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 [...] view
subjective values and probabilities
as interrelated constructs of decision theory’

(Davidson, 1974, p. 146)

why necessary?

You might say, I know what these things are.

will get to that later

I will return to this later ... first I want to show you the positive theory

habitual process

Action occurs in the presence of Stimulus.

Outcome follows action

Agent is thereby rewarded

Stimulus-Action Link is strengthened due to reward

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.

Btw, it’s not just what the notions of belief and desire are; we also need to say how they combine to produce actions in a way that allows us to justify predictions we have made (e.g. about when the rat will press the lever). All that has so far been left implicit!

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?

When we were looking at the representation, I was presenting decision theory as if we know subjective probabilities and preferences.

And I just say, oh, you know, how much do you prefer this amount of broccoli over that amount of broccoli? And then we can work out what actions is most rational for you to do.

That's the forward way of looking at it.

But what Ramsey Frank Ramsey famously showed. Is that you can actually go the other way.

So this is Ramsey's famous representation theorem.

If you observe somebody's actions, you can infer their subjective probabilities and preferences.

Why is this important?

Because it shows that those subjective probabilities and preferences are things which are characterised by the theory. Formally speaking, the theory can take for granted the idea that there are actions and outcomes, and it can tell you what it is for somebody to have a particular preference ranking, and it can tell you what it is for somebody to have particular subjective expectations or beliefs.

So this direction is super important to us.

If we can observe actions and then assign subjective probabilities and preferences, we've shown that it's reasonable to treat those things as constructs of decision theory.

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?)

ANS?: as long as there is a pair of `mirror gambles` between which the agent is not indifferent, we can be sure that they are not indifferent between A and B?

‘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)

Suppose that what you get depends on whether you draw a red or white ball from my bucket ...

Then your indifference between the two doors would allow me to infer that you think there is the same chance of getting either colour or ball.

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 axioms (background assumptions)

things the theory characterises

preference

subjective probability

rationality (?!)

The axioms can be regarded as implicitly defining

preference

and

subjective probability.

why necessary?

You might say, I know what these things are.

1. We as researchers need a shared understanding of belief and desire.

2. There are three potential sources of shared understanding: folk psychology, philosophy and decision theory.

3. Folk psychology does not provide a shared understanding.

4. Nor does philosophy.

Therefore:

5. We need decision theory to provide a shared understanding.

folk psychology

a source of common knowledge of principles

that implicitly define ‘intention’, ‘knowledge’, and the rest

Lewis (1972) vs Heider (1958)

As philosophers see
folk psychology ...

‘When someone is in so-and-so combination of mental states and receives sensory stimuli of so-and-so kind, he tends with so-and-so probability to be caused thereby to go into so-and-so mental states and produce so-and-so motor responses.’

(Lewis, 1972, p. 256)

folk psychology

a source of common knowledge of principles

that implicitly define ‘intention’, ‘knowledge’, and the rest

Lewis (1972) vs Heider (1958)

A problem arises from the observation that humans are notoriously free in ascribing mental states and powers. Heider & Simmel, 1944 study of people’s responses to the movements of simple geometric shapes is the canonical illustration of this: people ascribe intention and character traits to moving patches of light which, as they know, are not even physical objects let alone agents or thinkers. It is also common for people to talk about mobile phones trying to do things (most frequently, but not only, trying to kill them), as well as wanting, hating, liking, thinking and pretending.

One might aim to dismiss such cases as merely unserious extensions, comparable to talk of table legs or cabbage heads. But this invites us to ask where the line should be drawn between serious and unserious attributions of mental states. And that seems to take us in the wrong direction. We have replaced the task of drawing a line between thinkers and non-thinkers with the task of drawing a line between serious and unserious talk about thinkers. The latter problem seems no easier to solve. Worse, adult humans might benefit from over-or under-attributing mental states and powers. As long as this is possible, there can be no justification for supposing that any line demarcating serious from unserious talk will correspond to the line separating thinkers from thoughtless systems.

further obstacle: diversity, inter- and intra-personal

Expertise may differ from person to person in important ways, perhaps because we are at different points on the autistic spectrum or perhaps because of cultural differences between us (see, for example, Dixson, Komugabe-Dixson, Dixson, & Low, 2018). Relying directly on mundane expertise could not yield consensus on what systems do, think or feel; nor even on which systems are agents, persons or thinkers. This is the *Diversity Problem*: Different people have different models of minds and actions; and one person may operate with more than one model.

1. We as researchers need a shared understanding of belief and desire.

2. There are three potential sources of shared understanding: folk psychology, philosophy and decision theory.

3. Folk psychology does not provide a shared understanding.

4. Nor does philosophy.

Therefore:

5. We need decision theory to provide a shared understanding.

distinctive = has value distinct from true belief

KNOWLEDGE	yes	no
Is it a mental state?	Williamson (2000)	Hyman (1999)
Knowing entails believing?	Rose & Schaffer (2013)	Radford (1966)
Is it a form of belief?	Sosa (2007)	Williamson (2000)
Valuable for action?	Plato’s Meno	Kaplan (1985)
Is humanly attainable?	[others]	Unger (1975)
Depends on context?	Lewis (1996)	[lots]

Which things manifest agency?

‘The paramecium’s swimming through the beating of its cilia, in a coordinated way, and perhaps its initial reversal of direction, count as agency.’

(Burge, 2009, p. 259)

Do these two have a shared understanding of agency?

Compatible claims about different things? Or incompatible claims about one thing?

Nearly everyone in philosophy thinks that, overall, the reasons favour one of these views. But we also know that philosophers have been disagreeing for a good 2000 years and that the trend is not towards disagreements being overcome through the use of reason.

another obstacle ...

‘epistemic case intuitions are generated by [...] folk psychology’

Nagel (2012, p. 510)

‘some part of us finds it almost impossible not to categorise them as’ agents

Steward (2009, p. 229)

1. We as researchers need a shared understanding of belief and desire.

2. There are three potential sources of shared understanding: folk psychology, philosophy and decision theory.

3. Folk psychology does not provide a shared understanding.

4. Nor does philosophy.

Therefore:

5. We need decision theory to provide a shared understanding.

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

(Jeffrey, 1983, p. xi)

‘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)

why necessary?

You might say, I know what these things are.

for shared understanding!

so far ...

1. We understand what decision theory is;

2. ... and how it can be used to provide us as researchers with a shared understanding of belief and desire.

3. This is necessary because neither folk psychology nor philosophy provide a shared understanding.

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