>B>C>D>E
25: F
24: G

Simpson's social ordering would be something like A>B>C>D>E>F>G, but
electing the four highest ordered for a multiwinner election would elect
{A, B, C, D}. In this particular election, a better result for a method
that's aiming to represent everybody would be {A, B, F, G}, which is
what a proportional representation method would provide.

---------------------------- Original Message ----------------------------

Subject: Re: [EM] Minmax ranked method

From: "Kristofer Munsterhjelm" km_elmet@t-online.de

Date: Wed, November 8, 2017 1:40 pm

To: rbj@audioimagination.com

"EM" election-methods@lists.electorama.com

the reason i want to be square on this point is only that of advocacy.
i want to see a Condorcet method advocated for Ranked-Choice Voting instead of IRV.� i want to see RCV (Condorcet) adopted for use in
governmental elections.
i know that people, like me, that know only enough to be a little dangerous, will ask two questions (assuming their fine with the ranked ballot, but they are used to IRV).�

1. they will ask questions about the complexity of the tallying algorithm (which, for some reason, they think IRV is simpler), and

2. they'll say something about Arrow and ask about what i consider is the only conceptual problem with Condorcet which is what happens with a cycle.�
   because of those two issues i would probably always advocate that Ranked Pairs (margins) be the method adopted, even though i think that
   Schulze (margins) would be better (and you're confirming that Minmax would be worse) but they're all equivalent in outcome if there is a CW or if the Smith set is 3.
   i feel comfortable about that.� first of all, i think that in reality it will be very very rare that a cycle happens.�
   in Burlington 2009 we had 5 candidates out of which 4 were serious candidates (that they really campaigned) and 3 were all plausible winners.� of those three, one was the Plurality winner (of first choice votes), one was the Condorcet winner, and one was the IRV winner.� and the supporters
   of all three all said that they're guy deserved to win.� since the CW didn't win the IRV, the final round was between the Plurality and the ultimate IRV winner and the margin was only 252 votes out of 8900 total.� (the CW beats the IRV winner by 587 and beats the Plurality winner by
   930.)
   but the Condorcet ordering was solid for every subset of candidates.� we knew who was preferred pairwise over every other candidate.� then if you hypothetically remove the CW, then the IRV winner was clearly preferred pairwise over every remaining candidate.� if you
   remove both the CW and IRV winner, the remaining Plurality candidate was preferred over every other candidate remaining.� there was no doubt who was really preferred by the city and what the order of preference was.
   cycles are not gonna happen very often. almost never.
   now, perhaps,
   once in a blue moon a cycle happens, how often do you think the cycle will be any more complicated than a Smith set of 3?� i think it will never be any bigger than a Smith set of 3 because i think a Smith set of 3 will happen almost never.� and since Minmax and RP and Schulze pick the
   same candidate when the Smith set is 3 (and Minmax doesn't sound so good anyway), my advocacy is for RP, which in my opinion is much easier to explain to people than Schulze or Minmax.� and even though i saw Markus post some pretty compact legal language for Schulze, it seemed inpenetratable to
   me.
   that's the opinion of an armchair voting systems advocate.

--
r b-j � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."

On 11/08/2017 08:32 PM, robert bristow-johnson wrote:

I can think of two situations where cycles could happen more often:

1. The political landscape changes. E.g. Condorcet breaks two-party rule
   and there's real competition along multiple political dimensions again.

2. The organized participants/parties try to exploit the system.

For the first reason, I prefer systems that generalize well (like Ranked
Pairs or Schulze, contrasted with say Minmax/Simpson). Voting systems
should last, because it's really hard to change them, that kind of thing.

For the second reason, I prefer systems that are robust to tactical
nomination (usually clone independence).

But I wouldn't have a problem with someone proposing a Condorcet method
that doesn't really pass number one, because as long as it's not
something obviously flawed (like say "Condorcet if there's a CW,
otherwise the IRV winner"), just lasting until the kind of political
environment where there is real competition is a real improvement
compared to Plurality two-party rule.

Of course, one has to be careful here. FairVote could say that IRV is an
improvement upon Plurality too - but the problem with IRV is that it
breaks down too quickly (as you know). Approval, IMHO, has the risk that
miscalculation on the voters' behalf could produce some very
counterintuitive results and thus also a backlash. Approval is more a
"rather risky" thing, whereas IRV is a "definitely fails" thing.

However, I would want the system to have some reasonable resistance to
point number two. I seem to value tactical nomination resistance higher
than say, Mike, who values strategic voting resistance more highly.

There are degrees here as well. I'd consider Minmax's clone resistance
problems to be less severe than Borda's, since Borda's are so serious
that it's pretty much unusable.

In any event, I agree that Ranked Pairs is easier to explain than
Schulze. Schulze is probably at least as easy if you're talking to a
mathematician (since beatpaths can be defined quite elegantly in a
recursive manner), but Ranked Pairs seem more procedurally clear (sort
the pairs, lock in unless that causes a contradiction with what you've
already seen).

Do you have some nice clone and nomination related (real life large political election) example where Minmax/Simpson would be in trouble?

The first example in my mind is a case where one party nominates three equally liked candidates that end up in a loop, and therefore none of them wins, although one of them would have won without the loop. This is however not really a bad problem because it can be solved by nominating only two similar candidates. The probability of this kind of a loop is also very low (especially if there are clear differences between candidates, i.e. they are not indistinguishable to the voters).

Next example. There are three left wing parties that each have one candidate, and they end up in a loop as above. In this case it is not possible to tell one of the parties not to nominate any candidates. Since there are only three left wing parties, it is possible that those candidates have mutual majority. They could be the top three candidates in all the votes of the leftist voters. Now we have two cases. Either the looped votes indicate that there would be considerable dissatisfaction among the leftist voters (and others) if any of their candidates will be elected, in which case a right wing candidate could be a better winner. Or alternatively the looped votes are just an accident, and actually all left wing voters would be very happy to elect any of the leftist candidates. Since we have only ranked votes, we can not tell which one of those explanations is closer to the truth. Typically it is also not possible to check if the looped candidates have mutual majority (or are in ranked next to each others in many votes). It is thus hard to tell how "clone like" the looped candidates are, and if the loop vas a result of having "clone like" candidates, or just a loop that indicates unwillingness to elect the other candidates in the loop.

Observations:

1. loops are quite rare (especially when candidates have considerable differences (i.e. when they are not seen by voters as "all identical"))
2. if there is a loop, it is not easy to tell if it is a loop of "clone like" candidates or an indication of other kind of cyclic preferences
3. the preference matrix can't tell us if clones (votes where the looped candidates were ranked next to each others) had a major role in creating the loop
4. it can be better not to elect one of the top looped candidates (if being looped indicates interest to change that candidate to someone better, and there is a candidate that is more "stable")
5. if you use a clone proof method, it will always assume that top looped candidates are clones (in the sense that one of them must win), and that could sometimes be a mistake / unwanted result
6. three clones within one party can be avoided (if they are considered a risk)
7. from minmax point of view it is important to discuss if the target of the election is to elect a candidate that loses to others as little as possible, even in the presence of loops (is friendly fire an essential risk, or should pairwise losses be always counted as enemy fire)

If my party (or wing) had three serious potential winners, it would probably make sense to nominate them all, since the risk of not winning because of the loops is probably much lower than the risk of not winning because of not nominating a potential winner. Candidates may be nominated also for other reasons, like keeping the party in the limelights and hoping to win in the next election.

Juho