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 $$12,000.$What is the committee's most preferred level of funding $($i$.$e$.$ Condorcet winner$)?$ The subcommittee is composed of Frank, Geri, and David. What is the subcommittee's most preferred level of funding $($i$.$e$.$ Condorcet winner$)?$ Last year the full governance committee allocated $$3000$ for bonuses, and under committee rules this is the status quo level of funding $($it will be the bonus this year too, if the full committee makes no change$).$ Assuming the subcommittee brings a proposal to the full committee under a closed rule, will the subcommittee "open the gate" and bring a proposal to the floor and if so$,$ what would be its proposal? What would be the new bonus under this closed rule? Now assuming the subcommittee brings a proposal to the full committee under an open rule, will the subcommittee "open the gate" and bring a proposal to the floor and if so$,$ what would be its proposal? What would be the new bonus under this open rule? Now assume that the full governance committee follows a "zero$-$based budgeting" in which each year allocation for bonuses is initially set to $$0,$ and the committee proceeds to vote on any new proposal made by the subcommittee. Assuming the subcommittee brings a proposal to the full committee under a closed rule, what would be the final outcome in terms of bonus? Still assuming that the full governance committee follows a "zero$-$based budgeting" but now assuming the subcommittee brings a proposal to the full committee under a open rule, what would be the outcome in terms of bonus?