Paul Weirich

The Philosophy and Epistemology of Simulation: A Review

The philosophical literature on simulations has increased dramatically during the past 40 years. Many of its main topics are epistemological. For example, philosophers consider how the results of simulations help explain natural phenomena. This essay’s review treats mainly simulations in the social sciences. It considers the nature of simulations, the varieties of simulation, and uses of simulations for representation, prediction, explanation, and policy decisions. Being oriented toward philosophy of science, it compares simulations to models and experiments and considers whether simulations raise new methodological issues.The essay concludes that several features of simulations set them apart from models and experiments and make them novel scientific tools, whose powers and limits are not yet well understood.

The St. Petersburg gamble and risk

Pursuing a line of thought initiated by Maurice Allais (1979), I consider whether the mean-risk method of decision making introduced by Harry Markowitz (1959) and other resolves Karl Mengers (1934) version of the St. Petersburg paradox. I provide a conditional answer to this question. I demonstrate that given certain plausible assumption about attitudes toward risk, a certain plausible development of the mean-risk method does resolve the paradox. My chief premiss is roughly that in the St. Petersburg gamble the small chances for large prizes create big risks.

Expected Utility and Risk

The rule to maximize expected utility is intended for decisions where options involve risk. In those decisions the decision makers attitude toward risk is important, and the rule ought to take it into account. Allaiss and Ellsbergs paradoxes, however, suggest that the rule ignores attitudes toward risk. This suggestion is supported by recent psychological studies of decisions. These studies present a great variety of cases where apparently rational people violate the rule because of aversion or attraction to risk. Here I attempt to resolve the issue concerning expected utility and risk. I distinguish two versions of the rule to maximize expected utility. One adopts a broad interpretation of the consequences of an option and has great intuitive appeal. The other adopts a narrow interpretation of the consequences of an option and seems to have certain technical and practical advantages. I contend that the version of the rule that interprets consequences narrowly does indeed neglect attitudes toward risk. That version of the rule excludes the risk involved in an option from the consequences of the option and, contrary to what is usually claimed, cannot make up for this exclusion through adjustments in probability and utility assignments. I construct a new, general argument that establishes this in a rigorous way. On the other hand, I contend that the version of the rule that interprets consequences broadly takes account of attitudes toward risk by counting the risk involved in an option among the consequences of the option. I rebut some objections to this version of the rules, in particular, the objection that the rule lacks practical interest. Drawing upon the literature on ‘mean-risk’ decision rules, I show that this version of the rule can be used to solve some realistic decision problems.

The Explanatory Power of Models and Simulations: A Philosophical Exploration

Some computer simulations have explanatory goals. In a typical case, the computer simulation exemplifies a model generating a phenomenon under investigation. For the simulation to be explanatory, the model has to be explanatory. Models that fully explain phenomena are rare, but a model may offer a partial explanation of a phenomenon. It does this if an isomorphism holds between certain features of the model and certain features of a natural system realizing the phenomenon. The first two sections elaborate this account of a simulation’s explanatory power. The third section illustrates the account by applying it to Brian Skyrms’s (2004) simulations of the evolution of cooperation. The final section uses the account to suggest ways of increasing those simulations’ explanatory power.

Hierarchical Maximization of Two Kinds of Expected Utility

Causal decision theory produces decision instability in cases such as Death in Damascus where a decision itself provides evidence concerning the utility of options. Several authors have proposed ways of handling this instability. William Harper (1985 and 1986) advances one of the most elegant proposals. He recommends maximizing causal expected utility among the options that are causally ratifiable. Unfortunately, Harpers proposal imposes certain restrictions; for instance, the restriction that mixed strategies are freely available. To obtain a completely general method of handling decision instability, I step outside the confines of pure causal decision theory. I introduce a new kind of backtracking expected utility and propose maximizing it among the options that are causally ratifiable. In other words, I propose a hierarchical maximization of (1) conditional causal expected utility and (2) the new backtracking expected utility. I support this proposal with some intuitive considerations concerning the distinction between optimality and conditional optimality. And I prove that the proposal yields a solution in every finite decision problem.

Epistemology of modeling and simulation

While ontology deals with the question of being or existence, epistemology deals with the question of gaining knowledge. This panel addresses the challenge of how we gain knowledge from modeling and simulation. What is the underlying philosophy of science of M&S? What are our canons of research for M&S? Is it sufficient to apply the foundational methods of the application domains, or do we need to address these questions from the standpoint of M&S as a discipline? The invited experts illuminate various facets from philosophical, mathematical, computational, and application viewpoints.

Conditional Probabilities and Probabilities Given Knowledge of a Condition

The conditional probability of h given e is commonly claimed to be equal to the probability that h would have if e were learned. Here I contend that this general claim about conditional probabilities is false. I present a counter-example that involves probabilities of probabilities, a second that involves probabilities of possible future actions, and a third that involves probabilities of indicative conditionals. In addition, I briefly defend these counter-examples against charges that the probabilities they involve are illegitimate.

Interpersonal utility in principles of social choice

This paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utilitys descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory.

Utility Maximization Generalized

Theories of rationality advance principles that differ in topic, scope, and assumptions. A typical version of the principle of utility maximization formulates a standard rather than a procedure for decisions, evaluates decisions comprehensively, and relies on idealizations. I generalize the principle by removing some idealizations and making adjustments for their absence. The generalizations accommodate agents who have incomplete probability and utility assignments and are imperfectly rational. They also accommodate decision problems with unstable comparisons of options.

Risk's place in decision rules

To handle epistemic and pragmatic risks, Gärdenfors and Sahlin (1982, 1988) design a decision procedure for cases in which probabilities are indeterminate. Their procedure steps outside the traditional expected utility framework. Must it do this? Can the traditional framework handle risk? This paper argues that it can. The key is a comprehensive interpretation of an options possible outcomes. Taking possible outcomes more broadly than Gärdenfors and Sahlin do, expected utility can give risk its due. In particular, Goods (1952) decision procedure adequately handles indeterminate probabilities and the risks they generate.