I resolve elections as follows. Quorum for each is 4.

Arbitor
  Murphy      - endorse Jason
  Jason       - Jason
  ais523      - Jason
  Madrid      - secretsnail
  G.          - (Jason, secretsnail)
    Jason 4, secretsnail 1; Jason wins

Prime Minister
  Murphy      - (Murphy, nix)
  Jason       - (Jason, nix, Murphy, secretsnail, G.)
  ais523      - (Murphy, Jason, nix)
  nix         - (nix, Murphy, Jason)
  duck        - secretsnail
  Madrid      - secretsnail
  G.          - (nix, Murphy)
  secretsnail - (secretsnail, nix)
    secretsnail 3, Murphy/nix 2, Jason 1; Jason is eliminated
    nix/secretsnail 3, Murphy 2; Murphy is eliminated
    nix 5, secretsnail 3; nix wins

Registrar
  Murphy      - endorse nix
  Jason       - endorse nix
  ais523      - nix
  duck        - secretsnail
  secretsnail - secretsnail
  nix         - (nix, secretsnail)
  Madrid      - secretsnail
  G.          - (secretsnail, nix)
    nix 4, secretsnail 3; nix wins

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