We study a collective decision-making process in which people interested in an issue may participate, at a cost, in a meeting, and the resulting decision is a compromise among the participants' preferences. We show that the equilibrium number of participants is small and their positions are...

In this paper we consider problems of the following type: Let E = { e 1 , e 2 ,..., e n } be a finite set and $${\mathcal {F}}$$ be a family of subsets of E. For each element e i in E, c i is a given capacity and $${\mathcal {w}}$$ i is the cost of increasing capacity c i by one unit. It is...

In this paper we consider problems of the following type: Let E = { e <Subscript>1</Subscript>, e <Subscript>2</Subscript>,..., e <Subscript> n </Subscript> } be a finite set and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal {F}}$$</EquationSource> </InlineEquation> be a family of subsets of E. For each element e <Subscript> i </Subscript> in E, c <Subscript> i </Subscript> is a given capacity and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$${\mathcal {w}}$$</EquationSource> </InlineEquation> <Subscript> i </Subscript> is the cost of increasing capacity c <Subscript> i </Subscript> by one...</subscript></subscript></equationsource></inlineequation></subscript></subscript></equationsource></inlineequation></subscript></subscript></subscript>

In this work, a sharp upper bound on the law of the logarithm for the weighted sums of random variables with multidimensional indices is obtained. The main result improves the result in [Li, Rao and Wang, 1995. On strong law of large numbers and the law of the logarithm for weighted sums of...

We discuss a formal mathematical framework for certain coupling constructions via minorisation conditions, which are often used to prove bounds on convergence to stationarity of stochastic processes and Markov chain Monte Carlo algorithms.