Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg- Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer (...) based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting the (...) Arrow–Sen framework for social choice to study grading in groups. (shrink)

By applying Arrow’s impossibility theorem for social choice to scientific theory choice, Okasha concludes that there is no acceptable theory choice rule. Okasha identifies the only way out of the impossibility in enriching the input for the theory choice rule, following Sen’s work for social choice. However, such a route seems not to be available for ‘large scale’ theory choices—i.e. choices among ‘key theories’ which imply a change of paradigm—based on Kuhn’s criteria, since these criteria cannot provide a richer input. (...) The aim of the paper is to explore two lines of response to this conclusion. The first response proposes an example suggesting that Kuhn’s criteria may, indeed, provide sufficiently rich inputs. The second one proposes to use Kuhn’s criteria to evaluate prior probability and likelihood of the theories, and then take these as elements of the ‘Bayesian theory choice rule’ that avoids the impossibility. I will then argue against an objection to the second response, derived from Stegenga’s observation that a rule that translates the information provided by Kuhn’s criteria into prior probabilities suffers from Arrovian impossibility. Finally, I will answer a separate interesting question suggested by Stegenga’s observation. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

ABSTRACT In a recent article, Samir Okasha presented an argument that suggests that there is no rational way to choose among scientific theories. This would seriously undermine the view that science is a rational enterprise. In this article, I show how a suitably nuanced view of what scientific rationality requires allows us to sidestep this argument. In doing so, I present a new argument in favour of voluntarism of the type favoured by van Fraassen. I then show how such a (...) view of scientific rationality gives a precise interpretation of what Thomas Kuhn thought. _1_ Introduction _2_ Okasha’s Argument _3_ Rationality Can Be Silent _4_ Arrow Undermined _5_ The Informational-Basis Escape _6_ Theory Choice at the Level of the Individual Scientist _7_ Kuhn Vindicated _8_ Trade-offs and Partial Commensurability _9_ Conclusion. (shrink)

Emerging technologies are, by definition, full of surprises: developments that we cannot fully anticipate and that might have some bad outcomes as well as good ones. This presents a challenge for anyone trying to make forward‐looking policy decisions, including those who apply benefit‐cost analysis. BCA is now widely known and used, but it is also widely misunderstood—by many of its advocates as well as its detractors. In this essay, I will begin by examining some of the strengths and weaknesses of (...) BCA as a normative science. Yes, “normative science” is an oxymoron, and the incongruity it speaks to is a source of much of the controversy; BCA is an imperfect answer, but often the best available answer, to the question of how a society should go about making collective but not unanimous choices.I also want to take a hard look at the question of what we are evaluating. BCA is designed to weigh government actions, to see whether they are in the public interest; it is not designed to evaluate private actions. But if the government action is to approve a private action that otherwise would be prohibited, then the BCA inevitably must evaluate the latter. From the perspective of a government regulator, it is very tempting to shift the burden of proof onto private innovators—to obligate them to seek permission to proceed, and to demonstrate that their proposed actions have acceptable risks and will produce a net social benefit. But such burden‐shifting is not merely an administrative convenience; it has serious economic consequences that need to be examined. (shrink)