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Two characterizations of the dense rank

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  • García-Lapresta, José Luis
  • Martínez-Panero, Miguel

Abstract

In this paper, we have considered the dense rank for assigning positions to alternatives in weak orders. If we arrange the alternatives in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the alternatives in the top tier, 2 to all the alternatives in the second tier, and so on. We have proposed a formal framework to analyze the dense rank when compared to other well-known position operators, such as the standard, modified and fractional ranks. As the main results, we have provided two different axiomatic characterizations which determine the dense rank by considering position invariance conditions along horizontal extensions (duplication), as well as through vertical reductions and movements (truncation, and upward or downward independency).

Suggested Citation

  • García-Lapresta, José Luis & Martínez-Panero, Miguel, 2024. "Two characterizations of the dense rank," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    • Handle: RePEc:eee:mateco:v:111:y:2024:i:c:s0304406824000259
    DOI: 10.1016/j.jmateco.2024.102963
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