Belief revision, belief merging and voting

2017

Lecture Notes in Computer Science, 2010

In this paper we forge a connection between dynamic epistemic logics of belief revision on one hand and studies of collective judgement and multi-agent preference change on the other. Belief revision in the spirit of dynamic epistemic logic uses updating with relational substitutions to change the beliefs of individual agents. Collective judgement in social choice theory studies the collective outcomes of individual belief changes. We start out from the logic of communication and change (LCC), which is basically epistemic propositional dynamic logic (PDL) extended with update action modalities. We show how epistemic PDL can be made to handle belief operators. Our new version of epistemic/doxastic PDL does not impose any constraints on the basic relations. Because of this it does not suffer from the drawback of LCC that constraints on epistemic relations, such as transitivity and reflexivity, may get lost under updates that are admitted by the system. After introducing the base system without constraints, we study the effects of imposing a single constraint, namely the constraint that the agent's preference relations are linked. Linkedness is a natural extension of local connectedness to the multi-agent case. It assures that if Alice prefers y to x and Bob prefers z to x, then both Alice and Bob can make up their minds when given a choice between y and z. Since general belief changes may not preserve linkedness, we propose a recipe for belief change that does preserve it. Finally, we show that the resulting framework can be used to model consensus seeking procedures. We focus on the case of plenary Dutch meetings. In Dutch meetings, a belief change (or rather: preference change) is performed for all agents in the meeting if a majority believes (or: is in favour of) the proposition that is under discussion. A special case of these meetings is judgement aggregation, and we apply our framework to the discursive dilemma in Conjecture It is impossible to describe conditional belief and plain belief as single unary modalities in converse PDL.

2018

We define a consensus postulate in the propositional belief merging setting. In a nutshell, this postulate imposes the merged base to be consistent with the pieces of information provided by each agent involved in the merging process. The interplay of this new postulate with the IC postulates for belief merging is studied, and an incompatibility result is proved. The maximal sets of IC postulates which are consistent with the consensus postulate are exhibited. When satisfying some of the remaining IC postulates, consensus operators are shown to suffer from a weak inferential power. We then introduce two families of consensus operators having a better inferential power by setting aside some of these postulates.

Theoretical Aspects of Rationality and Knowledge, 1996

We introduce a basic framework for multi-agent belief revision in heterogeneous societies where agents are required to be consistent in their beliefs on shared variables. We identify several properties one may require a general multi-agent belief revision operator to satisfy, and show several basic implications of these requirements. Our work reveals the connection between multi-agent belief revision and the the-

Intelligent agents have to be able to merge informational inputs received from different sources in a coherent and rational way. Several proposals have been made for information merging in which it is possible to encode the preferences of sources [5,4,19,24,25,1]. Information merging has much in common with social choice theory, which aims to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection, frameworks for information merging should provide satisfactory resolutions of problems raised in social choice theory. We investigate the link between the merging of epistemic states and some results in social choice theory. This is achieved by providing a consistent set of properties—akin to those used in Arrow
s theorem [2]—for merging. It is shown that in this framework there is no Arrow-like impossibility result. By extending this to a consistent framework which includes properties corresponding to the notion of being strategy-proof, we show that results due to Gibbard and Satterthwaite [13,31,32] and others [6,3] do not hold in merging frameworks.

A Meeting of the Minds, Proceedings LORI Beijing, 2007

Procedia Computer Science, 2014

Belief merging is an active research field with many important applications. Most existing work addresses the belief merging issue using a centralised approach. In this paper, we investigate a distributed approach to the problem of belief merging. The contribution of this paper is twofold: (i) we develop a negotiation-based model for belief merging, and (ii) we investigate the computational complexity of the belief merging problem within the proposed framework. Through the proposed model of negotiation-based belief merging, we will present and discuss several significant logical properties and computational complexity results.

Belief revision games (BRGs) are concerned with the dynamics of the beliefs of a group of communicating agents. BRGs are "zero-player" games where at each step every agent revises her own beliefs by taking account for the beliefs of her acquaintances. Each agent is associated with a belief state defined on some finite propositional language. We provide a general definition for such games where each agent has her own revision policy, and show that the belief sequences of agents can always be finitely characterized. We then define a set of revision policies based on belief merging operators. We point out a set of appealing properties for BRGs and investigate the extent to which these properties are satisfied by the merging-based policies under consideration.

Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge - TARK '09, 2009

2010

Belief merging is often described as the process of defining a base which best represents the beliefs of a group of agents (a profile of belief bases). The resulting base can be viewed as a synthesis of the input profile. In this paper another view of what belief merging aims at is considered: the epistemic view. Under this view the purpose of belief merging is to best approximate the true state of the world. We point out a generalization of Condorcet's Jury Theorem from the belief merging perspective. Roughly, we show that if the beliefs of sufficiently many reliable agents are merged then in the limit the true state of the world is identified. We introduce a new postulate suited to the truth tracking issue. We identify some merging operators from the literature which satisfy it and other operators which do not.