Consensus reaching processes play a key role in the resolution of many group decision making problems, in which it is desirable to obtain a highly acceptable solution to all individuals involved in the problem. However, not much interest has been put on defining appropriate metrics to evaluate in further detail the consensus solution, regarding experts’ preferred ordering or ranking of alternat...

We study the following rather generic communication/coordination/computation problem: In a finite network of agents, each initially having one of the two possible states, can the majority initial state be computed and agreed upon by means of local computation only? We study an iterative synchronous application of the local majority rule and describe the architecture of networks that are always ...

In a linguistic framework, a new architecture of fuzzy-logic-based consensus model in group decision making is presented. Its most important feature is that it allows to develop a consensus reaching process guided by two types of linguistic consensus measures, consensus degrees and linguistic distances, which describe with a great exactness the current consensus situation. In this way, more hum...

In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believes the portions are equal. Moreover, the division takes at most n cuts, which is best possible. This extends prior work using methods from combinatorial topology to solve fair division problems. Several applications o...

This study explores the impact of using assessment items with competing theories to encourage students to practice evaluative reflection and collaborative argumentation in asynchronous discussions. Thirty undergraduate students from various departments worked in small groups and took turns collaboratively discussing the given item’s answer, reaching a consensus, and posting their consensual ans...

We study the problem of reaching a consensus in the estimates of multiple agents forming a network with time-varying connectivity. Our main focus is on constrained consensus problems where the estimate of each agent is constrained to lie in a different closed convex constraint set. We consider a distributed “projected consensus algorithm” in which the local averaging operation is combined with ...