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).
The authors introduce and study P-dominance and the induced P-core in a voting game.
Given a set of alternatives, the status quo is replaced by another alternative if a winning coalition of the players supports the change. Such a change may, however, induce further action and the new alternative may be replaced and so on, possibly resulting in a final alternative that is inferior to the original one. Seeing this problem several authors have introduced measures where the dominance only takes place when the subsequent deviation or deviations yield alternatives that are at least as good as the accepted alternative.
Elaborating on this idea the authors introduce rational chains, where each alternative is only abandoned if there is a winning coalition and a proposal that the proposal is preferred by the winning coalition to the status quo and the same applies to all alternatives in the triggered rational chain.We then say that the original alternative is P-dominated. The P-core collects P-undominated alternatives.
The P-core is always nonempty, but at the same time it is more selective than cores permitting dominance chains without the rationality criterion. The P-core also satisfies the no-regret property: If x P-dominates y via coalition S and x is in the P-core, then S prefers x, otherwise if a rational chain starting with x ends at x_q in the P-core, then x_q is preferred to y.
The paper relates P-dominance and the P-core to several models to solve such voting games while leaving the relations to concepts for farsighted coalitional games as open problems.
The review will appear in the Mathematical Reviews under ID 2542849.
Diffo Lambo, Lawrence; Tchantcho, Bertrand; Moulen, Joël (2009) A core of voting games with improved foresight. Math. Social Sci. 58 (2009), no. 2, 214–225.