An axiomatic theory of political representation

We discuss the theory of voting rules which are immune to gerrymandering. Our approach is axiomatic. We show that any rule that is unanimous, anonymous, and representative consistent must decide a social alternative as a function of the proportions of agents voting for each alternative, and must either be independent of this proportion, or be in one-to-one correspondence with the proportions. In an extended model in which voters can vote over elements of the unit interval, we introduce and characterize the quasi-proportional rules based on unanimity, anonymity, representative consistency, strict monotonicity, and continuity. We show that we can always (pointwise) approximate a single-member district quota rule with a quasi-proportional rule. We also establish that upon weakening strict monotonicity, the generalized target rules emerge

Measurement in Economics and Social Science

The paper discusses measurement, primarily in economics, from both analytical and historical perspectives. The historical section traces the commitment to ordinalism on the part of economic theorists from the doctrinal disputes between classical economics and marginalism, through the struggle of orthodox economics against socialism down to the cold-war alliance between mathematical social science and anti-communist ideology. In economics the commitment to ordinalism led to the separation of theory from the quantitative measures that are computed in practice: price and quantity indexes, consumer surplus and real national product. The commitment to ordinality entered political science, via Arrow’s ‘impossibility theorem’, effectively merging it with economics, and ensuring its sterility. How can a field that has as its central result the impossibility of democracy contribute to the design of democratic institutions? The analytical part of the paper deals with the quantitative measures mentioned above. I begin with the conceptual clarification that what these measures try to achieve is a restoration of the money metric that is lost when prices are variable. I conclude that there is only one measure that can be embedded in a satisfactory economic theory, free from unreasonable restrictions. It is the Törnqvist index as an approximation to its theoretical counterpart the Divisia index. The statistical agencies have at various times produced different measures for real national product and its components, as well as related concepts. I argue that all of these are flawed and that a single deflator should be used for the aggregate and the components. Ideally this should be a chained Törnqvist price index defined on aggregate consumption. The social sciences are split. The economic approach is abstract, focused on the assumption of rational and informed behavior, and tends to the political right. The sociological approach is empirical, stresses the non-rational aspects of human behavior and tends to the political left. I argue that the split is due to the fact that the empirical and theoretical traditions were never joined in the social sciences as they were in the natural sciences. I also argue that measurement can potentially help in healing this split

On Fuzzy Concepts

In this paper we try to combine two approaches. One is the theory of knowledge graphs in which concepts are represented by graphs. The other is the axiomatic theory of fuzzy sets (AFS). The discussion will focus on the idea of fuzzy concept. It will be argued that the fuzziness of a concept in natural language is mainly due to the difference in interpretation that people give to a certain word. As different interpretations lead to different knowledge graphs, the notion of fuzzy concept should be describable in terms of sets of graphs. This leads to a natural introduction of membership values for elements of graphs. Using these membership values we apply AFS theory as well as an alternative approach to calculate fuzzy decision trees, that can be used to determine the most relevant elements of a concept

From Bounded Rationality to Behavioral Economics

The paper provides an brief overview of the “state of the art” in the theory of rational decision making since the 1950’s, and focuses specially on the evolutionary justification of rationality. It is claimed that this justification, and more generally the economic methodology inherited from the Chicago school, becomes untenable once taking into account Kauffman’s Nk model, showing that if evolution it is based on trial-and-error search process, it leads generally to sub- optimal stable solutions: the ‘as if’ justification of perfect rationality proves therefore to be a fallacious metaphor. The normative interpretation of decision-making theory is therefore questioned, and the two challenging views against this approach , Simon’s bounded rationality and Allais’ criticism to expected utility theory are discussed. On this ground it is shown that the cognitive characteristics of choice processes are becoming more and more important for explanation of economic behavior and of deviations from rationality. In particular, according to Kahneman’s Nobel Lecture, it is suggested that the distinction between two types of cognitive processes – the effortful process of deliberate reasoning on the one hand, and the automatic process of unconscious intuition on the other – can provide a different map with which to explain a broad class of deviations from pure ‘olympian’ rationality. This view requires re-establishing and revising connections between psychology and economics: an on-going challenge against the normative approach to economic methodology.Bounded Rationality, Behavioral Economics, Evolution, As If

(WP 2014-03) Bounded Rationality and Bounded Individuality

This paper argues that since the utility function conception of the individual is derived from standard rationality theory, the view that rationality is bounded suggests that individuality should also be seen as bounded. The meaning of this idea is developed in terms of two ways in which individuality can be said to be bounded, with one bound associated with Kahneman and Tversky’s prospect theory and the ‘new’ behavioral economics and a second bound associated with Simon’s evolutionary thinking and the ‘old’ behavioral economics. The paper then shows how different bounded individuality conceptions operate in nudge economics, agent-based modeling, and social identity theory, explaining these conceptions in terms of how they relate to these two behavioral economics views of bounded rationality. How both the ‘new’ and ‘old’ individuality bounds might then be combined in a single account is briefly explored in connection with Kirman’s Marseille fish market analysis

Axiomatic Districting

In a framework with two parties, deterministic voter preferences and a type of geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts one party can win, given the distribution of individual votes (the \optimal gerrymandering rule"). As a corollary, we obtain that no districting rule can satisfy our axioms and treat parties symmetrically