On the selection of the same winner by all scoring rules |
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Authors: | Eyal Baharad Shmuel Nitzan |
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Institution: | (1) Department of Economics, University of Haifa, Haifa, 31905, Israel;(2) Department of Economics, Bar Ilan University, Ramat Gan, 52900, Israel |
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Abstract: | Different scoring rules can result in the selection of any of the k competing candidates, given the same preference profile, (Saari DG 2001, Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence, R.I.). It is also possible that a candidate, and even a Condorcet winning candidate, cannot be selected by any scoring rule, (Saari DG 2000 Econ Theory 15:55–101). These findings are balanced by Saari’s result (Saari DG 1992 Soc Choice Welf 9(4):277–306) that specifies the necessary and sufficient condition for the selection of the same candidate by all scoring rules. This condition is, however, indirect. We provide a sufficient condition that is stated directly in terms of the preference profile; therefore, its testability does not require the verdict of any voting rule. |
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