A seven$-$member governance committee of a corporation is charged with allocating funds for end$-$of$-$year bonuses, and a special subcommittee is appointed to research and then propose to the full committee a total value of all bonuses. The subcommittee must bring the proposal before the full committee under a predetermined amendment procedure $($either an open or closed rule$).$ All subcommittee and committee decisions are made using majority rule; the minimum that the committee may allocate is $$0$ and the maximum is $$12,000.$ The preferences of each member is single peaked and symmetric about each member's ideal point, and are arrayed as follows:

$-$ Bobby and Emma $$0$

$-$ Amy $$3,000$

$-$ Cathy $$6,000$

$-$ Frank $$10,000$

$-$ Geri $$11,000$

$-$ David $$12,000$