Application of Path Counting Problem and Survivability Function in Analysis of Social Systems

Tatsuo Oyama ()
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Tatsuo Oyama: National Graduate Institute for Policy Studies

A chapter in Strategic Management, Decision Theory, and Decision Science, 2021, pp 177-193 from Springer

Abstract: Abstract In the 1990s, the shortest path counting problem and its application in measuring the “importance” of a traffic road network were proposed; thereafter, it was generalized to the path counting problem. To measure the robustness of a network-structured system, the edge deletion connectivity function (EDCF) was defined, and the expected edge deletion connectivity function (EEDCF) for the network was obtained. The survivability function (SF) was proposed to approximate the EEDCF using an appropriate nonlinear function with two parameters. It was demonstrated that the SF can be used for solving various complex problems in several types of social systems. The EDCF indicates the relationship between the ratio of edges deleted from a network and the ratio of the number of edges in the network after deleting an arbitrary number of edges, to the total number of edges in the original network. The expected ratio of the number of paths connecting two different nodes in the network constitutes an EEDCF. The EEDCF was estimated using the Monte Carlo method. Subsequently, the SF was defined to approximate the EEDCF. The SF can be used to solve various social problems. This paper presents two examples of these applications—quantitatively measuring the robustness of a traffic road network in an urban area, and approximating the relationship between the vote share and seat share in the national election for the single-member voting system in Japan.

Keywords: Survivability function; Path counting problem; Edge deletion connectivity function; Expected edge deletion connectivity function; Monte Carlo method; Robustness of a network-structured system; Single-member voting system; Vote share; Seat share (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-16-1368-5_12

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DOI: 10.1007/978-981-16-1368-5_12

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