What Are Preferences?

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What Are Preferences?

So far we only thought about the kind of representation that is needed for decision theory. Next we need the theory itself. And the way to get to the theory is to ask, What Are Preferences?

Striking that this is how Jeffrey describes the aim of the book.

This book has ‘a philosophical end: elucidation of the notions of subjective probability and subjective desirability or utility’

(Jeffrey, 1983, p. xi)

This is very useful because we have so far assumed without explicating these notions, both in the philosophical theory and in the dual-process theory ...

Jeffrey will help us to understand Belief and Desire

This is important for linking decision theory with belief-desire. (Decision theory as a theory about the patterns humans find in behaviour (vs as a theory about the patterns that actually are in behaviour).)

‘we should think of
meanings and beliefs
as interrelated constructs of a single theory
just as we already view
subjective values and probabilities
as interrelated constructs of decision theory’

(Davidson, 1974, p. 146)

habitual process

Action occurs in the presence of Stimulus.

Agent is rewarded [/punished]

Stimulus-Action Link is strengthened [/weakened] due to reward [/punishment]

Given Stimulus, will Action occur? It depends on the strength of the Stimulus-Action Link.

‘goal-directed’ process

Action leads to Outcome.

Belief in Action-Outcome link is strengthened.

Agent has a Desire for the Outcome

Will Action occur? It depends on the Belief in the Action-Outcome Link and Agent’s Desire.

This book has ‘a philosophical end: elucidation of the notions of subjective probability and subjective desirability or utility’

(Jeffrey, 1983, p. xi)

ok, so how is this done?

is the evidential basis for ascribing an agent probabilities and preferences and how does the evidence the ascriptions?

For simplicity I have so far been speaking as if we wanted to introduce a procedure for deciding how to act. But of course that isn't our aim at all. Our ultimate aim is to be able to justify claims about attitudes---or at least to understand what sort of considerations might provide justification. We still have a way to go.

So far we have seen how subjective probabilities and desirabilities determine expected utilities for actions. If we knew the expected utilities of the actions available to an agent, we could make a prediction about how she will act. But to work out an agent's expected utilities we would need to know the probabilities she assigns to relevant conditions and how desirable she finds the various outcomes. How could we know this?

Difference scenario, bananas or chocolate. Both subjective probabilities and preferences unknown to us.

Subject opens the red door. What can we conclude? That they like bananas more than chocolate? Not necessarily.

I mean, if we knew their subjective probabilties, then maybe we could conclude that they like bananas more than chocolate.

But we don’t know their subjective probabilities. Suppose their subjective probabilities were like this. Then their choice does not tell us that they prefer bananas to chocolate.

cannot infer preferences unless we know subjective probabilities

revealed preferences Importance: transition from externally given criterion

‘the revealed preference revolution of the 1930s (Samuelson, 1938)

... replaced the supposition that people are attempting to optimize any externally given criterion (e.g., some psychologically interpretable motion of utility, perhaps to be quantified in units of pleasure and pain).

Chater (2014)

Up to this point we regarded decision theory as forward looking ...

TODO: Can’t remember how you figure out that agent is not indifferent between A and B. (Is this an axiom?)

‘Suppose that A and B are consequences between which the agent is not indifferent, and that N is an ethically neutral condition [i.e. the agent is indifferent between N and not N].

Then N has probability 1/2 if and only if the agent is indifferent between the following two gambles:

1. B if N, A if not

2. A if N, B if not’

(Jeffrey, 1983, p. 47)

What have we done?

Your actions are a function of two things,
subjective probabilities
and preferences.

Ramsey’s method allows us to
infer both of these
from observations of the actions you perform
plus some background assumptions (axioms).

Using Steele & Stefánsson (2020, p. §2.3) here.

But what did we assume in characterising preferences?

transitivity

For any A, B, C ∈ S: if A⪯B and B⪯C then A⪯C.

(Steele & Stefánsson, 2020)

completeness

For any A, B ∈ S: either A⪯B or B⪯A

continuity

‘Continuity implies that no outcome is so bad that you would not be willing to take some gamble that might result in you ending up with that outcome [...] provided that the chance of the bad outcome is small enough.’

Suppose A⪯B⪯C. Then there is a p∈[0,1] such that: {pA, (1 − p)C} ∼ B (Steele & Stefánsson, 2020)

independence

roughly, if you prefer A to B then you should prefer A and C to B and C.

Suppose A⪯B. Then for any C, and any p∈[0,1]: {pA,(1−p)C}⪯{pB,(1−p)C}

Steele & Stefánsson (2020, p. §2.3)

things the theory assumes

actions

outcomes

+ some background assumptions

things the theory characterises

preference

subjective probability

rationality (?!)

The axioms can be regarded as implicitly defining

preference

and

subjective probability.

More carefully,
preference and subjective probability
are constructs of decision theory.

ok but I really want to drive this home ...

We are not really interested in actually inferring. The demonstration that we can infer is what shows that the axioms are sufficient to define preference and subjective probability.

Ramsey’s method allows us to
infer both of these
from observations of the actions you perform
plus some background assumptions (axioms).

We are not really interested in actually inferring. The demonstration that we can infer is what shows that the axioms are sufficient to define preference and subjective probability.

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What Are Preferences?

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