On Tue, Apr 4, 2023, 9:48 PM Forest Simmons forest.simmons21@gmail.com
wrote:

A little more detail is warranted:

We're  talking about burial of the sincere CW by the  A faction ... so C
defeats A befor the burial and the A faction already unanimously ranks A
over C.

After the unilateral burial of C by the A faction, the A faction still
ranks A unanimously ahead of C.  So the pairwise counts between A and B are
not affevted... so C still beats A after the burial ... i.e. A does not
beat C after the burial ... which means that A is still a friend of C.

But the burial of C under B has changed B from a friend of C to an enemy
... that's the pairwise defeat change that precipitates the cycle creation!

Remember that by definition everybody is a friend of the sincere CW until
somebody votes insincerely.

Note that it wasn't the B faction that changed B from friend of C to enemy
of C ... it was an enemy faction A of B that effected the change.

So if the friends of C that don't want one of their enemies to convert them
into an enemy of C  ... if they want to make sure they don't get used for
that ... as a precaution they could truncate their ballot just below C ...
to prevent "later harm."

Most people trying to influence voters and policy makers ... have no clue
about these subtleties ... especially those pominently recently
recommending Borda based Condorcet completion methods ... which tend to be
even more susceptible to burial than Classical Condorcet.  In fact, plain
old nonCondorcet Borda is hyper susceptible to burial shenanigans due to
"teaming" ... just bury somebody under your whole team ... for burial on
steroids!

Zeal is good ... but zeal without knowledge... not so good ... but still
easily forgivable ... where humility is not also lacking.

I blush when I think of all the ill founded brash statements I made in my
first twenty years on the EM List ... and since then as well!

-Forest

On 4/4/23 07:23, Forest Simmons wrote:

Perhaps there is some kind of pigeonhole argument that could prove it,
but yes, it makes sense. Intuitively there's a Pareto front where, every
type of strategy resistance level, there's an optimal VSE method, and
that this optimum value shrinks the more strategy-resistant the method
is... because a constrained optimum is never better than an
unconstrained one. Of course, this informal argument does not show how
"expensive" strategy resistance is, only that we shouldn't be surprised
if there's some cost.

(Although the general argument could also be used to shown that
cloneproof methods, say, can't be any better VSE-wise than the best VSE
method without a constraint of cloneproofness, in that case it seems
that the price is much lower. Anyway.)

That's a good point. But we should be careful not to take this too far.
Suppose that we have a set of elections, e_1...e_n, and a subset of
these, call it ebA, where burial is advantageous in method A. Then
suppose ebB is a strict subset of ebA and denotes the elections where
burial is advantageous in method B.

Then all else equal, we would consider B to be a better method than A,
even though B seems to make burial less risky for buriers.

What we need to consider is under what elections are there nearby
elections where burying X doesn't make Y win, but makes Z win instead.
That's where burial backfires. Now if these are reduced, then you could
say that it's ambiguous whether the new method is better, because the
rate of burial would increase. But we don't know that this is the case
for the (A vs C) runoff overlay.

Or putting it differently: random ballot has no risk whatsoever for
burial... but no reward either, so it's okay.

I agree, it doees make the method much harder to analyze, though.
Perhaps I'll try to find an optimal runoff-based method using my optimal
strategy susceptibility analysis at some point and see what the rate is :-)

James Green-Armytage considered a different way to break UD: by having
allies of the honest CW be able to withdraw from the election.
https://jamesgreenarmytage.com/dodgson.pdf I haven't read the paper, but
from the abstract it seems he's saying that in 1D space, the resulting
method is strategy-proof (!)

-km

Here's a compromise:

Let A be the Agenda Uncovering winner.

If voters are sincere, A is my best estimate of who should be elected.

If A is defeated pairwise, then the votes are probably not sincere.

So if A is undefeated, elect A ... Else elect C, the Most Favorable Enemy
of A ... the candidate most likely to have been thrown under the bus by the
A voters to create an artificial cycle to their advantage.

If a sufficient number challenges the outcome, have a manual runoff between
A and C.

This won't punish A, but it will make the burial futile ... a big waste of
time ... putting some friction into the dynamics.

-Forest

On Wed, Apr 5, 2023, 2:28 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

For public proposal ...

1. Initialize the agenda order according to Implicit Approval ... ties
   resolved by top rank counts.
2. Let A be the most favorable candidate after Sink Sorting the sgenda.
3. Let C be the Most Favorable Enemy of A.
4. Let B be the Most Favorable Enemy of C.
5. If B's top count is greater than C's Implicit Approval, resolve the
   doubt beteeen B and C by Candidate Proxy.
6. Otherwise elect C.

For the Candidate Proxy Plurality doubt resolution the weight of each
candidate's vote is the number of ballots on which it was ranked top
(counted fractionally for equal top).

This candidate proxy device obviates a second trip to the polls by the
voters.

On Wed, Apr 5, 2023, 11:37 PM Forest Simmons forest.simmons21@gmail.com
wrote:

On Thu, Apr 6, 2023, 10:00 AM Forest Simmons forest.simmons21@gmail.com
wrote:

Example:

27 C>A
24 A (Sincere A>C)
49 B

The agenda order from least to most favorable is C<B<A

There is a beat cycle in cyclic order ABCA

The agenda has no pairs in need of pairwise rectification  ... so sink sort
does nothing.

The Most Favorable Enemy of A is indeed C ... (as in the archetypical
story).

The Most Favorable Enemy of C is B.

B's top rank share is 49, which is indeed greater than 27, which is C's
Implicit Approval ... so without some kind of special dispensation
exempting C from the Plurality Criterion, we cannot elect C,  even though
it is secretly known to be the sincere CW ... (by the State of California).

A sincere proxy vote between B and C resolves this issue ... showing that C
is actually preferred over B by a 51 to 49 majority.

In fact, A is one of the candidate proxies, and in this role she is eager
to vote her sincere preference of C over B ... nothing to lose ... much to
gain ... and partial redemption from her initial chicken defection perfidy!

-Forest

So C is elected ... despite the misleading appearance of a Plurality
Criterion violation. The A faction is lucky we went to the trouble of
undoing its truncation defection mischief ... instead of just standing back
to watch C get disqualified in favor of B ... the negative feedback it
deserved!

Perhaps this is the most gentle and expeditious way to warn would be
manipulators ... like little Johnny's mother told his teacher on the first
day of school ..."Johnny is a sensitive child ... if he ever does anything
bad, just hit the little kid next to him ..."

-Forest

Hi Forest and Kristofer,

A couple of old responses. I know Forest has continued to post new ideas.

Kristofer wrote:

I don't want to rule this out. Although I'm disputing here that chicken resistance actually
is about burial, maybe there's a way to frame it in that way that would make sense to me.

I have not studied so many Condorcet methods that (purport to) be chicken-resistant. One
would probably want a way to measure the characteristics of the method (beyond simply
whether it satisfies the CD criterion or some CD criterion). We might look to see reduced
truncation incentive. The difficulty here is that WV methods have, at face value, very low
truncation incentive, lower than Schwartz//IRV. You may end up with the conclusion that
chicken-resistant methods outperform only in very specific scenarios, which would not lead
me to think there is a connection to an impossibility result.

I note also that I dispute that it was warranted to define the CD criterion in such a way
that IRV or any Condorcet method would satisfy it. I've speculated that perhaps DSC comes
closest to the spirit of it. But DSC plainly encourages burial. I guess it makes sense: If
you're going to penalize truncation then sometimes actual burial (order reversal) will be
the result.

Forest wrote:

Part of what I want to point out is that you cannot only disappoint the faction that
truncated. You will also disappoint the faction that did what they were supposed to do. And
both factions have the ability to decide to vote differently in response to this potential.

This makes it speculative to believe the effect of chicken resistance is less truncation.
It could as easily be that the effect of chicken resistance is more favorite betrayal (or
fewer candidate nominations by the majority). In either event, will there be fewer cycles?
Sure. Will it be because there are only two candidates in the race? Possibly.

given that probably the easiest criticism of IRV is its failure to detect and take into
account pairwise majorities. Whatever magic a CD method can do by ignoring majorities, IRV
is already doing - and IRV has no truncation incentive, so it's probably doing it more
reliably.

This isn't to say I don't think the chicken dilemma is a problem. I don't want someone to
read my position as that I don't care about it. It's just that I think Mike did not give us
a plausible remedy.

Kevin
votingmethods.net

Kevin,

So far the only comprehensive solution that I see is this version of Chain
Climbing with a sincere runoff between the last pivot and the only
uneliminated candidate.

Without the sincerity check the method will inevitably filter out some (too
many?) good candidates along with the cycle instigators

Lacking an undefeated candidate .

1. Update the (implicit Approval) agenda by sink sorting it pairwise.
2. Let PIvot be the least favorable candidate on this updated agenda.
3. Eliminate friends(Pivot) including Pivot itself.
4. If only one candidate R remains uneliminated, rescue the last Pivot from
   the trash, and elect the sincere winner between it and R.
5. Else repeat steps 1 thru 5 until step 4 produces a winner.

Right now I am investigating the following simpler method to see if it can
work almost as well:

1. Let DCACC be the Defense Champion Approval Cutoff Candidate defined as
   the minMaxPairwiseOpposition candidate.
2. Elect the winner of a sincere runoff between DCACC and the Approval
   Winner determined by approval based on the DCACC cutoff.

That winner will either be the DCACC candidate itself or else the candidate
ranked ahead of it on the most ballots.

If the approval cutoff were inclusive, the DCACC would win too often so
that burial would not be discouraged enough.

If the cutoff were exclusive, the DCACC would be unfairly discriminated
against.

I think the right compromise is to define the DCACC approval to be the
average of its Implicit Approval and its Equal First Whole approval.

It will take some testing to see if this even yields a monotonic method.

So I agree ... we're not done yet. And Mike did bail out too soon!

-Forest

On Mon, Apr 10, 2023, 12:50 AM Kevin Venzke stepjak@yahoo.fr wrote:

Suppose someone provides a list of candidates already sorted pairwise.

Now do Benham elimination ... start at the loser end of the list and
eliminate candidates one by one until there is (according to a fresh set of
ballots) a CW among the uneliminated.

How much incentive if any to rank insincerely?

On Mon, Apr 10, 2023, 12:50 AM Kevin Venzke stepjak@yahoo.fr wrote:

On 11.04.2023 19:55, Forest Simmons wrote:

Since Condorcet is incompatible with LNH, there will be some incentive
to either truncate or random-fill (depending on the situation). I would
also imagine that if the strategists know the list ahead of time, and
they know that it's A>B>C>D, then if C is the CW, A is their favorite,
and A beats B pairwise, they'll have an incentive to engineer a false
cycle by burying C under B.

If they don't know the list, it's much harder to do. It reminds me of
the Conitzer and Sandholm preround, which makes strategy harder to
devise in practice, and just how hard depends on what information the
strategists have (see
https://www.cs.cmu.edu/~sandholm/voting_tweaks.ijcai03.pdf). (In
practice, this doesn't matter, because most elections have relatively
few candidates; it's just the "it depends on information" aspect that's
similar.)

-km

I've been thinking that the ballot set

49 C
26 A>B
25 B

could have come from truncation of sincere 25 B>A ...

Or ... it could have come from truncation of sincere 49 C>B ...

Or even burial of C under B from sincere 26 A>C.

So the sincere CW could have been A,B,or C.

So how do we know which two candidates to involve in the sincere runoff
match?

It seems that with all of this strategizing there must be enough
information floating around to know that some particular candidate X was
very likely not the sincere CW.

If X was C, then the runoff should be between A and B. In general, the
fresh ballot runoff should be between the two non-X candidates.

But how to officially decide the identity of X is not clear to me.

Suppose the basic method is agenda processing by Sink Swap Bubble.

Why not apply DMC Benham to the final list with the defeat matrix derived
from a fresh set of ballots?

It may not be a totally sincere solution, but it seems to me that it would
be adequate ... better than anything else we've got going now:

Suppose for the ballot set
49 C
26 A>B
25 B
The agenda is based on minPairwise Support from minmin to Maxmin...
unfavorable to favorable ... so
B<A<C is the starting agenda.

After one round of Sink Swap Bubble we have  C<B<A.  DMC Benham elects the
least favorable candidate on the list that defeats every more favorable
one.

So elect C if it defeats both A and B, else elect the pairwise winner
between A and B.

If C wins it is the fresh ballot CW ... so quite likely the sincere CW.

If A wins, then quite likely the sincere preference that was truncated to
give us our ballot set was the 25 B>A faction's.

If B got elected, the most likely explanation is that sincere 49 C>B got
truncated to 49 C.

Does this seem reasonable?

If Robert Bristow-Johnson's assessment is valid, it would be rare to lack a
ballot CW ... so this fresh set of ballots requirement would be a rare cost.

I think it would be worth it in a high stakes election ... as well as
highly informative ... and perhaps entertaining.

Am I way off base?

My main point is that we cannot expect the method by itself to discern from
the first ballot set alone who should win.

The three subversion of sincere CW scenarios were by simple unilateral
action.

Anybody have a better idea for a reasonably sincere completion?

Forest

On Tue, Apr 11, 2023, 1:52 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote: