A CRITICAL REAPPRAISAL OF SOME VOTING POWER PARADOXES

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed "natural" postulates that a measure of a priori voting power "should" satisfy, the violations of which are called "voting power paradoxes". In this paper two general measures of factual success and decisiveness based on the voting rule and the voters' behavior, and some of these postulates/paradoxes test each other. As a result serious doubts on the discriminating power of most voting power postulates are cast.Voting power, decisiveness, success, voting rules, voting behavior, postulates, paradoxes.

Air intakes for a probative missile of rocket ramjet

The methods employed to test air intakes for a supersonic guided ramjet powered missile being tested by ONERA are described. Both flight tests and wind tunnel tests were performed on instrumented rockets to verify the designs. Consideration as given to the number of intakes, with the goal of delivering the maximum pressure to the engine. The S2, S4, and S5 wind tunnels were operated at Mach nos. 1.5-3 for the tests, which were compartmentalized into fuselage-intake interaction, optimization of the intake shapes, and the intake performance. Tests were performed on the length and form of the ogive, the presence of grooves, the height of traps in the boundary layer, the types and number of intakes and the lengths and forms of diffusers. Attention was also given to the effects of sideslip, effects of the longitudinal and circumferential positions of the intakes were also examined. Near optimum performance was realized during Mach 2.2 test flights of the prototype rockets

- SHAPLEY-SHUBIK AND BANZHAF INDICES REVISITED.

We provide a new axiomatization of the Shapley-Shubik and the Banzhaf power indices in thedomain of simple superadditive games by means of transparent axioms. Only anonymity isshared with the former characterizations in the literature. The rest of the axioms are substitutedby more transparent ones in terms of power in collective decision-making procedures. Inparticular, a clear restatement and a compelling alternative for the transfer axiom are proposed.Only one axiom differentiates the characterization of either index, and these differentiatingaxioms provide a new point of comparison. In a first step both indices are characterized up to azero and a unit of scale. Then both indices are singled out by simple normalizing axioms.Power indices, voting power, collective decision-making, simple games

BARGAINING, VOTING, AND VALUE

This paper addresses the following issue: If a set of agents bargain on a set of feasible alternatives 'in the shadow' of a voting rule, that is, any agreement can be enforced if a 'winning coalition' supports it, what general agreements are likely to arise? In other words: What influence can the voting rule used to settle (possibly non-unanimous) agreements have on the outcome of negotiations? To give an answer we model the situation as an extension of the Nash bargaining problem in which an arbitrary voting rule replaces unanimity to settle agreements by n players. This provides a setting in which a natural extension of Nash's solution is obtained axiomatically. Two extensions admitting randomization on voting rules based on two informational scenarios are considered.Bargaining, voting, value, bargaining in committees.

POTENTIAL, VALUE AND PROBABILITY

This paper focuses on the probabilistic point of view and proposes a extremely simple probabilistic model that provides a single and simple story to account for several extensions of the Shapley value, as weighted Shapley values, semivalues, and weak (weighted or not) semivalues, and the Shapley value itself. Moreover, some of the most interesting conditions or notions that have been introduced in the search of alternatives to Shapley's seminal characterization, as 'balanced contributions' and the 'potential', are reinterpreted from this same point of view. In this new light these notions and some results lose their 'mystery' and acquire a clear and simple meaning. These illuminating reinterpretations strongly vindicate the complementariness of the probabilistic and the axiomatic approaches, and shed serious doubts about the achievements of the axiomatic approach since Nash's and Shapley's seminal papers in connection with the genuine notion of value.Coalition games, value, potential

Stochastic Approximation with Averaging Innovation Applied to Finance

The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation when the "innovations" satisfy some "light" averaging properties in the presence of a pathwise Lyapunov function. These averaging assumptions allow us to unify apparently remote frameworks where the innovations are simulated (possibly deterministic like in Quasi-Monte Carlo simulation) or exogenous (like market data) with ergodic properties. We propose several fields of applications and illustrate our results on five examples mainly motivated by Finance

Quaternary dichotomous voting rules

In this paper we provide a general model of "quaternary" dichotomous voting rules (QVRs), namely, voting rules for making collective dichotomous decisions (to accept or reject a proposal), based on vote profiles in which four options are available to each voter: voting ("yes", "no" or "abstaining") or staying home and not turning out. The model covers most of actual real-world dichotomus rules, where quorums are often required, and some of the extensions considered in the literature. In particular, we address and solve the question of the representability of QVRs by means of weighted rules and extend the notion of "dimension" of a rule.

Power measures derived from the sequential query process

We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual power in simple games, and show that, as for the Shapley-Shubik index, they extend naturally to measures for TU-games. In particular, the individual measures include all weighted semivalues. We single out the simplest measure in our family for more investigation, as it is new to the literature as far as we know. Although it is very different from the Shapley value, it is closely related in several ways, and is the natural analogue of the Shapley value under a nonstandard, but natural, definition of simple game. We illustrate this new measure by calculating its values on some standard examples.Comment: 13 pages, to appear in Mathematical Social Science

Optimal posting price of limit orders: learning by trading

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are fulfilled (using notably the co-monotony principle). We illustrate our results with numerical experiments on both simulated data and using a financial market dataset