8. Suppose we have three items (, , and ) and three people (Bob, Carol, and Ted). Assume that each person spreads 100 points over the items (as in the adjusted winner procedure) to indicate the relative worth of each item to that person.
Item | Bob | Carol | Ted |
---|---|---|---|
40 | 30 | 30 | |
50 | 40 | 30 | |
10 | 30 | 40 |
For each of the allocations listed below, indicate the following:
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Allocation 1: Bob gets , Carol gets , and Ted gets . (This is not Pareto-optimal.)
Allocation 2: Bob gets , Carol gets , and Ted gets . (This is not Pareto-optimal.)
Allocation 3: Bob gets , , and . (This is Pareto-optimal; explain why.)
Allocation 4: Bob gets , Carol gets , and Ted gets . (This is Pareto-optimal.)
Allocation 5: Bob gets , Carol gets , and Ted gets . (This is Pareto-optimal.)