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Two possible RCV ballot Approval definitions.

FS
Forest Simmons
Sun, Dec 26, 2021 1:38 AM

We have relied heavily on Implicit Approval for use in RCV methods that
require some preliminary nominal order ... methods like Approval Sorted
Margins, Sequential Pairwise Elimination, Chain Climbing, Agenda Based
Landau, etc.

Here are two possible alternative definitions:

1.A candidate is approved by ballot B if B ranks it above or equal to at
least one candidate X that is not pairwise defeated by any candidate ranked
higher than X on ballot B.

  1. A candidate is approved by ballot B if it is ranked above or equal to
    some candidate X that pairwise defeats some candidate Y that is not
    pairwise beaten by any Z ranked above candidate X on ballot B.

[Such an X would be essential to a certain kind of minimal covering of the
set of candidates covered by those candidates ranked on the ballot B in
question.]

In general, for both of these types of approval, any ballot Condorcet
candidate will be approved by every ballot that ranks it.

We have relied heavily on Implicit Approval for use in RCV methods that require some preliminary nominal order ... methods like Approval Sorted Margins, Sequential Pairwise Elimination, Chain Climbing, Agenda Based Landau, etc. Here are two possible alternative definitions: 1.A candidate is approved by ballot B if B ranks it above or equal to at least one candidate X that is not pairwise defeated by any candidate ranked higher than X on ballot B. 2. A candidate is approved by ballot B if it is ranked above or equal to some candidate X that pairwise defeats some candidate Y that is not pairwise beaten by any Z ranked above candidate X on ballot B. [Such an X would be essential to a certain kind of minimal covering of the set of candidates covered by those candidates ranked on the ballot B in question.] In general, for both of these types of approval, any ballot Condorcet candidate will be approved by every ballot that ranks it.