def admits_voi(cid: CID, decision: str, node: str) -> bool:
"""Return True if cid admits value of information for node.
- A CID admits value of information for a node X if:
i) X is not a descendant of the decision node, D.
ii) X is d-connected to U given Fa_D \ {X}, where U ∈ U ∩ Desc(D)
("Agent Incentives: a Causal Perspective" by Everitt, Carey, Langlois, Ortega, and Legg, 2020)
"""
if len(cid.agents) > 1:
raise Exception(
f"This CID has {len(cid.agents)} agents. This incentive is currently only \
valid for CIDs with one agent.")
if node not in cid.nodes:
raise Exception(f"{node} is not present in the cid")
if decision not in cid.nodes:
raise Exception(f"{decision} is not present in the cid")
if not cid.sufficient_recall():
raise Exception("Voi only implemented graphs with sufficient recall")
if node in nx.descendants(cid, decision) or node == decision:
return False
cid2 = cid.copy_without_cpds()
cid2.add_edge(node, decision)
req_graph = requisite_graph(cid2)
return node in req_graph.get_parents(decision)
def admits_ri(cid: CID, decision: str, node: str) -> bool:
"""
Return True if cid admits a response incentive on node.
- A CID G admits a response incentive on X ∈ V \ {D} if
and only if the reduced graph G* min has a directed path X --> D.
("Agent Incentives: a Causal Perspective" by Everitt, Carey, Langlois, Ortega, and Legg, 2020)
"""
if len(cid.agents) > 1:
raise Exception(
f"This CID has {len(cid.agents)} agents. This incentive is currently only \
valid for CIDs with one agent.")
if node not in cid.nodes:
raise Exception(f"{node} is not present in the cid")
if decision not in cid.nodes:
raise Exception(f"{decision} is not present in the cid")
if not cid.sufficient_recall():
raise Exception("Voi only implemented graphs with sufficient recall")
if node == decision:
return False
req_graph = requisite_graph(cid)
if find_all_dir_paths(req_graph, node, decision):
return True
return False