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Suppose each agent i is assigned a positive weight a_i. For every allocation x, define the welfare of x as the weighted sum of utilities of all agents in x, i.e.:

Suppose each agent i is assigned a positive weight a_i. For every allocation x, define the welfare of x as the weighted sum of utilities of all agents in x, i.e.:

假设每个主体''i''被赋予一个正权重。对于每个分配''x''，将''x''的福利定义为''x''中所有主体的配置的加权和，即。:

假设每个主体 ''i'' 被赋予一个正权重。对于每个分配 ''x'' ，将 ''x'' 的福利定义为 ''x'' 中所有主体的配置的加权和，即。: