[EM] Agenda Based Banks

[Susan Simmons]

So here is ABB (Agenda Based Banks):

First initialize a set named "TheBank" with the most promising agenda item as its only member.

Then, as long as even one agenda item pairwise beats every member of TheBank, deposit the least promising of these into TheBank.

Elect the final deposit.

This is even simpler to state and understand than Sequential Pairwise Elimination (SPE) based on the same agenda ...or any other elimination method for that matter.

Note that just as SPE has no need to explain or even mention "Condorcet Winner" or "Smith Set", this method ABB has no need to explain or even mention "Banks Set", except perhaps for historic background.

Similarly, here is a definition of ABL (Agenda Based Landau) that needs no explanation or even mention of "uncovered" or "Landau Set":

First initialize a set named "JJ" with the most promising agenda item together with all of the other items that do not beat it pairwise.

Then, while there remains even one item that is not beaten pairwise by any member of JJ, include into JJ the most promising such item X together with all other items that do not beat X.

Finally elect the last such X to be included into the set JJ.

So ABB is slightly simpler than ABL, but ABL has more respect for the most promising agenda item when that item has a short beat path to each of the other items.

Is this property of ABL more desirable than the (alleged) increased burial resistance of ABB?

Is it worth the (slight) loss of simplicity?

Although I have an emotional attachment to ABL, it seems to me that simple ABB is the better public proposal.

STAR/MJ style score/grade ballots would be adequate for constructing the pairwise win/loss/tie matrix, as well as for computing the agenda order once the basis for that order has been agreed upon ... whether above midrange approval, or a simple variant of that... like the one Ted Stern has suggested for use with Approval Sorted Margins (ASM):

Speaking of ASM, after SPE, ABB and ABL, it is one of the simplest and most intuitive ways to process an agenda. For comparison with ASM we reformulate SPE to output an entire ordered list of the candidates by sorting the agenda:

While there are still adjacent agenda items that are out of order pairwise, transpose the pair closest to the bad end of the agenda. Once sorted, the list has the first place winner at the good extreme.

That was SPE extended to full social order.

Now for ASM:

While there are still adjacent agenda items out of order pairwise, transpose the pair whose members are closest together in approval. Once sorted, the list has the first place winner at the good end of the list.

Like Kemeny-Young this method satisfies the Reverse Symmetry Property. Beyond that, unlike K-Y, it is marginally clone free, i.e. to the degree that the approval cutoff is treated as a virtual candidate.

Furthermore, K-Y is NP hard computationally, unlike ASM.

So whenever the agenda order is based on a score, grade-point, or other numerical system, ASM is infinitely superior to K-Y!

IMHO, these are the methods we should be considering .... ASM, SPE, ABL, and ABB, as defined above:-)






Sent from my MetroPCS 4G LTE Android Device


-------- Mensaje original --------
De: Susan Simmons <suzerainsimmons at outlook.com>
Fecha: 2/8/21 12:31 p. m. (GMT-08:00)
A: election-methods at lists.electorama.com
Asunto: Re: Agenda Based Banks

It turns out that this method as it stands is not monotonic, but if you omit the downward part, then the remaining simpler version is monotonic:

First initialize a set named "TheBank" with the most promising agenda item.

Then, as long as even one agenda item pairwise beats every member ofTheBank, deposit the least promising of these into TheBank.

Elect the final deposit.

This simple Banks compliant method is a generalization of TACC (Total Approval Chain Climbing).

The only thing I don't like about it is that even when the most promising agenda item is in the Banks set, as likely as not it will elect a different member of that set. My tweak was designed to overcome that "defect" while preserving Banks efficiency. But it's not worth the loss of monotonicity.

Furthermore, it may turn out that the supposed "defect" actually confers burial resistance ... for example ...

45 A>B (sincere A>C)
25 B>C
30 C>A

Ballot pairwise beat cycle: A>B>C>A

Agenda: C<B<A
(based on implicit approval, for example)

TheBank deposits are C, then B... so B wins.... the A faction burial of C backfires by getting its least favorite B elected!




Sent from my MetroPCS 4G LTE Android Device

-------- Mensaje original --------
De: Susan Simmons <suzerainsimmons at outlook.com>
Fecha: 1/8/21 2:15 p. m. (GMT-08:00)
A: election-methods at lists.electorama.com
Asunto: Agenda Based Banks


First initialize a set named "TheBank" with the most promising agenda item.

Then, as long as even one agenda item is beaten pairwise by every member of TheBank, add the most promising of these to TheBank.

After that, as long as even one agenda item pairwise beats every member ofTheBank, deposit the least promising of these into TheBank.

Finally, elect the member of TheBank that pairwise beats all of its other members.

I believe that this method satisfies mono-raise as long as the agenda does.

If so, then this is the best agenda based method so far, because (1) no other agenda based method is simpler to describe or compute, and (2) it always elects from a proper subclass of Landau called "Banks", without need for any mention of "covering" or for that matter, "Condorcet", "Landau", or "maximal chain".

If this is true, then there is no good excuse for continuing to propose make-shift tweaks of second and third rate election methods. In particular, ignorance and misplaced zeal are not good excuses!

Sent from my MetroPCS 4G LTE Android Device
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