19
Example D about here
________________________________________________________________________
observe that 5 players choose 4 different combinations. Combination 0000 (1) receives
the approval of 3 of the 5 players at distance d = 1 and is the unique winner under FB
m
.
Note that the most dissatisfied players will be the 2 players whose top preference is
the antipodal combination, 1111 (4). If these 2 players misrepresent their top preference
as 1100 (5) in Example Db, they induce combinations 1000 (2), 0100 (3), and 1100 (5) as
the winners, each of which receives the approval of 4 players at distance d = 1.
6
Because
these three winning combinations are closer to the true top preference of the 2
dissembling players [combination 1111 (4) in Da] than is combination 0000 (1), their
misrepresentation is rational, rendering FB
m
manipulable.
7
Q.E.D.
We next turn to a real-life dispute that suggests how FB
n
might be used in practice.
It raises new issues (the possibility of abstention; ties among FB
n
outcomes) for which we
suggest some pragmatic solutions.
5. An Application to an Environmental Dispute
On April 25, 1954, a three-week conference of 32 states, representing 95 percent
of the world’s shipping tonnage, convened in London. It included 18 developed states
from Europe, North America, and Australasia; of the others, 3 were from Eastern Europe,
4 from Asia, 6 from Latin America, and 1 from Africa.
6
Because combination 0000 (1) receives approval from 3 players, four combinations listed in Example Db
receive approval from a majority of players. However, we assume that the FB
m
winners are those
combinations—namely, the three combinations, 1000 (2), 0100 (3), and 1100 (5)—that receive the most
approvals.
7
FB
m
is called the “majoritarian compromise” in Hurwicz and Sertel (1999), Sertel and Sanver (1999), and
Sertel and Yilmaz (1999), wherein it is analyzed as a voting procedure with majority rule rather than a
bargaining procedure, as in Brams and Kilgour (2001). But the fallback process is essentially the same
under both interpretations, whether the decision rule is simple majority, qualified majority, or unanimity.
Convention