In this paper, I present a new decision procedure for the ideal membership problem for polynomial rings over principal domains using discrete valuation domains. As a particular case, I solve a fundamental algorithmic question in the theory of multivariate polynomials over the integers called “Kronecker’s problem”, that is the problem of finding a decision procedure for the ideal membership prob...

Automatically constructing novel representations of tasks from analysis of state spaces is a longstanding fundamental challenge in AI. I review recent progress on this problem for sequential decision making tasks modeled as Markov decision processes. Specifically, I discuss three classes of representation discovery problems: finding functional, state, and temporal abstractions. I describe solut...

In 1976 I was looking for a suitable subject for my PhD thesis. My thesis advisor Arie Hordijk and I found a lot of inspiration in Derman’s book (Finite state Markovian decision processes, Academic Press, New York, 1970). Since that time I was interested in linear programming methods for Markov decision processes. In this article I will describe some results in this area on the following topics...

In this paper I present an axiomatic choice theory for Bayesian decision makers. I use this model to define choice-based subjective probabilities that truly represent Bayesian decision makers’ prior and posterior beliefs. I argue that because of the limitations of the traditional analytical framework, no equivalent results may be obtained for theories that invoke Savage’s (1954) idea of a state...

Consider the single-agent decision problem, where the agent chooses the optimal action a ∈ A to maximize her expected utility. The utility depends on the state of nature θ ∈ Θ, and for the remainder of this lecture, we assume that Θ = {θ1, ..., θN} is a finite set with N elements. Assume also that the (state dependent) utility function u(a, θ) is continuous in a for all θ and A is compact. Let ...

In both cases, I couldn’t have prevented the ensuing death. However, intuitively, whereas I am morally responsible (‘‘responsible,’’ for short) for Victim’s death in Shooting, I am not responsible for the child’s death in Sharks. Shooting is a ‘‘Frankfurt-style’’ case. In a Frankfurt-style case, it has been argued, an agent is responsible for something that he couldn’t have prevented. Thus, in ...

In discussions on democratic legitimacy, Christiano’s position is often characterized as a monistic position, i.e. a strong and persuasive version of fair deliberative proceduralism. Democracy is thus seen as a realization of public equality in collective decision-making. The presented case for democracy is non-instrumental, and the quality of outcomes produced by a democratic decision-making p...

This paper examines the cognitive and behavioral foundations of decision-making at the individual level. It is based on a study conducted with 86 graduate students and a model that combines the highly mindful cognitive control capabilities and the less-mindful routinization propensity to explain decision-making performance. The paper offers three contributions. First, I introduce and empiricall...

This paper introduces models of status quo bias based on the concept of decision avoidance, by which a decision maker may select the status quo in order to avoid a difficult decision. These models capture the experimental finding that the status quo is more frequently chosen in larger choice sets. This phenomenon violates the predictions of current preference-based models of status quo bias tha...

Recent work on decision-making suggests that we are a conglomeration of multiple decision-making information-processing systems. In this paper, I address consequences of this work on decision-making processes for three philosophical conceptualizations that can be categorized as forms of dualism. 1. A rejection of Cartesian dualism. Although most scientists reject the existence of a separate non...