docs: def AppMoVMaximin(profile):
      """
      Returns an integer that is equal to the margin of victory of the election profile, that is,
      the smallest number k such that changing k votes can change the winners.
  
      :ivar Profile profile: A Profile object that represents an election profile.
      """
  
      # Currently, we expect the profile to contain complete ordering over candidates.
      elecType = profile.getElecType()
      if elecType != "soc" and elecType != "toc":
          print("ERROR: unsupported profile type")
          exit()
  
      # Initialization
      n = profile.numVoters
      m = profile.numCands
  
      # Compute the original winner d
      wmgMap = profile.getWmg()
      # Initialize each Copeland score as infinity.
      maximinscores = {}
      for cand in wmgMap.keys():
          maximinscores[cand] = float("inf")
  
      # For each pair of candidates, calculate the number of votes in which one beat the other.
  
      # For each pair of candidates, calculate the number of times each beats the other.
      for cand1, cand2 in itertools.combinations(wmgMap.keys(), 2):
          if cand2 in wmgMap[cand1].keys():
              maximinscores[cand1] = min(maximinscores[cand1], wmgMap[cand1][cand2])
              maximinscores[cand2] = min(maximinscores[cand2], wmgMap[cand2][cand1])
      d = max(maximinscores.items(), key=lambda x: x[1])[0]
  
      #Compute c* = argmax_c maximinscores(c)
      scores_without_d = maximinscores.copy()
      del scores_without_d[d]
  
      c_star = max(scores_without_d.items(), key=lambda x: x[1])[0]
  
      return (maximinscores[d] - maximinscores[c_star])/2