James Green-Armytage wrote:

        This is new to me. Under what conditions/assumptions does approval have
an order reversal incentive? Can you give an example where order reversal
achieves something that cannot be achieved equally well without order
reversal?

It's sometimes called skip voting.

Something close to the following was in "Approval Voting" by Brams and Fishburn:

There are four candidates, and the voters are in two groups:
Group I:  a=b>c=d
Group II: c=d>a=b

If the two groups differ in size by more than one vote, an additional voter cannot determine which group wins. If this voter's preference order is a>b>c>d he should vote only for a and c. In other words, the voter has incentive to reverse his preference order for b and c (never for a or d).
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