White Manipulation in Judgment Aggregation

Distributive systems consisting of autonomous and intelligent components need to be able to reason and make decisions based on the information these components share. Judgment aggregation investigates how individual judgments on logically connected propositions can be aggregated into a collective judgment on the same propositions. It is the case that seemingly reasonable aggregation procedures may force the group to hold an inconsistent judgment set. What happens when the agents realize that the group outcome will be inconsistent? We claim that, in order to avoid an untenable collective outcome, individuals may prefer to declare a non-truthful, less preferred judgment set. Thus, the prospect of an individual trying to manipulate the social outcome by submitting an insincere judgment set is turned from being an undesirable to a “virtuous” (or white) manipulation. We define white manipulation and present the initial study of it as a coordinated action of the whole group

Complexity Results for Manipulation, Bribery and Control of the Kemeny Judgment Aggregation Procedure

We study the computational complexity of several scenarios of strategic behavior for the Kemeny procedure in the setting of judgment aggregation. In particular, we investigate (1) manipulation, where an individual aims to achieve a better group outcome by reporting an insincere individual opinion, (2) bribery, where an external agent aims to achieve an outcome with certain properties by bribing a number of individuals, and (3) control (by adding or deleting issues), where an external agent aims to achieve an outcome with certain properties by influencing the set of issues in the judgment aggregation situation. We show that determining whether these types of strategic behavior are possible (and if so, computing a policy for successful strategic behavior) is complete for the second level of the Polynomial Hierarchy. That is, we show that these problems are $\Sigma^p_2$-complete

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.

Pareto Optimality and Strategy Proofness in Group Argument Evaluation (Extended Version)

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences

Manipulation in group argument evaluation.

Given an argumentation framework and a group of agents, the individuals may have divergent opinions on the status of the arguments. If the group needs to reach a common po- sition on the argumentation framework, the question is how the individual evaluations can be mapped into a collective one. This problem has been recently investigated in [1]. In this paper, we study under which conditions these operators are Pareto optimal and whether they are manipulable.Collective decision making; Argumentation; Judgment aggregation; Social choice theory;

Reasons, Coherence, and Group Rationality

Philosophy and Phenomenological Research, EarlyView

Group deliberation and the transformation ofjudgments: an impossibility result

While a large social-choice-theoretic literature discusses the aggregation ofindividual judgments into collective ones, there is relatively little formalwork on the transformation of individual judgments in group deliberation. Idevelop a model of judgment transformation and prove a baselineimpossibility result: Any judgment transformation function satisfying someinitially plausible condition is the identity function, under which no opinionchange occurs. I identify escape routes from this impossibility result andargue that successful group deliberation must be 'holistic': individualscannot generally revise their judgments on a proposition based on judgmentson that proposition alone but must take other propositions into account too. Idiscuss the significance of these findings for democratic theory.group deliberation, judgment aggregation, judgmenttransformation, belief revision

Judgment aggregation by quota rules

It is known that majority voting among several individuals on logically interconnected propositions may generate irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds some (proposition-specific) threshold. After characterizing quota rules, we prove necessary and sufficient conditions under which their outcomes satisfy various rationality conditions. We also consider sequential quota rules, which adjudicate propositions sequentially, letting earlier judgments constrain later ones. While ensuring rationality, sequential rules may be path-dependent. We characterize path-independence and prove its equivalence to strategy- proofness under mild conditions. Our results generalize earlier (im)possibility theorems.Judgment aggregation, quota rules, collective rationality, path-dependence, strategy-proofness, formal logic