Interventionist Decision Theory and Determinism Thomas Blanchard Illinois
Interventionist Decision Theory and Determinism Thomas Blanchard (Illinois Wesleyan University) “Causes, Norms and Decisions” Leibniz Universität Hannover 17 August 2018
Introduction • Ahmed (2014 a, 2014 b, 2015): CDT (but not EDT) faces difficulties in cases involving decision-makers who believe in determinism • My goal: examine how Interventionist Decision Theory (Meek and Glymour 1994, Hitchcock 2015, Stern 2017) can help the causalist solve the issue
Determinism • Determinism: A system of laws is deterministic iff two worlds that obey the laws and perfectly match at a certain time perfectly match at all times
Standard CDT • Standard CDT (Gibbard-Harper): Maximize Counterfactual Expected Utility (CEU) • CEU of an action = your estimate of how well things would go if you were to perform that action… • U(a) = ∑y Cr(a □→ Y=y)V(a, Y=y) • Counterfactuals are evaluated in accordance with the standard Lewisian semantics
Lewis’s Semantics • The past is fully counterfactually independent of the present • All closest possible worlds perfectly match the state of the actual world at any time in the past • Allows standard CDT to correctly handle medical Newcomb problems: SMOKE GENE CANCER
Lewis’s Semantics • Under determinism, Lewis’s semantics makes the laws counterfactually dependent on what I do • Suppose the laws are deterministic and I lower my hand now • Every closest world where I raise my hand perfectly matches the state of the actual world at any time in the past • So in every such world the laws are different than in the actual world
Betting on the Laws • Alice is extremely confident that a certain deterministic system of laws L is true • I will in fact assume she is certain of L • Two options: assert or deny the truth of L • Her sole desire is to tell the truth L=1 L=0 Assert=1 1 0 Assert=0 0 1
Betting on the Laws L=1 L=0 Assert=1 1 0 Assert=0 0 1 • Standard CDT: denying L is rational • Utility of asserting = Cr(Assert=1 □→ L=1) • Utility of denying = Cr(Assert=0 □→ L=0) • “Assert=1 □→ L=1” entails “Assert=0 □→ L=0” • Suppose that “Assert=1 □→ L=1” is true • The closest worlds where Assert=1 and the closest worlds where Assert=0 share the same past • Under determinism they must disagree over the laws • Hence L is false in the closest worlds where Assert=0 • Hence Cr(Assert=0 □→ L=0) ≥ Cr(Assert=1 □→ L=1)
Incompatibilism to the Rescue? • The case is a counterexample to standard CDT only if deliberation is compatible with belief in determinism • Standard CDT can be saved by assuming incompatibilism • But convincing arguments for incompatibilism are hard to come by
Causal and Counterfactual Dependence • The recommendation to assert L is perfectly in line with the guiding idea of CDT • Gibbard-Harper theory goes wrong here because of a mismatch between causal and counterfactual dependence • Might suggest that Betting on the Laws merely shows that GHT isn’t the correct version of CDT
The Deeper Problem for CDT • To give the right result in Betting on the Laws, we will have to require decision-makers to hold the laws fixed when comparing options • But under determinism this means that decision-makers must see the past as dependent on what they do • Worry: any such decision theory will sometimes recommend to act for the sake of influencing a past outcome
Interventionist Decision Theory • Expected utility of an action = your estimate of how well things will go if the action is the result of an intervention • U(a) = ∑y Cr(Y=y/do(a))V(do(a), Y=y)
IDT and Smoking Gene I SMOKE GENE CANCER
IDT and Betting on the Laws L=1 L=0 Assert=1 1 0 Assert=0 0 1 U(Assert=1) = Cr(L=1/do(Assert=1)) U(Assert=0) = Cr(L=0/do(Assert=0))
IDT and Betting on the Laws • Since Alice is certain of L… • … Cr(L=1/do(Assert=1)) = 1 • and Cr(L=0/do(Assert=0)) = 0 • So IDT correctly recommends asserting L • Presupposes that both credences are well-defined • This means that L must allow for both kinds of interventions to occur • As long as L is remotely plausible this will be true
IDT and Betting on the Laws • On IDT, Alice should only take into account nomically possible worlds (worlds consistent with L) when deliberating • The laws do not vary depending on what she does • The past isn’t held fixed during her deliberation • Alice must regard certain aspects of the past as varying with the interventions she considers • This raises two worries
Backward Dependence • Under determinism deliberators who follow IDT must regard the past as varying depending on which options they consider, • So won’t IDT sometimes recommend to act for the sake of a past cause of one’s action?
Smoking Gene Reexamined • Assume that the agent believes in a deterministic system of laws • Suppose that the intervention variable takes the form of a coin toss: the agent smokes if it hands heads, abstains if it lands tails D I SMOKE GENE CANCER • Let D take value 1 if the angle, velocity of the throw are such that the coin lands heads, 0 otherwise • Which intervention occurs is correlated with D • Since D is uncorrelated with Gene, under those interventions Smoke remains uncorrelated with Gene
Is the restriction to nomically possible interventions problematic? • Another worry is that the restriction to nomically possible interventions is problematic • Suppose again that the agent facing Smoking Gene believes in determinism • Make it part of the agent’s belief that it is a strict deterministic law that one smokes iff one has the gene • No nomically possible interventions that break the dependence between Smoke and Gene
Is the restriction to nomically possible interventions problematic? • This is a very implausible belief to have • On any remotely plausible theory of the world, whether one smokes depends on many other factors besides the gene (availability of cigarettes, incentives re smoking, the mental state of the agent, etc. ) • Cf. Russell (1913): no deterministic law linking local events has any chance of being true in our world
Is the restriction to nomically possible interventions problematic? • As long as the deterministic theory in which the agent believes is remotely realistic, IDT will give the verdict the causalist wants • On any such theory, whether the agent smokes depends on many other factors besides the gene • These factors will serve as interventions on Smoke that will break its dependence on Gene
IDT and Nomic Dependence • What if the past outcome nomically depends on the agent’s options? • I. e. , if it is a matter of deterministic law that the outcome occurs iff the agent acts in a certain way • In medical Newcomb problems this is extremely unrealistic • But there are cases like that don’t involve any strange beliefs on the agent’s part (Ahmed 2014 b)
IDT and Nomic Dependence • What does IDT say about cases where a past outcome nomically depends on the agent’s options? • I. e. , if it is a matter of deterministic law that the outcome occurs iff the agent acts in a certain way • This is implausible if the past outcome is a local event • But there are cases like that don’t involve any strange beliefs on the agent’s part (Ahmed 2014 b)
Betting on the Past • Suzy is extremely confident that a certain deterministic system of laws L is true • Two options: raising (Raise=1) or not raising her hand (Raise=0) • Q is a variable describing possible complete states of the world a century ago such that given L, Q=1 iff Raise=1 • Suzy’s (sole preference) is that Q takes value 1
Betting on the Past • Ahmed: this is a counterexample to standard CDT • Assuming that Suzy can deliberate, she should raise her hand • Standard CDT says otherwise since Q is counterfactually independent of what she does
Betting on the Past • Ahmed: this is a counterexample to standard CDT • Assuming that Suzy can deliberate, she should raise her hand • Standard CDT says otherwise since Q is counterfactually independent of what she does • What about IDT? • One thought is that on interventionism this is a case of backward dependence • But this would be a hollow victory for the causalist
Betting on the Past • Ahmed: this is a counterexample to standard CDT • Assuming that Suzy can deliberate, she should raise her hand • Standard CDT says otherwise since Q is counterfactually independent of what she does • What about IDT? • One thought is that on interventionism this is a case of backward dependence • But this would be a hollow victory for the causalist Q Raise
Betting on the Past • Ahmed: this is a counterexample to standard CDT • Assuming that Suzy can deliberate, she should raise her hand • Standard CDT says otherwise since Q is counterfactually independent of what she does • What about IDT? • One thought is that on interventionism this is a case of backward dependence • But this would be a hollow victory for the causalist Q Raise
Exogenous Interventions • In a model that includes Q and Raise, the idea of intervening on Raise becomes problematic • Interventions have to be exogenous • When you have a system of variables, an intervention on one of these variables should come `from the outside’ of the system
Exogenous Interventions • In a model that includes Q and Raise, the idea of intervening on Raise becomes problematic • Interventions have to be exogenous • When you have a system of variables, an intervention on one of these variables should come `from the outside’ of the system
Exogenous Interventions I • What does it mean for the intervention to be exogenous? • There is no way of wiggling the values of the variables in the system that will influence the value of I SMOKE GENE CANCER
Exogenous Interventions • Any conceivable `intervention’ can be influenced by wiggling Q • Suppose that X represents whether Suzy decides to raise her hand • Wiggling Q changes the probability that she will decide of raising her hand X Q • The idea of an (exogenous) intervention on Raise is ill-defined here • Also means that there is no causal relation between Q and Raise • Cf. Pearl (2009), Hitchcock (2007), Woodward (2007) Raise
IDT and Betting on the Past Q • On IDT it therefore seems plausible to say that Suzy cannot rationally deliberate • This is to endorse incompatibilism about the case • Can be motivated by the idea that to rationally deliberate what I do must be `up to me’ Raise
A Worry L N ASSERT • With respect to this model exogenous interventions on Assert becomes impossible • Incompatibilism about Betting on the Past leads to blanket incompatibilism
Proposal 1 L N ASSERT L ASSERT • There is at least one appropriate model of Alice’s decision situation in which the notion of an intervention on Assert is well-defined
Proposal 1 L N ASSERT I L ASSERT • There is at least one appropriate model of Alice’s decision situation in which the notion of an intervention on Assert is well-defined • Proposal 1: rational deliberation is possible if there is at least some appropriate model of the situation in which interventions are welldefined
Proposal 2 L N ASSERT L ASSERT • Solution 2: whether Alice can rationally deliberate depends on which model is considered
Thank you!
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