June 2007 Puzzle Solutions

1. A and C will form a coalition together. A prefers C because A will then receive the most money. C also prefers A to any other coalition, because C will get the most money in that case and is involved in a smaller alliance.

2. 67 percent would be best for B. Then B would be part of the {A, B, E} coalition and B would get the fraction 25/70 of the money. District A also would get more with this coalition than with any other winning coalition of which it would be a part. If the cutoff were 75 percent, A would team up with C, D and E,  and B would get nothing (which is why B would never favor that cutoff). We have already seen that 51% is bad for B.

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