For ℓ_t utilities, individual fair share guarantees are computable and compatible with Pareto efficiency; for ℓ1 and ℓ2 utilities, strategyproofness, efficiency, and even the weakest single-minded fairness cannot all hold whenever there are at least three alternatives.
We claim that any solutionq∗ of (2) induces a Nash equilibrium of the budget-aggregation game
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Individual Fairness in Budget Aggregation
For ℓ_t utilities, individual fair share guarantees are computable and compatible with Pareto efficiency; for ℓ1 and ℓ2 utilities, strategyproofness, efficiency, and even the weakest single-minded fairness cannot all hold whenever there are at least three alternatives.