[EM] Ultimate SPE Agenda Processing: Sink Swap Bubble

[Forest Simmons]

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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