Judgment aggregation and agenda manipulation

In recent years, judgement aggregation has emerged as an important area of social choice theory. Judgement aggregation is concerned with aggregating sets of individual judgements over logically connected propositions into a set of collective judgements. It has been shown that even seemingly weak conditions on the aggregation function make it impossible to find functions that produce rational collective judgements from all possible rational individual judgements. This implies that the step from individual judgements to collective judgements requires trade-offs between different desiderata, such as universal domain, rationality, epistemological quality, and unbiasedness. The typical application for judgement aggregation is the problem of group decision making. Juries and expert committees are the stock examples. However, the relevance of judgement aggregation goes beyond these cases. In this survey, I review some core results in the field of judgement aggregation and social epistemology and discuss their implications for the analysis of distributed thinking.

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model.

Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are logically connected propositions. The problem is how a collective judgment on logically interconnected propositions can be defined from individual judgments on the same propositions. It turns out that, despite the fact that the individuals are logically consistent, the aggregation of their judgments may lead to an inconsistent group outcome, where the reasons do not support the conclusion. However, in this paper we claim that collective irrationality should not be the only worry of judgment aggregation. For example, judgment aggregation would not reject a consistent combination of reasons and conclusion that no member voted for. In our view this may not be a desirable solution. This motivates our research about when a social outcome is `compatible' with the individuals' judgments. The key notion that we want to capture is that any individual member has to be able to defend the collective decision. This is guaranteed when the group outcome is compatible with its members views. Judgment aggregation problems are usually studied using classical propositional logic. However, for our analysis we use an argumentation approach to judgment aggregation problems. Indeed the question of how individual evaluations can be combined into a collective one can also be addressed in abstract argumentation. We introduce three aggregation operators that satisfy the condition above, and we offer two definitions of compatibility. Not only does our proposal satisfy a good number of standard judgment aggregation postulates, but it also avoids the problem of individual members of a group having to become committed to a group judgment that is in conflict with their own individual positions.

Judgment aggregation studies how to aggregate individual judgments on logically correlated propositions into collective judgments. Different logics can be used in judgment aggregation, for which Dietrich and Mongin have proposed a generalized model based on general logics. Despite its generality, however, all nonmonotonic logics are excluded from this model. This paper argues for using nonmonotonic logic in judgment aggregation. Then it generalizes Dietrich and Mongin’s model to incorporate a large class of nonmonotonic logics. This generalization broadens the theoretical boundaries of judgment aggregation by proving that, even if these nonmonotonic logics are employed, certain typical impossibility results still hold.

Abstract: : This article attempts to provide individual‐level support to findings of longitudinal macro‐level studies of the relation between economic variables and electoral outcomes in the Federal Republic. The theoretical framework is one of incumbency‐oriented vs. policy‐oriented political responses to collective vs. individual economic judgments (Kiewiet, 1983). The data base consists of 25 surveys from 1961 through 1984. Empirical analysis comprises three steps: First, the relation between economic judgments and partisan sympathies is analyzed, since it appears likely that part of the covariations between voting and such judgments is spurious due to a common dependence upon partisan orientations. Second, the impact of both kinds of economic judgments upon voting over time is investigated with and without controls for partisan affiliation. Finally, the impact over time of macropolitical and macroeconomic variables on individual political response patterns to economic judgments is estimated at the longitudinal macro‐level. The analysis demonstrates that collective economic judgments are generally a more potent predictor of electoral choice than individual economic judgments, and that there is clear empirical evidence both for the incumbency‐oriented and the policy‐oriented hypothesis linking such judgments to the vote.

Drawing on dual process theory, we suggest that the benefits that arise from combining different individual judgments will be heightened when these judgments are based on different cognitive processes. We test this hypothesis in two experimental studies in which participants were prompted to make judgments relying on an analytical process, on their intuition, or in a control condition in which no particular instructions were given. Our results show that an aggregation of intuitive and analytical judgments provides more accurate estimates than any other aggregation procedure, and that this advantage increases with the number of judgments that are aggregated. Moreover, we find evidence that this result is driven by a lower correlation between errors of intuitive and analytical judgments compared to errors of judgments that are based on the same cognitive process or judgment errors in the control condition.

Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends on the individual judgements on the proposition under consideration.

International audience

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p263.pdf **Abstract:** We simulate voting rules for multiwinner elections in a model of judgment aggregation that distinguishes between rationality and feasibility constraints. These constraints restrict the structure of the individual judgments and of the collective outcome computed by the rule, respectively. We extend known results regarding the simulation of single-winner voting rules to the multiwinner setting, both for elections with ordinal preferences and for elections with approval-based preferences. This not only provides us with a new tool to analyse multiwinner elections, but it also suggests the definition of new judgment aggregation rules, by generalising some of the principles at the core of well-known multiwinner voting rules to this richer setting. We explore this opportunity with regards to the principle of proportionality. Finally, in view of the computational difficulty associated with many judgment aggregation rules, we investigate the computational complexity of our embeddings and of the new judgment aggregation rules we put forward.

The U.S. Environmental Protection Agency (EPA), under the authority of the Clean Air Act (CAA), is required to promulgate National Ambient Air Quality Standards (NAAQSs) for criteria air pollutants, including ozone. Each NAAQS includes a primary health-based standard and a secondary or welfare-based standard. This paper considers only the science used for revision of the primary standard for ozone in 2008. This paper summarizes deliberations of a small group of scientists who met in June 2007 to review the scientific information informing the EPA Administrator’s proposed revision of the 1997 standard. The Panel recognized that there is no scientific methodology that, in the absence of judgment, can define the precise numerical level, related averaging time, and statistical form of the NAAQS. The selection of these elements of the NAAQS involves policy judgments that should be informed by scientific information and analyses. Thus, the Panel members did not feel it appropriate to offer either their individual or collective judgment on the specific numerical level of the NAAQS for ozone. The Panel deliberations focused on the scientific data available on the health effects of exposure to ambient concentrations of ozone, controlled ozone exposure studies with human volunteers, long-term epidemiological studies, time- series epidemiological studies, human panel studies, and toxicological investigations. The deliberations also dealt with the issue of background levels of ozone of nonanthropogenic origin and issues involved with conducting formal risk assessments of the health impacts of current and prospective levels of ambient ozone. The scientific issues that were central to the EPA Administrator’s 2008 revision of the NAAQS for ozone will undoubtedly also be critical to the next review of the ozone standard. That review should begin very soon if it is to be completed within the 5-year cycle specified in the CAA. It is hoped that this Report will stimulate discussion of these scientific issues, conduct of additional research, and conduct of new analyses that will provide an improved scientific basis for the policy judgment that will have to be made by a future EPA Administrator in considering potential revision of the ozone standard.

4 - SIMPLICITY: IMPOSSIBILITY THEOREMS

Judgment aggregation is a collective decision making framework where the opinions of a group of agents is combined into a collective opinion. This can be done using many different judgment aggregation procedures. We study the computational complexity of computing the group opinion for several of the most prominent judgment aggregation procedures. In particular, we show that the complexity of this winner determination problem for analogues of the Kemeny rule, the Slater rule and the Young rule lies at the Θp2-level of the Polynomial Hierarchy (PH). Moreover, we show that the problem has a complexity at the Δp2-level of the PH for the analogue of Tideman's procedure with a fixed tie-breaking rule, and at the Σp2-level of the PH for the analogue of Tideman's procedure without a fixed tie-breaking rule.

Manipulation of judgment aggregation procedures has first been studied by List [14] and Dietrich and List [8], and Endriss et al. [9] were the first to study it from a computational perspective. Baumeister et al. [2, 3, 6] introduced the concepts of bribery and control in judgment aggregation and studied their algorithmic and complexity-theoretic properties. However, their results are restricted to Hamming-distance-respecting preferences and their results on bribery apply to the premise-based procedure only. We extend these results to more general preference notions, including closeness-respecting and top-respecting preferences that are due to Dietrich and List and have been applied to manipulation in judgment aggregation by Baumeister et al. [4, 5]. In addition, our results apply to uniform premise-based quota rules that generalize the premise-based procedure.

Introduction to Judgment Aggregation

Drawing on dual-process theory, we suggest that the benefits that arise from combining several quantitative individual judgments will be heightened when these judgments are based on different cognitive processes. We tested this hypothesis in three experimental studies in which participants provided estimates for the dates of different historical events (Study 1, N = 152), made probabilistic forecasts for the outcomes of soccer games (Study 2, N = 98), and estimated the weight of individuals on the basis of a photograph (Study 3, N = 3,695). For each of these tasks, participants were prompted to make judgments relying on an analytical process, on their intuition, or (in a control condition) on no specific instructions. Across all three studies, our results show that an aggregation of intuitive and analytical judgments provides more accurate estimates than any other aggregation procedure and that this advantage increases with the number of aggregated judgments.