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
def admits_dir_voc(cid: CID, decision: str, node: str) -> bool:
"""
Return True if a single-decision cid admits direct positive value of control for node.
- A single-decision CID G admits positive value of control for a node X ∈ V \ {D} if and
only if there is a directed path X --> U in the reduced graph G∗.
- The path X --> U may or may not pass through D.
- The agent has a direct value of control incentive on D if the path does not pass through D.
- The agent has an indirect value of control incentive on D if the path does pass through D
and there is also a backdoor path X--U that begins backwards from X (...<- X) and is
active when conditioning on Fa_D \ {X}
"""
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")
agent_utilities = cid.all_utility_nodes
req_graph = requisite_graph(cid)
if not admits_voc(cid, decision, node):
return False
for util in agent_utilities:
if node == util or util in nx.descendants(req_graph, node):
x_u_paths = find_all_dir_paths(req_graph, node, util)
if any([decision not in path for path in x_u_paths]):
return True
return False
def test_requisite_graph(self) -> None:
cid = get_trim_example_cid()
self.assertFalse(requisite(cid, 'D2', 'D1'))
self.assertTrue(requisite(cid, 'D2', 'Y2'))
self.assertCountEqual(cid.get_parents('D2'), ['Y1', 'Y2', 'D1', 'Z1', 'Z2'])
self.assertEqual(len(cid.edges), 12)
req_graph = requisite_graph(cid)
self.assertEqual(len(req_graph.edges), 7)
self.assertCountEqual(req_graph.get_parents('D2'), ['Y2'])
def admits_ri(cid: CID, decision: str, node: str) -> bool:
"""
Return True if a single-decision cid admits a response incentive on node.
- A single decision 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 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 node == decision:
return False
req_graph = requisite_graph(cid)
if find_all_dir_paths(req_graph, node, decision):
return True
return False
def admits_voc(cid: CID, decision: str, node: str) -> bool:
"""
Return True if a single-decision cid admits positive value of control for node.
- A single-decision CID G admits positive value of control for a node X ∈ V \ {D}
if and only if there is a directed path X --> U in the reduced graph G∗.
"""
req_graph = requisite_graph(cid)
agent_utilities = cid.all_utility_nodes
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 node == decision:
return False
for util in agent_utilities:
if node == util or util in nx.descendants(req_graph, node):
return True
return False
