On the leximin and utilitarian overtaking criteria with extended anonymity |
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Authors: | Kohei Kamaga Takashi Kojima |
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Institution: | 1. Graduate School of Economics, Waseda University, 1-6-1 Nishi-waseda, Shinjuku-ku, 169-8050, Tokyo, Japan
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Abstract: | We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin
counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step
Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links
indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second,
we characterize another utilitarian extension, called S{\mathcal{S}}-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S{\mathcal{S}}-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S{\mathcal{S}}-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step
Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing
the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity. |
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