Revisiting Epistemic Logic with Names

This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional “names”. We make three contributions. First, we study its model theory, providing adequate notions of bisimulation and frame morphisms, and use them to study the logic’s expressive power and definability. Second, we show that the logic has a natural neighborhood semantics, which in turn allows to show that the axiomatization in [10] does not rely on possibly controversial introspective properties of knowledge. Finally, we extend the logic with common and distributed knowledge operators, and provide a sound and complete axiomatization for each of these extensions. These results together put the original epistemic logic with names in a more modern context and opens the door for a logical analysis of epistemic phenomena where group membership is uncertain or variable

Liquid Democracy: An Analysis in Binary Aggregation and Diffusion

The paper proposes an analysis of liquid democracy (or, delegable proxy voting) from the perspective of binary aggregation and of binary diffusion models. We show how liquid democracy on binary issues can be embedded into the framework of binary aggregation with abstentions, enabling the transfer of known results about the latter---such as impossibility theorems---to the former. This embedding also sheds light on the relation between delegation cycles in liquid democracy and the probability of collective abstentions, as well as the issue of individual rationality in a delegable proxy voting setting. We then show how liquid democracy on binary issues can be modeled and analyzed also as a specific process of dynamics of binary opinions on networks. These processes---called Boolean DeGroot processes---are a special case of the DeGroot stochastic model of opinion diffusion. We establish the convergence conditions of such processes and show they provide some novel insights on how the effects of delegation cycles and individual rationality could be mitigated within liquid democracy. The study is a first attempt to provide theoretical foundations to the delgable proxy features of the liquid democracy voting system. Our analysis suggests recommendations on how the system may be modified to make it more resilient with respect to the handling of delegation cycles and of inconsistent majorities

Binary Voting with Delegable Proxy: An Analysis of Liquid Democracy

The paper provides an analysis of the voting method known as delegable proxy voting, or liquid democracy. The analysis first positions liquid democracy within the theory of binary aggregation. It then focuses on two issues of the system: the occurrence of delegation cycles; and the effect of delegations on individual rationality when voting on logically interdependent propositions. It finally points to proposals on how the system may be modified in order to address the above issues

Comparing Social Network Dynamic Operators

Numerous logics have been developed to reason either about threshold-induced opinion diffusion in a network, or about similarity-driven network structure evolution, or about both. In this paper, we first introduce a logic containing different dynamic operators to capture changes that are 'asynchronous' (opinion change only, network-link change only) and changes that are 'synchronous' (both at the same time). Second, we show that synchronous operators cannot, in general, be replaced by asynchronous operators and vice versa. Third, we characterise the class of models on which the synchronous operator can be reduced to sequences of asynchronous operators.Comment: In Proceedings TARK 2023, arXiv:2307.0400

On the graph theory of majority illusions

The popularity of an opinion in one's direct circles is not necessarily a good indicator of its popularity in one's entire community. For instance, when confronted with a majority of opposing opinions in one's circles, one might get the impression that they belong to a minority. From this perspective, network structure makes local information about global properties of the group potentially inaccurate. However, the way a social network is wired also determines what kind of information distortion can actually occur. In this paper, we discuss which classes of networks allow for a majority of agents to have the wrong impression about what the majority opinion is, that is, to be in a 'majority illusion'

Priority Merge and Intersection Modalities

We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for priority merge for which we also provide a complete set of reduction axioms

The Wisdom of the Small Crowd: Myside Bias and Group Discussion

The my-side bias is a well-documented cognitive bias in the evaluation of arguments, in which reasoners in a discussion tend to overvalue arguments that confirm their prior beliefs, while undervaluing arguments that attack their prior beliefs. The first part of this paper develops and justifies a Bayesian model of myside bias at the level of individual reasoning. In the second part, this Bayesian model is implemented in an agent-based model of group discussion among myside-biased agents. The agent-based model is then used to perform a number of experiments with the objective to study whether the myside bias hinders or enhances the ability of groups to collectively track the truth, that is, to reach the correct answer to a given binary issue. An analysis of the results suggests the following: First, whether the truth-tracking ability of groups is helped or hindered by myside bias crucially depends on how the strength of myside bias is differentially distributed across subgroups of discussants holding different beliefs. Second, small groups are more likely to track the truth than larger groups, suggesting that increasing group size has a detrimental effect on collective truth-tracking through discussion

The Fluid Mechanics of Liquid Democracy

Liquid democracy is the principle of making collective decisions by letting agents transitively delegate their votes. Despite its significant appeal, it has become apparent that a weakness of liquid democracy is that a small subset of agents may gain massive influence. To address this, we propose to change the current practice by allowing agents to specify multiple delegation options instead of just one. Much like in nature, where --- fluid mechanics teaches us --- liquid maintains an equal level in connected vessels, so do we seek to control the flow of votes in a way that balances influence as much as possible. Specifically, we analyze the problem of choosing delegations to approximately minimize the maximum number of votes entrusted to any agent, by drawing connections to the literature on confluent flow. We also introduce a random graph model for liquid democracy, and use it to demonstrate the benefits of our approach both theoretically and empirically.Comment: Simulation code is available at https://github.com/pgoelz/flui

A Logic for Social Influence through Communication

Abstract. We propose a two dimensional “social network plausibility framework ” to model doxastic influence through communication in a social network. To do so, we combine two approaches: on the one hand, a hybrid logic setting, to model the social network itself (who is related to whom), and on the other hand, dynamic epistemic logic, to model the distribution of beliefs among agents (who believes what) and belief changes induced by communication events (what is said to whom and how do the hearers revise their beliefs). Combining both, we show how to design some particular communication protocols in this new framework to represent some level of social doxastic influence, assuming that the communicating agents are sincere and trust each other.