IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2104.02131.html
   My bibliography  Save this paper

Political structures and the topology of simplicial complexes

Author

Listed:
  • Andrea Mock
  • Ismar Volic

Abstract

We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible agents. We translate the wedge, cone, and suspension operations into the language of political structures and show how these constructions correspond to merging structures and introducing mediators. We introduce the notions of the viability of an agent and the stability of a political system and examine their interplay with the simplicial complex topology, casting their interactions in category-theoretic language whenever possible. We introduce a refinement of the model by assigning weights to simplices corresponding to the number of issues the agents agree on. In addition, homology of simplicial complexes is used to detect non-viabilities, certain cycles of incompatible agents, and the (non)presence of mediators. Finally, we extend some results from [1], bringing viability and stability into the language of friendly delegations and using homology to examine the existence of R-compromises and D-compromises.

Suggested Citation

  • Andrea Mock & Ismar Volic, 2021. "Political structures and the topology of simplicial complexes," Papers 2104.02131, arXiv.org, revised Dec 2021.
    • Handle: RePEc:arx:papers:2104.02131
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2104.02131
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Abdou, Joseph M. & Keiding, Hans, 2019. "A qualitative theory of conflict resolution and political compromise," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 15-25.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rajsbaum, Sergio & Raventós-Pujol, Armajac, 2022. "A Combinatorial Topology Approach to Arrow's Impossibility Theorem," MPRA Paper 112004, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mock, Andrea & Volić, Ismar, 2021. "Political structures and the topology of simplicial complexes," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 39-57.
    2. Oksana Ivanivna Myhalets, 2020. "Semantic Peculiarities of the Verbs with the Highest Degree of Polysemy Denoting Conflict Actions," Academic Journal of Interdisciplinary Studies, Richtmann Publishing Ltd, vol. 9, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2104.02131. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.