[EM] Ultimate SPE Agenda Processing: Sink Swap Bubble

[Forest Simmons]

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 at gmail.com>
wrote:

> I would like to run by you guys an example of a new type of agenda based
> method that returns a beatpath finish order.
>
> The input is precisely the same input needed for Sequential Pairwise
> Elimination ... namely an agenda of alternatives, along with a pairwise win
> loss tie table.
>
> The SPE finish order is obtained by bubble sorting the agenda order
> pairwise.
>
> To pairwise sort a list of alternatives you repeatedly rectify adjacent
> pairs that are out of order pairwise ... until there  no longer remain any
> adjacent pairs out of order ... the same way drill sergeants get the new
> 'cruits lined up in order of height for their manual of arms and marching
> drill.
>
> When rectification priority is given to out of order pairs closer to the
> unfavorable end of the agenda, we call the pairwise sort a "bubble sort."
>
> The SPE finish order is the order of the bubble Sorted agenda.
>
> On the other hand, when rectification priority is given to pairs nearer
> the favorable end of the agenda, the process is called"sink sorting".
>
> The head of the sink sort finish order is called the "Definitive Majority
> Choice" (DMC) alternative.
>
>  Both the SPE and DMC finish orders are vulnerable to burial and "chicken
> defection" gambits ... to which the following brand new agenda processing
> method seems to be highly resistant:
>
> After sink sorting the agenda, (perversely!) transpose the pair at the
> favorable end of the resulting list ... before a final bubble sort to
> arrive at the final finish order.
>
> In stack based Reverse Polish Notation lingo, we could call the method ...
> "Agenda Sink Swap Bubble."
>
> This method satisfies Independence from Smith Dominated Alternatives ISDA,
> because both Sink and Bubble move Smith solidly to the favorable end of the
> list.
>
> Example:
>
> 45 A>B(Sincere A>C)
> 30 B>C
> 25 C>A
>
> The A faction seems to be counting on an agenda order of (unfavorable to
> favorable) C B A, which would result in a win for A, which is both the SPE
> and DMC winner, not to mention Classical Condorcet(winning votes) winner.
>
> But under Agenda Sink Swap Bubble (ASSB) ...
> the Sink does nothing because no adjacent pair is out of order pairwise.
>
> The Swap  transposes the pair located at the favorable (right) end of the
> list ... resulting in the list C A B.
>
> "Bubble" starts on the left (unfavorable) end ... resulting in A C B.
>
> So B ends up at the favorable end of the finish order ... a big
> disappointment to the A faction buriers.
>
> This method has a sincerity check:
>
> Take the finish order and apply another short Swap Bubble combo ...
> resulting in the order ... "challenge" ... B A C ... with C at the head.
>
> A fresh binary, conclusive vote (with fresh ballots) is taken to decide
> once and for all between the original finish order and the challenge finish
> order ... the question is which of these two finish orders do you prefer?
>
> Because C is the sincere CW and B is the sincere Condorcet Loser ... it is
> almost certain that a majority of the participating  voters will prefer the
> challenge order .. which ranks C first and B last.
>
> Clean & Nifty ... or what?
>
> Try it out on your favorite scenario involving a burial or chicken
> defection.
>
> Thanks!
>
> -Forest
>
>
>
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