On the number of blocks required to access the core

The following review has been written for Mathematical Reviews on the paper written by +Sylvain Béal, Eric Rémila, and Philippe Solal.

On the accessibility of the core (Review)

This paper by Yang (2010) belongs to a recent wave of literature that study the core of a cooperative game as a dynamic concept. Sengupta and Sengupta (1996) have shown that from any imputation the core can be accessed by a finite number of blocks. Kóczy (2006) provided an alternative blocking sequence and showed that the number of blocks required is bounded. The present paper relies on the proof of Sengupta and Sengupta by using z-dominance and provides an explicit bound on the length of z-dominance paths: the number of active coalitions, that is, coalitions with a payoff higher than the sum of their members' individual payoffs.

Finessing a point: augmenting the core (Review)

The competition between two election candidates is modelled in a policy space, where the voters are represented by their ideal points and the candidates by their position on the policy. A voter will support the candidate whose programme is closer to his ideal point, using Euclidean distance. The candidate supported by at least q voters, where q is the quota, is elected. For simple majority q is simply the smallest integer that is at least half of the number of voters.

The class of efficient linear symmetric values for games in partition function form (Review)

The paper studies linear, symmetric and efficient (LSE) solutions or values for games in partition function form. The family of such solutions is rather broad and includes the Shapley value, the Consensus value and the Myerson value just to mention some.

Review of "Protectionism and blocking power indices" by Francesc Carreras

A separating family

Most of the voting power literature has focussed on the ability to make or change decisions. This is surprising given the way the voting rules  in many of the well-known applications, such as the European Union Council of Ministers have been designed. Indeed the attention has been more on how to prevent change rather than how to foster it. This paper is an exception.

A core of voting games with improved foresight - a review

I regularly review papers for Mathematical Reviews. The task does not always come at the right time, but otherwise it is very rewarding: the papers I get are usually very interesting, and are often published in journals I do not normally read (the one below is an exception).