In a state OC, there are two parties, X and Y, have their supporters geographically clustered. You have to design the district structure for single-member-district plurality elections. A district must come in a single piece (be contiguous), and it must include between 11 and 13 voters.

You are helping the political party Y draw new districts, and your goal is to help them win as many seats as possible. Below are four possible ways you can draw your first district (A, B, C, D). Which one gives the political party Y a chance to maximize their seats?

Question

In a state OC, there are two parties, X and Y, have their supporters geographically clustered. You have to design the district structure for single-member-district plurality elections. A district must come in a single piece (be contiguous), and it must include between 11 and 13 voters.

You are helping the political party Y draw new districts, and your goal is to help them win as many seats as possible.  Below are four possible ways you can draw your first district (A, B, C, D).  Which one gives the political party Y a chance to maximize their seats?

BlackTom AI · Accepted Answer

Question restatement: You’re drawing the first single-member district under rules: each district must be contiguous and include between 11 and 13 voters. There are four options for the first district (A, B, C, D). The goal is to help party Y win as many seats as possible with this first district design.

Option C: This choice would be evaluated first by looking at how it groups voters. If C ends up creating a district that is either too fragmented or fails to include the required 11–13 voters, it would be invalid or suboptimal. In many redistricting problems, a district that leaves Y’s voters too dispersed across other districts reduces Y’s total seat count, or creates wasted votes (over-concentration) in spare districts. If C clusters X voters heavily or yields a district with too few Y-supporters, it would typically be a weak choice for maximizing seats.

Option B: The prompt states that B is the answer. Interpreting B as the optimal plan usually means it creates a contiguous district with 11–13 voters that includes a favorable mix for Y—likely concentrating Y-supporters just enough to win that district while not overpacking them into a single district. A well-constructed B would balance compactness, contiguity, and partisan advantage to maximize the number of districts Y can win across the map. In other words, B probably uses a favorable boundary that splits opposing (X) voters across districts in a way that Y can win more seats overall, without violating the voter-count constraint.

Option A: This option could be reasonable in some scenarios, but if A fails to meet the 11–13 voter requirement, or if its boundary causes Y to win only a small number of districts due to inefficient packing or splitting, it would not maximize seats. If A leaves too many X voters in this district or creates a district that Y barely wins or loses, its overall impact on total seats would be limited.

Option D: D might appear visually appealing or contiguous, but it could be vulnerable if it creates a district with an unfavorable mix for Y (e.g., too many X voters in the district, or causing a dilution effect in surrounding districts). If D results in fewer districts won by Y due to misallocation of voters or creating a border that reduces Y’s leverage in other districts, it would be less favorable for maximizing seats, even if it satisfies contiguity and the 11–13 voter rule.

Additional notes on the decision logic: In single-member plurality (first-past-the-post) systems, maximizing seats often hinges on how efficiently you pack the opposing party’s voters and how you split their voters across districts. The best option typically creates a district that Y can win by a comfortable margin while ensuring the remaining districts are structured to give Y more opportunities to win additional seats. A correct choice should also adhere strictly to contiguity and the 11–13 voter constraint, since any violation would invalidate that option regardless of partisan effects.

Summary assessment: Option B is identified as the best choice because it most effectively leverages the given constraints to maximize Y’s potential seat count, by crafting a contiguous district with an appropriate voter count and an advantageous distribution of Y vs X supporters. Options C, A, and D either fail to maximize seats under the same constraints or rely on boundary choices that would reduce Y’s overall seat count due to inefficient vote distribution or boundary fragility.

VPM Spring 2025 Final B QB

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类似问题

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