Questions: An arts council is meeting to decide on the allocation of a 50,000 grant to fund art projects in the community. The council consists of three members, each representing different artistic disciplines. Their voting weights are based on the number of artists in their respective groups. The members and their weights are as follows: David represents the Visual Arts Guild with a weight of 4 votes. Linda represents the Performing Arts Coalition with a weight of 3 votes. Katie represents the Literary Society with a weight of 2 votes. The Quota is 5.

An arts council is meeting to decide on the allocation of a 50,000 grant to fund art projects in the community. The council consists of three members, each representing different artistic disciplines. Their voting weights are based on the number of artists in their respective groups. The members and their weights are as follows: David represents the Visual Arts Guild with a weight of 4 votes. Linda represents the Performing Arts Coalition with a weight of 3 votes. Katie represents the Literary Society with a weight of 2 votes. The Quota is 5.
Transcript text: An arts council is meeting to decide on the allocation of a $50,000 grant to fund art projects in the community. The council consists of three members, each representing different artistic disciplines. Their voting weights are based on the number of artists in their respective groups. The members and their weights are as follows: David represents the Visual Arts Guild with a weight of 4 votes. Linda represents the Performing Arts Coalition with a weight of 3 votes. Katie represents the Literary Society with a weight of 2 votes. The Quota is 5.
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Solution

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To determine how the $50,000 grant can be allocated among the different artistic disciplines represented by the council members, we need to understand the voting system and how decisions are made based on the given weights and quota.

Explanation

  1. Voting Weights and Quota:

    • David, representing the Visual Arts Guild, has 4 votes.
    • Linda, representing the Performing Arts Coalition, has 3 votes.
    • Katie, representing the Literary Society, has 2 votes.
    • The quota for a decision to pass is 5 votes.

  2. Decision-Making Process:

    • For any proposal to be approved, it must receive at least 5 votes.
    • This means that no single member can make a decision unilaterally, as the highest individual weight is 4 (David's).

  3. Possible Coalitions:

    • David and Linda: Together, they have 4 + 3 = 7 votes, which exceeds the quota. This coalition can approve a proposal.
    • David and Katie: Together, they have 4 + 2 = 6 votes, which also exceeds the quota. This coalition can approve a proposal.
    • Linda and Katie: Together, they have 3 + 2 = 5 votes, which meets the quota. This coalition can approve a proposal.

  4. Implications for Grant Allocation:

    • Any two members can form a coalition to approve a proposal for the allocation of the grant.
    • This setup encourages collaboration and negotiation among the members to reach a consensus on how the funds should be distributed.

  5. Considerations:

    • The members may consider the needs and impact of the grant on their respective disciplines.
    • They might also take into account past funding, current projects, and future plans to make a balanced decision.

In conclusion, the allocation of the $50,000 grant will depend on the ability of the council members to form coalitions that meet or exceed the quota of 5 votes. This encourages a collaborative approach to decision-making, ensuring that the interests of multiple artistic disciplines are considered.

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