Here's an example of another standard test case for Sink Swap Bubble
("Bubba" for short).

48 C
28 A>B
24 B (sincere is B>A)

The smallest faction has thrown the sincere CW under the bus ... knowing
that most Condorcet methods, including classical wv methods like Ranked
Pairs, would break the resulting ABCA beat cycle at the weakest defeat A>B,
leaving B as the winner.

The agenda, whether based on Implicit Approval or MaxPairwiseSupport or the
ratio of Favorite to Anti-favorite lottery probabilities ... has B on the
favorable end with greatest Implicit Approval and MaxPS values of 52 ... as
well as greatest ratio of f to f', because f'(B)=0 ... while A is at the
unfavorable end of the lottery in all three standard measures.

The order from worst to best is A C B.

Standard SPE and DMC make no change in this order because it is a beatpath
order B>C>A ... so no out of order pair.

Let's see what Bubba does:

Sink does nothing.
Swap changes the order to A<B<C.
Bubble changes the order to B<A<C ... the finish order of the method ...
thus disappointing the defecting faction with a finish order polar opposite
to their sincere preferences ...

When will they learn that you cannot mess with Bubba?

Check;
One more Swap Bubble combo step produces the challenge order ...
C<B<A, which the majority will support in the conclusive sincere pairing
... because A is the sincere CW and C is the sincere Condorcet Loser.

A note on conventional agenda lingo: traditionally the "Top of the agenda"
is the unfavorable end ... because it is an elimination agenda ... and the
top priority items for elimination are the items at the bad end of the
agenda.

We respect this tradition, but mainly avoid confusion by referring to
favorable vs unfavorable ... or good vs bad ends of the list, rather than
top or bottom.

Does that make sense?

Maybe next time we can talk about the f/f' ratio if anybody wants to ... I
already did in another thread on agenda setting, but it certainly bears
repeating wherever there is interest.

Here I will just explain why f'(B)=0 in the above example.

If you draw a ballot at random B will never be at the bottom of the ballot
unless it is tied for last with A ... so the tie can only be broken by a B
ballot which has only A and C at Bottom.

In sum, A and C have positive anti-favorite probabilities ... but B does
not.

In general, determination of these probabilities involves a Markov Process
... so don't be surprised if the probabilities don't just jump out at you.

Alternatively, instead of resolving ties by drawing additional ballots ...
one can use a spinner to choose randomly among the tied (for bottom)
candidates ... which is the same as symmetric completion or counting equal
bottom fractionally instead of whole.

In this case you would get ...
f'(B)=24%, f'(A)=24%+12%,=36%,
and f'(C)=28%+12% ... which should add up to 100%.

Yes, 24+24+12+28+12=60+40=100

The respective ratios of f to f' are
28/36 for A, 24/24 for B, and 48/36 for C ... so the agenda order would be
...
A<B<C.

Sink changes that to A<C<B
Swap changes that to A<B<C
Bubble changes that to B<A<C
Etc. You gotta get up early to sneak a fast one past Bubba!

-Forest

On Fri, Mar 31, 2023, 9:49 PM Forest Simmons forest.simmons21@gmail.com
wrote:

Hi Forest,

Le samedi 1 avril 2023 à 10:31:08 UTC−5, Forest Simmons forest.simmons21@gmail.com a écrit :

I've said this before, but I'm not a fan of this kind of method because, what if you're
wrong about the sincere preferences? Then by electing C, you're actually punishing the A>B
voters for not using compromise strategy. This muddies the water as to what behavior
"chicken resistance" is actually incentivizing.

Can we really be so confident that an unstated preference hides a specific meaning?

I also ask what you think of this modified scenario:

48 C
28 B (sincere is B>A)
24 A>B

I guess you'll say that B is allowed to win because B is both the sincere and voted CW. But
that's a different question from what a "chicken-resistant" method should do, if we
really believe in this approach.
 
Kevin
votingmethods.net

On 3/31/2023 9:49 PM, Forest Simmons wrote:

Using a sorting technique is similar to what I worked out years ago for
estimating(!) Condorcet-Kemeny results.

The following code includes the function
"calc_votefair_insertion_sort_popularity_rank" which describes the
sorting algorithm in the comments.

https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/votefair_ranking.cpp

This algorithm uses a variation of standard "insertion sorting."

The nice characteristic of this sorting algorithm is that sorting only
requires pairwise reversals between two adjacent candidates, and the
sequence scores (which are the inverse of the scores John Kemeny refers
to) can be compared just by looking at two pairwise vote counts.  In
other words, none of the other pairwise counts in the pairwise matrix
are involved when choosing whether to swap those two adjacent candidates.

Clarification:  As Kristofer points out, there are contrived (highly
cyclic) cases where the results do not match Kemeny results.  Yet the
top 7 or so candidates can be identified and run through the full Kemeny
calculations to identify the winner.  It's possible the Kemeny winner
from the full set of candidates does not get identified as one of the
top 7 candidates, but in those contrived cases any winner would be
controversial (in the same way that an algorithm for finding the highest
mountain would produce controversial results if it were used to find the
highest sand dune in a desert).

If anyone has questions, just ask.

Richard Fobes
The VoteFair guy

On 3/31/2023 9:49 PM, Forest Simmons wrote:

On 02.04.2023 19:20, Richard, the VoteFair guy wrote:

I'd like to also clarify that mixed integer programming solvers can do
Kemeny of Smith sets of size 20 or more in reasonable time. If I recall
correctly, state of the art like CPLEX or Gurobi can do up to 40, but
I'm not completely sure I got those figures correct.

If the sorting approach is Monte Carlo (takes a fixed time though being
incorrect with small probability), then MIP is Las Vegas (always correct
but sometimes takes a very long time) - though the analogy is incomplete
as they're deterministic algorithms.

In practice, it may not matter; but then, in practice, we could use a
polytime election method, get similar results, and please theoreticians
too :-)

-km

Improved procedures for counting Kemeny-Young interest me to the degree
that they shed light on the de-cloned version based on the Swap Cost metric
rather than the Kendall-tau metric.

Kendall-tau does not make the cost of a single swap depend on the relative
popularity of the two candidates being swapped.

In contrast, the Swap Cost metric of swapping A>B to B>A is the product
ab', where a is alternative A's random ballot favorite probability, and b
is B's random ballot anti-favorite probability.

These probabilities are deterministic values that can be found in the same
way that you can calculate the deterministic fraction 1/36 to be the
probability of "snake eyes" on the first roll of a pair of fair dice.

So a reversal that raises B by lowering A has a democratic cost jointly
proportional to the popularity of A and the "anti-popularity" of B.

In this context a natural a-priori nominal order places A ahead of B iff
a/a'>b/b'.

The Kendall-tau metric yields no such nominal order because Kendall-tau is
insensitive to the relative popularity of the transposing candidates; every
swap has the same cost regardless of the relative levels of democratic
support of the candidates involved in the swap.

Having a natural nominal order gives a natural agenda order that can be
refined by sorting pairwise counts; for example.

-Forest

On Sun, Apr 2, 2023, 1:36 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On Sat, Apr 1, 2023, 9:30 AM Kevin Venzke stepjak@yahoo.fr wrote:

Until we can read minds, we cannot be sure, but some scenarios are more
likely than others.

I'm not committed to any particular definition of chicken or burial
resistance ... I'm more interested in prevention than cure.

If there is a ballot cycle, prevention has probably failed ... at least in
the three faction case ... it seems much much more likely in that case that
the cycle was created artificially than inadvertently.

Consider the beat cycle XYZX with with X at the top of the agenda and Z at
the bottom. It seems to me (all else being eaual) the two most likely
scenarios are that Z was the sincere CW ... but (1) successfully buried
under Y by the machinations of the A faction counting on a standard wv
method that would make A win. Or ...  that (2) the X faction truncation of
Z created the cycle that gives X the win under RP(winning agenda), SPE, or
DMC.

Our method disappoints the faction X responsible for creating the cycle by
electing Y, the candidate that the burial or truncation insincerely helped
(by raising or by truncating below) to create the cycle subverting the
sincere CW ... namely Z.

The sincerity check will actually elect Z ... but most electorates will
think the check is too costly... so they will have to be content to
disappoint the faction guilty of creating the insincere cycle ... cycle
prevention for future elections.

In that case the winner is from the middle of the Smith set Y ... the same
candidate you would get if it turned out that Z was not the sincere winner.

Better than random ballot Smith in any case ... including better prevention
than random ballot Smith.

Here's the model that convinces me that in the 3 faction case cycles are
almost surely artificial: The 3 village model. Each village runs one
candidate and everybody in the village copies their candidate's preference
ballot ... based on distances between "villages" whetherby geography or
issue space.

Suppose without loss in generality that A and B are teo closest candidates
so that B is A's second choice and A is B's second choice.

If no village has 50%+ of the voters, then C is the sincere Condorcet Loser
... so the larger of the A or B faction is the sincere CW regardless of W's
second choice ... or truncation ... or symmetric completion.

The only unilateral way of creating a cycle is for the second place faction
(the smaller of A or B) to truncate or bury its second choice.  Let's say
...

a A>B
b B
c C

This truncation creates an ABCA cycle.that B would win under most Condorcet
methods.

If the B faction nuries A, then C becomes the ballot CW ... no way they are
going to gry that. For that reason it seems obvious to me that insincere
CW's are the last thing we need to worry about.

Of course, there are all kinds of reasons for ending up with four or more
factions with only 3 candidates ... and a few of these witll even  have
sincere cycles  ... but once you have constructed such  a cycle you realize
it is much much more likely that a cycle in insincere than natural.

So let's make sure our methods do the right thing for the most likely
scenarios before we start worrying too much about "sincere cycles."

It has taken me a long time to come to this way of thinking, and I'm not
set in stone ... but I believe that any positive reinforcement for
insincere cycle creation is very bad ... and adopting wv Condorcet is a
step in that bad direction.

This BUBBA proposal discourages formation of these cycles while being
simple, seamless, monotone, clone free, and ISDA.

Have you seen any other Universal Domain method that can compete on these
counts?

On 4/1/23 18:27, Kevin Venzke wrote:

This is about chicken resistance in general, no? I suspect there's a
more general impossibility result hiding here: that methods that are
burial resistant and Condorcet (in the way the Smith-IRV hybrids or
Friendly is) have to make uncharitable interpretations of ballots that,
if they were honest, would imply a very different candidate should be
elected. (I have no proof of this, but it seems a reasonable hunch.)

It's kind of like the "weak centrist! Condorcet winner! weak centrist!
Condorcet winner!" thing cardinal proponents mention.

So if I'm right, then either we can choose a method that produces a very
good result with honesty, or one that deters burial strategy, but not
both. And then the ultimate deluxe method (in one sense) would be
something along the lines of:

• Conduct an election with "honest" method X and "suspicious method" Y
  (or putting it differently, "compromise resistant" X and "burial
  resistant" Y).
• If the winners are equal, we're done.
• Otherwise do a manual runoff, where the voters' behavior will be
  honest (majority rule with two candidates is incentive compatible).
  Elect the winner.

But that might be asking for too much in the complexity department.

If you were to agree with the cardinal proponents, then X could even be
something like Smith|Range (| being normalization) or STAR. But I tend
to agree with rb-j that cardinal ballots are undefined. Even von
Neumann-Morgenstern utility elicitation can be really difficult -- I've
tried it a few times.

-km

On Mon, Apr 3, 2023, 2:20 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

This is exactly what I have found. Classical Condorcet assumes honest,
sincere voters with imperfect estimation of the truth ... wv majorities
have the best chance of discerning that truth. But, as examples show ...
these methods are easily subverted by unscrupulous opportunistic
sophisticated voyers.... and as you and Kevin have noted, methods that
punish burial and defection must sacrifice VSE ... until the unscrupulous
learn it will almost always back fire.  When everybody learns that lesson,
the sincere CW will be a ballot CW much more frequently.

Well put!

And then the ultimate deluxe method (in one sense) would be

That's easier said than done ... definitely needs more explorstion.

It turns out that Agenda chain Climbing is of the highly burial resistant
type, while Agenda Uncovering is better for honesty ... remember it says ...
Elect the most favorable agenda alternative unless it is covered ... in
which case elect the most favorable alternative that covers it ... unless
it too is covered.... in which case elect the most favorable alternative
that covers it ...etc. ... An ideal Landau method for honest voters.

But hears the subtle difficulty of a combo method:

Suppose C is the sincere CW and A creates a cycle by burial of C under the
bus B. The honest methods, including wv, SPE, Agenda Uncovering, etc. ...
all choose A. The burial resistant methods all choose the bus B.

A sincere runoff between A and B will choose A.

On the other hand, the sincerity checks of Bubba and Agenda Chain Climbing
will restore C.

But restoring C makes burial less risky for the buriers!

It's like parents trying to figure out how to discipline their children
without negative consequences. Alfie Kohn wrote the book on that topic ...
"Punished by Rewards" ...

Richard,

Your post stimulated my thinking to improve the sort of sorting to be used
in the following version of Agenda Based Banks (ABB) a strain of ABB bred
specifically for negative feedback to buriers:

1. Elect the undefeated candidate (among the uneliminated) if there is one
   ...otherwise...
2. Update the agenda by sorting it pairwise with wv defeat strength
   priority.
3. Designate the least favored agenda candidate as LFAC.
4. Update the agenda by eliminating from it all of the friends of LFAC
   including LFAC itself.
5. Repeat until a candidate is elected in step 1.

The new sort of sort introduced in step 2  prioritizes for pairwise
rectification the adjacent pair with greatest winning votes defeat strength
... which is the defeat strength of  Classical Condorcet. In this context
it is the bait that lures the burying faction into a trap:

If the burying faction A is strong enough to bury C the sincere CW under
the bus B, then the Smith Set will be that cycle with cyclic order ABCA ,
and having C as the least favored agenda candidate, and hopefully (from
their POV) the C>A defeat as the weakest wv defeat in the cycle.

So after all of the non-Smith members are eliminated, the remaining agenda
will be either (1) A>B>C or (2) B>A>C.

In the first case no rectification is needed ... so the pairwise sort does
nothing. The LFAC is C, which is eliminated with its friend A ... leaving
the bus B as winner ... making the A faction kick itself for throwing their
sincere second choice C under bus B.

In the second case both adjacent Pairs are out of order, and the A faction
is counting on the top pair being rectified first so that C will stay
buried, and their candidate A will come out on top.

This is the trap they have been lured into ... since they are counting on
wv to break the cycle, it is very likely that the C>A defeat is the weakest
defeat, so that the wv sort rectifies the stronger defeat A>B, putting A at
the most favorable end of the agenda ... as in the first case above ... and
with the same disappointing outcome for the over-wise A supporters!

They were counting on the elimination of the buried candidate C, but were
not counting on C's friends (of which they are one) being dragged down with
it.

Is the burying candidate always a friend of the buried sincere Condorcet
Winner?

Yes, otherwise the unilateral burial could not create a cycle.

Isn't that nifty?

-Forest

On Sun, Apr 2, 2023, 10:20 AM Richard, the VoteFair guy <
electionmethods@votefair.org> wrote: