Collective economic decisions and the discursive dilemma

Most economic decisions involve judgments. When decisions are taken collectively, various judgment aggregation problems may occur. Here we consider an aggregation problem called the "discursive dilemma", which is characterized by an inconsistency between the aggregate judgment on the premises for a conclusion and the aggregate judgment on the conclusion itself. It thus matter for the decision whether the group uses a premise- or a conclusion-based decisionmaking procedure. The current literature, primarily within jurisprudence, philosophy, and social choice, consider aggregation of qualitative judgments on propositions. Most economic decisions, however, involve quantitative judgments on economic variables. We develop a framework that is suitable for analyzing the relevance of the discursive dilemma for economic decisions. Assuming that decisions are reached either through majority voting or by averaging, we find that the dilemma cannot be ruled out, except under some restrictive assumptions about the relationship between the premise-variables and the conclusion.Collective economic decisions, Judgement aggregation, Inconsistency

A liberal paradox for judgment aggregation

In the emerging literature on judgment (as opposed to preference) aggregation, expert rights or liberal rights have not been investigated yet. When a group forms collective beliefs, it may assign experts with special knowledge on certain propositions the right to determine the collective judgment on those propositions; and, when a group forms collective goals or desires, it may assign individuals specially affected by certain propositions similar rights on those propositions. We identify a problem similar to, but more general than, Sen's `liberal paradox': Under plausible conditions, the assignment of such rights to two or more individuals (or subgroups) is inconsistent with the unanimity principle, whereby propositions accepted by all individuals must be collectively accepted. So a group respecting expert or liberal rights on certain propositions must sometimes overrule its unanimous judgments on others. The inconsistency does not arise if either different individuals' rights are `disconnected' or individuals are `agnostic/tolerant' or `deferring/empathetic' towards other individuals' rights. Our findings have implications for the design of mechanisms by which groups (societies, committees, expert panels, organizations) can reach decisions on systems of interconnected propositions.liberal paradox, liberal right, expert right, subgroup rights, unanimity principle, judgment aggregation, empathy, deferral, tolerance, agnosticism

Judgment aggregation in search for the truth

We analyze the problem of aggregating judgments over multiple issues from the perspective of whether aggregate judgments manage to efficiently use all voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives where voters' disagreements stem from conflicts of information rather than of interest. Combining the two bodies of literature, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. Assuming that voters share a preference for true collective judgments, we analyze the resulting strategic incentives and determine which voting rules efficiently use all private information. We find that in certain, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of ‘yes’ votes exceeds a particular quota

Approximate Judgement Aggregation

In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them (e.g., transitivity when describing preferences). We consider the issue of judgement aggregation from the perspective of approximation. That is, we generalize the previous results by studying approximate judgement aggregation. We relax the main two constraints assumed in the current literature, Consistency and Independence and consider mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small portion of the inputs. The main question we raise is whether the relaxation of these notions significantly alters the class of satisfying aggregation mechanisms. The recent works for preference aggregation of Kalai, Mossel, and Keller fit into this framework. The main result of this paper is that, as in the case of preference aggregation, in the case of a subclass of a natural class of aggregation problems termed `truth-functional agendas', the set of satisfying aggregation mechanisms does not extend non-trivially when relaxing the constraints. Our proof techniques involve Boolean Fourier transform and analysis of voter influences for voting protocols. The question we raise for Approximate Aggregation can be stated in terms of Property Testing. For instance, as a corollary from our result we get a generalization of the classic result for property testing of linearity of Boolean functions.judgement aggregation, truth-functional agendas, computational social choice, computational judgement aggregation, approximate aggregation, inconsistency index, dependency index

Strategy-proof judgment aggregation.

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.

Social Epistemology

International audienceSocial epistemology studies knowledge in social contexts. Knowledge is 'social' when its holder communicates with or learns from others (Epistemology in groups), or when its holder is a group as a whole, literally or metaphorically (Epistemology of groups). Group knowledge can emerge explicitly, through aggregation procedures like voting, or implicitly, through institutions like deliberation or prediction markets. In the truth-tracking paradigm, group beliefs aim at truth, and group decisions at 'correctness', in virtue of external facts that are empirical or normative, real or constructed, universal or relativistic, etc. Procedures and institutions are evaluated by epistemic performance: Are they truth-conducive? Do groups become 'wiser' than their members? We review several procedures and institutions, discussing epistemic successes and failures. Jury theorems provide formal arguments for epistemic success. Some jury theorems misleadingly conclude that 'huge groups are infallible', an artifact of inappropriate premises. Others have defensible premises, and still conclude that groups outperform individuals, without being infallible

Social epistemology

International audienceSocial epistemology studies knowledge in social contexts. Knowledge is 'social' when its holder communicates with or learns from others (Epistemology in groups), or when its holder is a group as a whole, literally or metaphorically (Epistemology of groups). Group knowledge can emerge explicitly, through aggregation procedures like voting, or implicitly, through institutions like deliberation or prediction markets. In the truth-tracking paradigm, group beliefs aim at truth, and group decisions at 'correctness', in virtue of external facts that are empirical or normative, real or constructed, universal or relativistic, etc. Procedures and institutions are evaluated by epistemic performance: Are they truth-conducive? Do groups become 'wiser' than their members? We review several procedures and institutions, discussing epistemic successes and failures. Jury theorems provide formal arguments for epistemic success. Some jury theorems misleadingly conclude that 'huge groups are infallible', an artifact of inappropriate premises. Others have defensible premises, and still conclude that groups outperform individuals, without being infallible

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