Bart gave a good example of when order-reversal benefits a voter in
Approval.
One thing that I've read is that order-reversal in Approval won't help if,
for each voter, i, there's a constant, Ki, such that every candidate other
than i or j is Ki/Kj time more likely to be in a tie or near-tie with i than
with j.
For a particular voter, i and j are in a tie or near-tie if tht voter's
ballot can make or break a tie between i and j.
Ties and near-ties with only two members are assumed, for simplicity. That
assumption is reliably accurate in public elections, and is good even in
committee voting, where 2-candidate ties and near-ties are significantly
more likely than 3-candidate ties and near-ties.
But note that not only must the condition in the 2nd paragraph be violated
to a sufficient degree to make order-reversal a good strategy, but the voter
must know that, and must know the details of that situation, in order for
order-reversal to make any sense.
So it's no surprise that at least one author knowledgable on the subject
said that order-reversal should be ignored as an Approval strategy.
Mike Ossipoff
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