Aggregation theory and the relevance of some issues to others

I propose a general collective decision problem consisting in many issues that are interconnected in two ways: by mutual constraints and by connections of relevance. Aggregate decisions should respect the mutual constraints, and be based on relevant information only. This general informational constraint has many special cases, including premise-basedness and Arrow''s independence condition; they result from special notions of relevance. The existence and nature of (non-degenerate) aggregation rules depends on both types of connections. One result, if applied to the preference aggregation problem and adopting Arrow''s notion of (ir)relevance, becomes Arrow''s Theorem, without excluding indifferences unlike in earlier generalisations.mathematical economics;

Aggregation Theory and the Relevance of Some Issues to Others

International audienceI propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people's judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people's judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow's Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation

Beyond the DSGE Straitjacket

Academic macroeconomics and the research department of central banks have come to be dominated by Dynamic, Stochastic, General Equilibrium (DSGE) models based on micro-foundations of optimising representative agents with rational expectations. We argue that the dominance of this particular sort of DSGE and the resistance of some in the profession to alternatives has become a straitjacket that restricts empirical and theoretical experimentation and inhibits innovation and that the profession should embrace a more flexible approach to macroeconometric modelling. We describe one possible approach

Aggregation and the relevance of some issues for others

A general collective decision problem is analysed. It consists in many issues that are interconnected in two ways: by mutual constraints and by connections of relevance. The goal is to decide on the issues by respecting the mutual constraints and by aggregating in accordance with an informational constraint given by the relevance connections. Whether this is possible in a non-degenerate way depends on both types of connections and their interplay. One result, if applied to the preference aggregation problem and adopting Arrow''s notion of (ir)relevance, gives Arrow''s Theorem, without excluding indifferences unlike in the existing general aggregation literature.mathematical economics;

The Tyranny of a Metaphor

Debates on the practical relevance of ideal theory revolve around Sen's metaphor of navigating a mountainous landscape. In *The Tyranny of the Ideal*, Gerald Gaus presents the most thorough articulation of this metaphor to date. His detailed exploration yields new insight on central issues in existing debates, as well as a fruitful medium for exploring important limitations on our ability to map the space of social possibilities. Yet Gaus's heavy reliance on the navigation metaphor obscures questions about the reasoning by which ideal theories are justified. As a result, Gaus fails to notice the ways in which his theory of the Open Society resembles the ideal theories he aims to dismiss. Ironically, Gaus winds up neglecting the ways in which the Open Society might tyrannize our efforts to realize greater justice. (This article is part of a symposium on Gaus's *The Tyranny of the Ideal*.

Introduction to Judgment Aggregation

This introduces the symposium on judgment aggregation. The theory of judgment ag­gregation asks how several individuals' judgments on some logically connected propo­sitions can be aggregated into consistent collective judgments. The aim of this intro­duction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impos­sibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium.Judgment aggregation, Arrow's theorem, Escape routes

Voting and the Cardinal Aggregation of Judgments

The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections