This procedure is composed of two sub-procedures ... one to construct an "advanced placement" chain headed by the most favorable agenda item ... and another to complete the chain by a process of chain climbing. First sub-procedure: initialize a chain 'c' as the empty set. Then while there exists (even vacuously) some agenda item that is defeated by every member of 'c', incorporate the most favorable such item into 'c'. Final sub-procedure: while any agenda item defeats every member of 'c', incorporate the most favorable such item into 'c'. After executing both sub-procedures, elect the head of the finished chain. This method is definitely Banks efficient. I'm pretty sure that it is also monotonic and (unlike ordinary chain climbing) Independent from Pareto Dominated Alternatives (IPDA). I'll send proof sketches soon (if it continues to hold up). -Forest

There will have to be a 3.0 version ... localized versions of these two sub-procedures ... to be alternated with each other to build a denser chain as a foundation for the final base camp supporting the final ascent to the summit! El mié., 27 de jul. de 2022 2:30 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > This procedure is composed of two sub-procedures ... one to construct an > "advanced placement" chain headed by the most favorable agenda item ... and > another to complete the chain by a process of chain climbing. > > First sub-procedure: initialize a chain 'c' as the empty set. Then while > there exists (even vacuously) some agenda item that is defeated by every > member of 'c', incorporate the most favorable such item into 'c'. > > Final sub-procedure: while any agenda item defeats every member of 'c', > incorporate the most favorable such item into 'c'. > > After executing both sub-procedures, elect the head of the finished chain. > > This method is definitely Banks efficient. I'm pretty sure that it is also > monotonic and (unlike ordinary chain climbing) Independent from Pareto > Dominated Alternatives (IPDA). > > I'll send proof sketches soon (if it continues to hold up). > > -Forest > > >

This time for sure ... Initialize 'c' as the empty set. Then ... While_1 some agenda element defeats every member of 'c' , let X be the most favorable such element ... Then While_2 some other agenda element defeated by X defeats every member of 'c', incorporate the most favorable such element into 'c'. EndWhile_2 Then incorporate X into 'c'. EndWhile_1 Finally, elect the final value of X, i.e. the member of 'c'.that defeats all of its other members. Note the logical structure of the procedure: While_1 .... While_2 ... EndWhile_2 .... EndWhile_1 .... Thanks for your patience! -Forest El mié., 27 de jul. de 2022 6:18 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > There will have to be a 3.0 version ... localized versions of these two > sub-procedures ... to be alternated with each other to build a denser chain > as a foundation for the final base camp supporting the final ascent to the > summit! > > El mié., 27 de jul. de 2022 2:30 p. m., Forest Simmons < > forest.simmons21@gmail.com> escribió: > >> This procedure is composed of two sub-procedures ... one to construct an >> "advanced placement" chain headed by the most favorable agenda item ... and >> another to complete the chain by a process of chain climbing. >> >> First sub-procedure: initialize a chain 'c' as the empty set. Then while >> there exists (even vacuously) some agenda item that is defeated by every >> member of 'c', incorporate the most favorable such item into 'c'. >> >> Final sub-procedure: while any agenda item defeats every member of 'c', >> incorporate the most favorable such item into 'c'. >> >> After executing both sub-procedures, elect the head of the finished chain. >> >> This method is definitely Banks efficient. I'm pretty sure that it is >> also monotonic and (unlike ordinary chain climbing) Independent from Pareto >> Dominated Alternatives (IPDA). >> >> I'll send proof sketches soon (if it continues to hold up). >> >> -Forest >> >> >>

Here's a Banks efficient version that more closely mimics our proven Landau efficient method. First, for comparison a slight reformulation of Agenda Based Landau: Definition: For each agenda item X, let thrall(X) be the set of agenda items defeated by X. Initialize X as the most favorable item on the agenda. While some agenda item Y defeats both X and every member of thrall(X), let the most favorable such Y be the new value of X. Now for the analogous Banks efficient method: Initialize X as the most favorable agenda item. Then while some agenda item Y defeats both X and every member of chain(X), replace X with the most favorable such Y. To complete the definition, we need to define chain(X): Chain(X) is the covering chain of thrall(X) constructed by the following procedure ... Initialize 'chain' as the empty set. Then ... While some Z in thrall(X) defeats every member of 'chain', incorporate the most favorable such Z into 'chain'. EndWhile. As you can see, the difference between the two methods is that the rôle of thrall(X) in the first method is taken over in the second method by a set chain(X) that covers thrall(X). El mié., 27 de jul. de 2022 2:30 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > This procedure is composed of two sub-procedures ... one to construct an > "advanced placement" chain headed by the most favorable agenda item ... and > another to complete the chain by a process of chain climbing. > > First sub-procedure: initialize a chain 'c' as the empty set. Then while > there exists (even vacuously) some agenda item that is defeated by every > member of 'c', incorporate the most favorable such item into 'c'. > > Final sub-procedure: while any agenda item defeats every member of 'c', > incorporate the most favorable such item into 'c'. > > After executing both sub-procedures, elect the head of the finished chain. > > This method is definitely Banks efficient. I'm pretty sure that it is also > monotonic and (unlike ordinary chain climbing) Independent from Pareto > Dominated Alternatives (IPDA). > > I'll send proof sketches soon (if it continues to hold up). > > -Forest > > >