Work in progress
Here are some papers which have not yet appeared in print, but are at some stage of development.
“Preferential Attachment and the Search for Successful Theories”
Multiarm bandit problems have been used to model the selection of competing scientific theories by boundedly rational agents. In this paper, I define a \emph{variable-arm} bandit problem, which allows the set of scientific theories to vary over time. I show that Roth-Erev reinforcement learning, which solves multiarm bandit problems in the limit, cannot solve this problem in a reasonable time. However, social learning via preferential attachment combined with individual reinforcement learning which discounts the past, does.
“Learning to Signal in a Dynamic World”
Sender-receiver games, first introduced by David Lewis in Convention, have received increased attention in recent years as a formal model for the emergence of communication. Skyrms (2010) showed that simple models of reinforcement learning often succeed in forming efficient, albeit not necessarily minimal, signalling systems for a large family of games. Later, Alexander, Skyrms, and Zabell (2011) showed that reinforcement learning, combined with forgetting, frequently produced both efficient and minimal signalling systems. In this paper I define a dynamic sender-receiver game in which the state-action pairs are not held constant over time, and show that neither of these two models of learning learn to signal in this environment. However, a model of reinforcement learning with discounting of the past does learn to signal; it also gives rise to the phenomenon of linguistic drift.
“Why the Angels Cannot Choose”
The Pasadena game, first introduced by Nover and Hajek (2004), has generated a substantial amount of discussion regarding what value an ideal rational agent should assign to the game. Yet little attention has been devoted to the question of what is an ideal rational agent, and in what sense decision theory may be said to apply to one. I show that, given one arguably natural set of constraints on the preferences of an idealised rational agent, such an agent is forced to be indifferent among a large family of goods, and hence cannot choose among them. This result provides an upper bound on the kinds of idealising assumptions which can be made for rational agents, beyond which the very notion of decision theory becomes untenable.
“Decision Theory Meets the Witch of Agnesi”
Decision theory offers the following rule for how rational agents ought to choose: take whatever action serves to maximise your expected utility. Although it is generally recognised that choice under uncertainty may generate cases where the agent cannot maximise her expected utility, it is typically thought that rational agents can maximise their expected utility if they have full knowledge of the outcomes and full knowledge of the probability distribution over outcomes. In this paper I construct a gamble which satisfies these last two conditions but, nevertheless, a rational agent cannot assign a value to the gamble (even though it is clearly in the interest of the rational agent to participate) because no expected value exists. This gamble differs from the St. Petersburg paradox in that it involves both positive and negative payoffs, and it differs from the Pasadena game in that the method of weak expectations does not work.
“‘From Each According to His Abiltity’: The Evolution of Respect for Needs”
Much work has been done attempting to show how processes of cultural evolution can give rise to a general tendency to share-and- share alike. However, one shortcoming with these models is that they tend to assume perfect symmetry between players and, at the same time, to omit differences in need. In developing a more sophisticated bargaining model which includes both resource production and resource division, we show how cultural evolutionary processes can give rise, under certain circumstances, to a universal respect for needs.
This paper needs some work, but I’m fond of the argument. It’s an attempt to say something interesting about the fact that the cellular automaton rule 110 is capable of universal computation.
