[EM] List Based Banks

[Forest Simmons]

 This procedure takes a list L of candidates and (with the aid of a defeat
table) produces a maximal list L' that is totally ordered by the pairwise
defeat relation.

This means (1) that every member of L' is defeated by every member listed
ahead of it, while defeating every member listed after it, and (2) no other
member of L can be accommodated by L' while maintaining this total order
property (1).


Initialize L' as the empty list. Then ...

While the list L of unprocessed candidates is not empty ..

Let variable T (for temporary) be the candidate at the top of L ... then ..

If
    T can be accommodated by L',
Then
      insert it into L' respecting the pairwise order,
And
    move the candidates defeated by T ahead of the other remaining members
of L, while maintaining their order relative to each other.
EndIf
Remove T from L.
EndWhile

At this point L is depleted and L' is a maximal chain.

By definition the head of this chain (the candidate at the top of L') is a
member of the Banks set.

Suppose the initial list L is in order of cardinal scores, and the head of
the list is elected, then as a single winner election method, it is
monotone, clone free,  IPDA (Independent from Pareto Dominated
Alternatives), Banks efficient, efficiently precinct summable, etc.

When the Smith set has fewer than four members, this List Based Banks
method always elects the highest score Smith member.

We need simulations and other experiments to see how this method fits in
Kevin's seven benchmark profiles, other interesting profiles, etc.

Of particular interest: compare this LBB method with SPE (agenda based)
Sequential Pairwise Elimination.

-Forest
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20221119/bdabfa19/attachment.htm>