Changing for the Better: Preference Dynamics and Agent Diversity
Fenrong Liu

Abstract:
This thesis investigates two main issues concerning the behavior of
rational agents, preference dynamics and agent diversity.

We take up two questions left aside by von Wright, and later also the
multitude of his successors, in his seminal book Logic of Preference in
1963: reasons for preference, and changes in preference. Various notions
of preference are discussed, compared and further correlated in the
thesis. In particular, we concentrate on extrinsic preference. Contrary
to intrinsic preference, extrinsic preference is reason-based, i.e.
one's preference for one option over another has a reason. A logical
model is proposed and its properties are determined. Dynamics come in
naturally, since reasons for the preferences can change. Logical systems
and formal results regarding dynamical preference change are then
presented. 

Preference arises from comparisons between alternatives. A first option
is to compare situations. Abstractly speaking, preferences are in this
case between propositions, viewed as sets of possible worlds. The
reasons can then be based on a `betterness' relation over possible
worlds. Propositional preference arises as a lift from this primitive
relation. A standard modal logical approach is taken and we use a
modality for the betterness relation in the language. We then model
preference change by techniques from dynamic epistemic logic (DEL),
where a typical action, e.g. a suggestion or a command can change the
betterness ordering of the worlds, and thereby the propositional
preference. Dynamic reduction axioms are obtained to encode exactly how
such a change takes place. We obtain a complete dynamic preference
logic.

A second option is to compare objects as such. Concretely, properties of
the objects often determine the preference over the objects. Properties
are now the reasons. Inspired by Optimality Theory (OT), we propose a
priority sequence, an ordering of properties. Various ways of getting a
preference from the priority sequence are investigated, though we mostly
follow the OT approach. We use a fragment of first-order logic to
describe the situation. Here, on the dynamic side, it is priority change
that leads to preference change. Using the DEL methodology again we
propose a complete set of reduction axioms concerning the possible
dynamic operations on priority sequences.

Not surprisingly, the above two views are closely related. After all,
possible worlds can be thought of as objects! On the basis of a
systematic comparison of the two views, we develop a two level
perspective, in which the models themselves are structured in layers. In
particular, correspondence results between the changes at the level of
the possible worlds and the changes at the level of the priority
sequences are proved. We end up by sketching a two-level preferential
predicate logic to describe more complex circumstances in which
situations and objects are compared simultaneously.

But we do not see this as the whole story. Preference does not live by
itself, it is often intermingled with epistemic notions of knowledge and
belief. One can have different intuitions about how this entanglement
operates. A few options are discussed, and proposals for logical models
are presented. When moving to dynamics, we now see a picture of
knowledge update, belief revision and preference change taking place
symbiotically, often unconsciously as in real life.

The resulting picture in the thesis is one of agents that process
information and adjust beliefs and preferences in many different ways.
There is no logically prescribed unique norm for doing this. The second
part of the thesis takes this general phenomenon of diversity of agents
as its focus, since it raises many issues for logical systems and the
idealized agents which they normally presuppose. In reality, agents can
differ across a wide spectrum of cognitive abilities and habits: in
their memory capacity, observation power, inferential power,
introspective ability, and revision policies when facing new
information.

Two kinds of agents, perfect recall agents, and memory-free agents are
studied thoroughly, in the setting of playing games. We show how current
dynamic logics can be `parametrized' to allow for this memory diversity,
with new characterizations of agent types resulting in complete
dynamic-epistemic logics. The other dimension of the reality of diverse
agents is that, however different they are, they often do manage to
coordinate with each other successfully. While this theme has been
prominent in game theory and multi-agent systems, it has received hardly
any attention in logic. We analyze this interaction between different
agents by looking at concrete scenarios which model their types
explicitly.

Finally, we analyze the issue of agent diversity in its generality,
discussing what dynamic logics would have to look like to become a
full-fledged account of agents of different capacities and tendencies
that pursue and sometimes achieve their goals in irreducibly social
settings.