Dynamic Decision-Making and Planned Preference Change

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Dynamic Decision-Making and Planned Preference
Change

• Katie Steele
• University of Sydney

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Ulysses Dynamic Decision Problem
O1 on course for Ithaca
leave sirens
2
unconstrained
O2 forever with sirens
remain with sirens
1
tied to mast
O3 on course for Ithaca, with rope burn
Current preferences O1 gt O3 gt O2
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Normative Question

• How to define a rational choice in the dynamic
  decision-making context?
• What expectations about future beliefs and
  desires count as rational?
• My position dynamic model just an expanded
  representation of the standard static decision
  problem. (Ulysses problem is a valid dynamic
  decision problem.)

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(Strict) Conditionalisation

• Prfinal(Q) Prinitial(QE)
• (E represents what agent has learnt/become
  certain of.)
• (Prinitial(EQ) ? Prinitial(Q)) /
  Prinitial(E)
• What does the rule demand of a rational agent?
• dictates how beliefs should change with time?
• or a mere plan for updating beliefs?

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Desire Analogue of Conditionalisation?

• ConditionalisationD Ufinal(Q) Uinitial(QE)
• where U(QE) U(Q E)
• SumU(wj) ? Pr(wj Q E)
• (Here the wj are all worlds in which Q E is
  true.)
• SumU(wj) ? Pr2(wj Q)
• where Pr2() Pr( E)
• (Here the wj are all worlds in which Q is
  true.)
• E.g. U(go to beachraining) U(go to beach and
  raining)

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Interpreting diachronic belief/desire norms

• Either
• Belief/desire diachronic norms come apart from
  decision norms
• Or else interpret conditionalisation (and maybe
  conditionalisationD) so that the rule is amenable
  to Ulysses plight.

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Diachronic Dutch Book Arguments

• I think there is a plausible version of the
  diachronic DBA for conditionalisation as a plan
  for updating beliefs.
• (follows Skyrms 1993).
• A non-conditionaliser will sometimes choose a
  strategy that is dominated by another strategy
  that would have been available, were the agent to
  plan on updating via conditionalisation.
• Losses are measured according to the utility for
  money, which is assumed to be stable with time.

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Asymmetry between belief and desire?

• So an agent should always at least plan to update
  their beliefs in accordance with
  conditionalisation
• But what is the case for desires? Even if we are
  deflationary about diachronic norms, it seems
  plausible that an agent can plan to update their
  desires contrary to conditionalisationD.
• (e.g. agent currently prefers smoking to not
  smoking, but they actually plan to have the
  opposite preference)

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Diachronic DBA for Desire?

• How can there be a plausible diachronic DBA for
  desire-updating when we are missing an important
  ingredient a stable utility function against
  which to measure sure losses?
• We can show that an agent who does not subscribe
  to conditionalisationD can suffer a sure loss
  (due to a better strategy being unavailable to
  them) relative to their current utility function
• But why should this matter if the agents
  desires at the future time in question are
  respected?

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A suggestion for planned changes in desire

• Agent plans a change in desire to the extent that
  they pursue a strategy in part because they find
  the predicted change in desire attractive.
• Motivated by current higher order desires about
  what ones utility function will be at various
  future times.
• Just need to describe possible prospects in
  sufficient detail so that they include this kind
  of utility information.

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Ulysses Dynamic Decision Problem
O1 on course for Ithaca
leave sirens
2
unconstrained
O2 forever with sirens
remain with sirens
1
tied to mast
O3 on course for Ithaca, with rope burn
Current preferences O1 gt O3 gt O2
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Ulysses Again
take harp
O1 Unew
Stop on island
2
leave harp
O2 Unew
1
Continue to Ithaca
O3 Uold
O3 gt O2 gt O1 But also (O1 Unew) gt (O2
Unew) gt (O3 Uold)
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Genuine desire change?

• Examples to motivate planned changes in desire
  involve centred prospects.
• e.g. prefer smoking to not smoking now but
  prefer to prefer not smoking to smoking later
• But these are not the sort of prospects that are
  evaluated in the decision model. Rather, whole
  world histories that include smoking at time t.
• Not so obvious that an agent would seek an
  alternative utility function over whole world
  histories that they do not currently hold