# [EM] order reversal incentive in approval?

James Green-Armytage James_Green-Armytage at antioch-college.edu
Mon Jun 13 20:10:56 PDT 2005

```I 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?
>
Bart, you replied:
>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).

Bart, thank you for your reply. The answer to the question of whether
approval has any order-reversal incentive seems to depend on precisely
what we mean when we say that a method has an order-reversal incentive.
One possible way to look at it is via this perfect information case:
Assume that all the ballots have been cast except for the ballots of a
group of people with perfect coordination and identical preferences. Given
method X, can these voters ever get a preferable result by voting a
more-preferred candidate below a less-preferred candidate?
If you define order-reversal incentive in this way, I think that approval
voting does not have any incentive for order-reversal.

Sincerely,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm

```