I've just found your posting, and this is just a brief preliminary comment:

I, and often others, have just been assuming that each faction votes
uniformly.  I haven't looked at all at what percentage of the CWs's
voters would have to plump, to thwart and penalize burial.

But my preliminary answer is that at least those voters have some way to
deter burial. The would-be buriers don't know what percentage will plump,
and uncertainty can deter.

Michael Ossipoff

On Tue, Nov 8, 2016 at 11:25 PM, C.Benham cbenham@adam.com.au wrote:

On Tue, Nov 8, 2016 at 11:25 PM, C.Benham cbenham@adam.com.au wrote:

In Burlington, IRV got repealed because it didn't "protect" the CWv.

The Burlington Republicans would have had to favorite-bury in order to
"protect" the CWs.

As for "imagine", yes it can't always be reliably-predicted who's the CWs,
That isn't a good reason to make it difficult to "protect" the expected or
evident CWs.

When you let the CWv lose, you have an angry majority after the election,
as exemplified in Burlilngton. For many people, the CWs is the best that
they can get, and that's a reason to make it easy to "protect" the expected
or evident CWs.

You wrote:

(when perhaps there is no sincere CW or some other candidate
is the sincere CW) you want to have a "defensive truncation" strategy
available* inside* a method with a very strong random-fill incentive?

(endquote)

As a deterence against burial, sure.

I admit that it's difficult to improve on Approval, and that such
improvement is usually/mostly illusory. But, as I've said, organizations,
activists, and many progressive parties want rankings. And ranking might
soften or partly avoid the voting-errors of overcompromisers & rival
parties.

Polls with Approval & Score balloting showed voters doing better with Score
than with Approval. Maybe rankings, too, would soften voting-errors.

You wrote:

And you should add (and stress) that it needs plumping by *all  *of the
"CWs voters to make it impossible for burial to succeed", and not ,say,
merely 93% of them (with the other 7% sincerely fully ranking):

(endquote)

In your example below, I find nothing wrong with B winning. The example has
no CWv. As you yourself have said, the voting-system can't read the voters'
minds.

After the election, the important thing about electing the CW is to avoid
having an angry majority. In your example, the winner was the candidate
over whom the fewest voters preferred someone else. That isn't a bad result.

You speculate that A was the CWs in the example.

If A was the CWs, then plumping by even 100% of the A voters wouldn't have
foiled the burial by the B voters.

Your "CW" (Candidate A) is a peculiarly unsupported CWs.

"Protecting" such a CWs wasn't what wv was proposed, offered & advocated
for.

When I first proposed wv in the late '80s, I showed its "protection" of a
middle CWs who is supported from both sides. I never claimed that it could
"protect" a CWs who is entirely unsupported by preferrers of any other
candidate. "Protection" of an entirely outside-unsupported CWs was never
the intended purpose of wv.

You "CWs" is entirely unsupported by preferrers of any other candidate.

You said that maybe the B voters are indifferent between A & C (...that
their sincere preferences are "B".), or that maybe their sincere 2nd choice
is A.

In the former scenario, we have 3 factions with no support for anyone other
than their favorite.

In the 2nd scenario, the B voters, preferring A as their 2nd choice,
reverse that preference to bury B.  ...and the C voters, few in number,
give no support to A. In both scenarios, A isn't supported by the
preferrers of any other candidate.

So, is that the big-bad bad-example for MDDTR & wv?

43: A
03: A>B
44: B>C  (sincere may be B or B>A)
10: C

100 ballots.  C>A 54-46,  A>B 46-44,  B>C 47-10.  Top Ratings A46 > B44 >
C10.  Approvals: C54 > A46 > B44.

Here MDDTR  (like MDDTA and WV and Margins and MMPO and Jameson's latest
"holy grail")  all elect the possibly burying voters' favourite, B.

(endquote)

"Possiblely burying". The voting system needn't worry about "possibly". As
I said, you've sometimes pointed out that the voting system can't read
voters' minds. What the voting-system is given, in your example, is the
fact that there's no CWv, and that B is the candidate to whom fewest voters
prefer someone else. The election of B will result, after the election, in
the least-opposed winner.

Somehow the rest of your post got deleted. I'll reply to it later.

Michael Ossipoff

If we'd elected A in your example, we'd be electing the only candidate over
whom most of the voters have indicated preference for someone else.

Michael Ossipoff
On Nov 8, 2016 8:28 PM, "C.Benham" cbenham@adam.com.au wrote:

Approval & Score would probably elect A, if it was clear that C was
unlikely to win, & that it was effectively between A & B.

I'm not saying that A is a wrong winner in general.  ...only in a
rank-balloting election. If you invite people to rank, then you add should
honor their rankings.

Michael Ossipoff
On Nov 8, 2016 8:28 PM, "C.Benham" cbenham@adam.com.au wrote:

On 11/10/2016 1:16 AM, Michael Ossipoff wrote:

Mike,

Thanks for pointing that out!

46: A
44: B>C  (sincere is B>A)
10: C

100 ballots.  C>A 54-46,  A>B 46-44,  B>C 44-10. Top Ratings:  A46 >
B44 > C 10.    Approvals: C54 > A46 > B44.

A is the sincere CW.  MDDTR elects B.

From this we see that MDDTR /doesn't/ have "wv-like strategy".  A is
the sincere CW and all of  A's supporters plumped for A,
but nonetheless the Buriers' favourite, B, won.  Winning Votes would
have elected C.

Also we see that MDDTR  fails the Plurality criterion.  (The scenario
looks like an old Margins bad-example that a WV advocate
might have given).

So to sum up,  MDDTR  doesn't have "wv-like strategy", but does fail
Mono-add-Plump and Plurality and has a strong random-fill
incentive.

I vastly prefer 3-slot TTR,TR  (aka ICT).

Chris Benham

I'd said:

Sure. I said that.

I'd said:

Incorrect.

Here's what I just finished saying:

"Your "CW" (Candidate A) is a peculiarly unsupported CWs.

"  "Protecting" such a CWs wasn't what wv was proposed, offered &
advocated for.

"When I first proposed wv in the late '80s, I showed its "protection" of a
middle CWs who is supported from both sides. I never claimed that it could
"protect" a CWs who is entirely unsupported by preferrers of any other
candidate. "Protection" of an entirely outside-unsupported CWs was never
the intended purpose of wv.

"You "CWs" is entirely unsupported by preferrers of any other candidate."

"wv-like strategy" can only refer to strategy-properties that I claim for
wv. At no time did I ever guarantee that wv will "protect" the CW under the
conditions of your example.

No such guarantee can be made, not have I made one.

"But wait, wv does  thwart & penallize burial in Chris's example!"

...but not because of any guarantee that can be made for wv. Not because of
any guarantee-able & guaranteed wv property.

In your example, wv elects C, thwarting & penalizing the burial, because of
an accident of faction-sizes.

(Try reversing the size-relation of A & B.)

Sure, by suitable adjustment of faction-sizes,any pairwise-count method
could achieve (whatever you think is) the right result, in a cycle.

So, not electing B in your example is not a test of "wv-like strategy".

Your example isn't a test of "wv-like strategy", and has no resemblance to
the conditions for which that property was defined, and for which wv was
proposed.

And yes, I made it clear, with many examples, what wv's desirable
properties are.

...by an accident of faction-sizes, not as an instance of any guarantee
that can be or has been made for wv properties. Electing a CWs with no
support from preferrers of any other candidate has never been claimed as a
wv property, and is not a "wv-like strategy" property.

And I'll remind you that you neglected to comment on vulnerability to
truncation. Could that be because, even in your example, truncation by B
voters wouldn't succeed in taking the election from A to elect B?

I'll also remind you that truncation from one side, which could be innocent
(careless, hurried, lazy or principled), will likely be considerably more
frequent than burial.

But, in MDDTR, voters should be advised to not rank short of the CWse
(expected or evident CWs), because indifference is the threat to MDDTR's
success. Any candidate rank-order distinction that you don't bother to make
when you vote, just might not be reflected in the outcome.

But, then, that's pretty much true of rank-methods in general.

Yes, in the standard chicken-dilemma example, MDDTR elects A, and that's a
violation of the Plurality Criterion. Try to forgive MDDTR for electing the
most favorite-popular candidate who isn't majority-beaten  :^)

(Of course that's a way of saying MDDTR's rule but it hardly sounds
unjustified, by general objective standards, independent of any rule.)

Incorrect. See above.

...but IRV's, Benham's & Woodall's failure of Mono-Raise is ok  :^)

Mono-Add-Plump failure is where X loses in spite of your favoring X on
the ballot that you add. X is made to lose because you added a ballot, and
the fact that you favored X on that ballot has nothing to do with how or
why it happened. X would have been made to lose if you'd added any of many
other kinds of ballot.

Mono-Raise failure: X loses for no reason other than because you moved X up.

Notice the difference?

I answered, above, about Plurality.

Because of LNHa, you can safely rank your inbetween (neither strong top-set
not strong bottom-set) in sincere order, below top & above bottom.
...ranking them all with respect to eachother, and giving to all of them
the "protection" of wv.  Adding a candidate to that ranking can't harm
anyone whom you've ranked higher.

It doesn't have "wv-like strategy". When you demote a good candidate whose
voters you don't trust, you're giving hir no "protection" from burial, and
hir voters have no way of "protecting" hir from burial.  And s/he also has
no "protection" from truncation, including innocent, non-strategic
truncation.

Michael Ossipoff

I said:

In your example, wv elects C, thwarting & penalizing the burial, because of
an accident of faction-sizes.

(Try reversing the size-relation of A & B.)

(endquote)

Alright, someone could say, "But if you revere those 2 faction-sizes, then
A won't be the CWv".

So yes, an anti-burial guarantee for wv can be made, even for examples like
this one.

...and MDDTR doesn' share that more general anti-burial guarantee.

But that doesn't change the fact that all of my examples of wv's CWs
"protection" guarantees had the CWs preferred from both sides, and
supported from one wing, the wing opposite the truncating or burying wing.

That's the "wv-like strategy" that I've been referring to.

...even though wv has an additional anti-burial guarantee, or even though
its anti-burial guarantee is stronger and more general.

After all, I said "wv-like", not "wv-identical". I never said that MDDTR is
wv.

Michael Ossipoff

On Wed, Nov 9, 2016 at 7:11 PM, Michael Ossipoff email9648742@gmail.com
wrote:

On 11/10/2016 11:48 AM, Michael Ossipoff wrote:

Mike,

I'm not completely clear on the exact definition of this
property/criterion that you think is worth giving up compliance with
Mono-add-Plump
and Plurality to have.

I'm afraid I find the justification "most favorite-popular candidate who
isn't majority-beaten" to be quite oblique and arbitrary-sounding.

"Majority-beaten" can go away if we add a few ballots that just plump
for nobody, so big deal. Either elect the candidate that is doing the
"majority-beating" or forget about it.

Chris  Benham

(Replying farther down)

On Wed, Nov 9, 2016 at 10:07 PM, C.Benham cbenham@adam.com.au wrote:

I assumed that no one is indifferent between the CWs and any other
candidate.
...which means that the CWs has lots of support from the preferrers of
other candidates.

In fact, I assumed, without explicitly saying so, that voters & candidates
were on a 1D spectrum, with 2 "wings" (sets of voters separated by the
CWs), and that the truncation (innocent or strategic) or burial all came
from one wing, so that one wing all unanimously ranked the CWs over the
other wing's candidates.

So the CWs has a preference majority against everyone, and has a voted
pairwise majority against all of the candidates of the strategizing wing.

I don't know how well that holds up with more dimensions, with Euclidean or
city block distance.

Maybe the mathematicians can help with that. Forest?

In the meantime, maybe I should just say that "wv-like strategy" is only
defined for 1D, with the above-stated assumptions as stipulations.

Majority is a familiar notion. Losing to another candidate by a majority is
a reasonable enough grounds for disqualification, if not everyone is.

Among the non-disqualified candidates, choosing the most favorite one
sounds too natural to be called "arbitrary".

And the rule to elect the most favorite candidate who doesn't have someone
else ranked over hir by a majority has uniquely many of the best
properties. ...practical properties that make voting easier & make
sincerity safer.

Fine. So then I recommend that, in an MDDT election: If your candidate is
particularly in danger of majority-disqualification, you should recruit as
many voters as possible to plump for no one.

...or wait...Better yet, tell them to rank the candidates you like (and
suggest that they should like too) over the ones you don't like.

But, whatever you do, get the vote out. Giving an incentive to get everyone
to vote--Is that a bad thing? We'd have a big turnout.

And then, when one of those people shows up to vote, are they just going to
say to to themselves, "He said that it would be in my best interest to come
here & plump for no one."? Would that be in their best interest? Or might
they realize that, having come to the polling place, it might be even
better to preferentially rank the candidates whom they like more.

So, by all means, get the vote out.

Michael Ossipoff

Well, by the definition of a CWs, the CWs is preferred to each other
candidate by more people than vice-versa, and that doesn't depend on how
many dimensions there are.

With n dimensions, of course the dimensions might not all share a common
median for the distribution, but, for the purpose of wv-like properties, I
assume that they do, and that there's always a CWs.

But if the voters are uniformly-distributed, or if they're continuously,
symmetrically distributed about that common median (I assusme that at least
one of those is so) then, not only is the CWs preferred to each of other
candidates by more voters than vice-versa, but s/he also has a pairwise
preference-majority over each of the other candidates.

When I say "the median", I mean the common distribution-median for all of
the dimensions.

Regarding the line that connects the median to a candidate who is away from
the median, and regarding the plane that perpendicularly bisects that line,
a majority of the points in the distribution are on the median side of that
plane.

I suggest that the n-dimensional generalization of a "wing" is the set of
candidates on one side of a plane that includes the median.

Of course, because the CWs has a pairwise preference majority over each of
the other candidates, no candidate can have a preference majority over the
CWs.

As I was saying, for the purpose of defining wv-like strategy properties, I
stipulate that only one wing stratgegizes, and the other wing votes
sincerely.

So, by these assumptions, with wv, or MMPO, or MDDTR, truncation from one
side can't take the win from the CWs, because the truncators' candidate has
a voted majority against him (The CWs is voted over hir by a majority), and
the CWs doesn't have a majority against hir (because no candidate has a
pairwise preference majority against hir, and no one is burying).

And if some candidate's preferrers bury against the CWs, making a voted
pairwise majority against hir, and if all the people preferring the CWs to
the buriers' candidate (those people are a majority, for the reason that I
stated)
decline to vote the buriers' candidate over anyone, then the burier's
candidate can't hava a majoriity over anyone, including the candidate
they've insincerely ranked over the CWs.

So the wv's, MMPO's & MDDTR's automatic protection against truncation, and
their deterrence of burial, apply regardless of the dimensionality.

Michael Ossipoff

On Wed, Nov 9, 2016 at 10:57 PM, Michael Ossipoff email9648742@gmail.com
wrote: