El sáb., 22 de ene. de 2022 6:28 p. m., Daniel Carrera dcarrera@gmail.com
escribió:

Mike Ossipoff once reported explaining Schulze to the complete satisfaction
of his non-technical girlfriend, by using an equivalent, but more
intuitive, "beatpath" formulation of Schulze:

A beatpath is a chain of defeats leading from one candidate to another. A
chain is no stronger than its weakest link.

We say that X strongly beats Y when  X has a stronger beatpath to Y than
Y's strongest beatpath to X.

Elect the candidate that strongly beats every other candidate.

[The existence of such a candidate follows from the transitivity of the
"strongly beats" relation. No need to bring this up unless your friend asks
how you know that such a candidate exists.]

On Sat, Jan 22, 2022 at 11:35 PM Forest Simmons forest.simmons21@gmail.com
wrote:

[friendly_sarcasm] Yeah, the TV ad just writes itself! [/friendly_sarcasm]

More seriously though, phrasing it like that does help. I still think it's
quite difficult. I'm not confident that I will remember this explanation in
8 months. Also, it is one thing to explain the algorithm and another to
convince me that the algorithm makes sense. That's another place where I
think RP has an advantage. If an overwhelming majority is adamant that A >
B, then you gotta respect that; it's just democracy. Whereas if people
generally say C > A but they are a little "meh" about it, then maybe that's
the one to throw away. Also, I didn't have to look up RP to remember that,
and I'm confident I'll remember it 8 months from now. I think it's just the
principle of basic fairness, whereas Schulze feels like it's trying to be
too clever and I don't intuitively trust what would come out of that.

Cheers,

Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University

That's not so bad.  I consider that the most concise explanation of Schulze with normal language that I have read.  Must include that the strength of each link in the chain is either the winning margin or just the winning votes in that pair of candidates.

Not yet suitable for legislation.  But is a really good way of expressing the algorithm.

I think I will.  I had already understood Schulze (with margins or with winning votes) but hadn't had as concise an explanation as that.  Sometimes it needs coming up with the best term for a single concept.  In this case "strongly beats".

For Bottom-Two_Runoff, I came up with the term "lesser voter support" to differentiate from having fewer votes.

I now have written some crude, untested, C code for Ranked Pairs and I just really don't see how to turn it into language plausibly suitable for legislation.

Yup.  I think that's what Nic was thinking.

well that Ossipoff interpretation helped me a lot.  It very nearly spells out the fundamental defining principle that is unique to Schulze.

Markus, are you listening in?  What do you think of the Mike Ossipoff expression of the Schulze method?  Maybe you had already expressed it as such and I just missed it.

--

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

"Imagination is more important than knowledge."

.
.
.

Here's a poor man's version of beatpath:

Anybody qualified to vote is also qualified to nominate a finish order.

Elect the candidate at the head of the strongest finish order among those
nominated.

The strength of a finish order is the strength of its weakest link. The
strength of a link X_k--->X_(k+1) is the number of ballots on which X_k is
ranked ahead of X_(k+1).

El sáb., 22 de ene. de 2022 9:47 p. m., Daniel Carrera dcarrera@gmail.com
escribió:

On Sun, Jan 23, 2022 at 12:31 AM robert bristow-johnson <
rbj@audioimagination.com> wrote:

Yeah, it's tough. Here's my best attempt, but I don't think I would
actually show this to a legislator:

(X) Every candidate is compared against every other candidate in a
one-to-one matchup. For each matchup, the candidate that is preferred above
the other by a simple majority of ballots is the winner of that matchup and
the other candidate is the loser. The margin of victory is the number of
ballots that rank the winner of the matchup above the loser, minus the
number of ballots that rank the loser above the winner. The presiding
official shall make a list of matchups, sorted in order of margin of
victory, with the matchup with the largest margin of victory at the top of
the list and the matchup with the lowest margin of victory at the bottom.
The presiding officer will use this list of matchups to produce a final
ranking of all candidates. The construction of the final ranking begins
with the inclusion of the first matchup (the one with the highest margin of
victory). The presiding officer will consider each matchup in order of
margin of victory. If the matchup conflicts with the preferences already
indicated in the final rankings, that matchup is set aside and the
presiding officer shall continue to the next matchup. After the last
matchup (the one with the lowest margin of victory) has been considered,
the presider shall identify the candidate with the highest final ranking,
who is then elected.

Cheers,

Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University

Culi,

Great site!

And great first EM post.

Your "first minus last" score for each candidate is equivalent to what some
of us call the implicit fractional approval score, which is your score plus
the total number of ballots, all divided by two.

Yours is simpler for people that are comfortable with integer arithmetic.
The advantage of ours is that it is just the number of Top votes plus half
of the number of non-Bottom votes ... no possibility of getting negative
scores.

Now here is the best (IMHO) use of your suggested scores:

While more than one candidate remains, among these, eliminate the highest
score candidate that does not pairwise defeat the one with the lowest score.

Unlike the elimination method you suggested, this method, "Fractional
Implicit Approval Chain Climbing," FIACC, is monotonic, clone free, and
Banks efficient.

As long as equal rankings and truncations are allowed, we can confidently
(but humbly) affirm that FIACC is the best known "Universal Domain" method
with these three properties.

Universal Domain means RCV style ballots only.

A Banks candidate is one that stands at the head of a maximal chain of
candidates ordered by pairwise victory.

Every Banks candidate is also a Landau candidate, which means it has a
beatpath of two or fewer steps to any other candidate.

If a method is not Landau efficient, then (embarrassingly) sometimes it
will elect a candidate that is covered by some other candidate. This other
candidate has a valid complaint or Pareto dominance over the winner with
respect to pairwise wins, ties, and losses:

Candidate X covers Y iff it not only defeats Y, but also defeats every
candidate defeated by Y.

Of the well known methods, only Kemeny-Young and Copeland are Landau
efficient. But they both lack monotonicity, among other failings in
comparison with our simple FIACC method.

In particular, unlike Copeland, FIACC is highly resistant to Chicken and
Burial attacks.

And unlike K-Y, FIACC is computationally tractable, while K-Y is
non-polynomially hard.

I know that's a lot to digest ... but you can do it one bite at a time with
patience.

The method is simple ... and the three basic properties (monotonicity,
clone independence, and Condorcet efficiency) are easy to understamd.

It's only the Banks and Landau efficiency (that distiguish it from Ranked
Pairs, Schulze, River, etc) that are a challenge to fully appreciate.

To emphasize the simplicity of the method itself, I repeat the complete
definition here for reference:

While more than one candidate remains, among these, eliminate the highest
score candidate that does not pairwise defeat the one with the lowest score.

Assuming you know what "scores" we're talking about and what "pairwise
defeat" means, that procedure completely and unambiguously defines the
method.

Do you know anybody who can do the same for their favorite complete method
with the same unambiguous precision in fewer than twenty-five words?

[Copeland is not by itself a complete method, just like Condorcet is not a
complete method ... they require "completions" to resolve ubiquitous ties
and cycles.]

Once again, welcome, and thanks for your great first post to the EM list,
and invitation to your site.

-Forest

Forest

El sáb., 22 de ene. de 2022 12:03 p. m., culitif@tuta.io escribió:

Hey Forest,

Thanks so much for the feedback and the kind welcome! That certainly is a lot to digest, but I did find your definition of it really helpful. I've been kinda busy recently, but I'd definitely love to take a crack at coding/implementing and visualizing the system at some point in the near future!

Would a system that uses the implicit fractional approval score really be equal to a system that takes the first and last place votes for each candidate? 
-Culi

Jan 23, 2022, 11:29 AM by forest.simmons21@gmail.com:

El lun., 24 de ene. de 2022 3:53 p. m., culitif@tuta.io escribió:

Let F(X), L(X), and MR(X), respectively, be the number of ballots on which
X is voted First, Last, or Middle Ranks, me respectively.

Then the total number of ballots is the number T = F(X)+L(X)+MR(X), so your
score CULI(X)=F(X)-L(X).

Now substitute the RHS of these two equations  into the expression

CULI(X)+T,
and simplify the result:

(F(X)-L(X)) +(F(X)+L(X)+MR(X))

= 2F(X) +MR(X)

Now divide both sides by two:

(CULI(X)+T)/2=(2F(X)+MR(X))/2

.5CULI(X) +.5T = F(X)+.5*MR(X)

So multiplying your score CULI(X) by a positive constant (.5) and adding
another constant (.5*T) yields the fractional approval score that most
people prefer, because it eliminates negative scores that bother some
people.

All of this is based on two facts

1. x>y if and only if x+c> y+c

and

2. p>q if and only if rp>rq,
   for any positive r.

Put these together and you have

rt+k>rv+I  if and only if t>v
(povided r is positive)

"Positive affine transformations preserve order."