[EM] Sorting algorithms applied to candidate ranking

Tue Apr 4 21:48:44 PDT 2023

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 at votefair.org> wrote:

> On 3/31/2023 9:49 PM, Forest Simmons wrote:
>  > The SPE finish order is obtained by bubble sorting the agenda order
>  > pairwise.
>
> 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:
> > 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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> info
> ----
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>
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