[EM] Two possible RCV ballot Approval definitions.

Forest Simmons forest.simmons21 at gmail.com
Sat Dec 25 17:38:07 PST 2021

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

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