Special domains and nonmanipulability

We investigate domains on which a nonmanipulable, nondictatorial social choice function exists, having at least three distinct values. We do not make the assumptions of Kalai and Muller (1977). We classify all such 2-person functions on the domain which is the cyclic group Z_m. We show that for any domain containing Z_m, existence for 2 voters and existence for some n > 2 voters are equivalent. We show that for an n-person, onto, nonmanipulable social choice function F on Z_m, F(P₁, P₂,…, P_n) {x₁, x₂,…, x_n} always, x_i being the most preferred alternative under preference P_i. We show that no domain containing the dihedral group admits such a social choice function. We show that there exists a domain on which all k-tuples are free for arbitrarily large k, for which such a social choice function does exist.     

从城市设计的角度谈高层建筑及总平面的设计

从分析高层建筑在城市中的特殊地位着手，阐述了高层建筑总平面设计与城市规划和城市设计的关系，提出高层建筑的总平面设计从城市设计的角度去认识，在符合城市立法标准的前提下，应从视觉通廊的维护、城市公共空间的设计以及城市轮廓线的创造这三方面去考虑。宏观上把握对城市的认知，微观上针对基地的具体特点，只有这二者的全面考虑，才是对高层建筑总平面设计的完整理解     

Optional sampling of submartingales with scanned index sets

The implication of Doob's optional sampling theorem in general fails to hold for submartingales with partially ordered index sets. Under an additional assumption on the index set (scanning property) we prove optional sampling theorems which are general enough to cover all previous results and, moreover, can be applied for continuous time sampling plans.     

RUSSELL'S ALTERNATIVE TO THE AXIOM OF CHOICE

We prove the independence of some weakenings of the axiom of choice related to the question if the unions of wellorderable families of wellordered sets are wellorderable.     

Validating the Gravity-Based Competitive Location Model Using Inferred Attractiveness

The attractiveness of retail facilities is an essential component of models analyzing competition among retail facilities. In this paper we introduce an innovative method for inferring retail facility attractiveness. Readily available data from secondary sources about customers' buying power and sales volumes obtained by competing retail facilities are used. The gravity-based competitive facility location model is used to predict sales. The attractiveness of the retail facilities are inferred from these data.The procedure is used to confirm the gravity competitive facility location model. Inferred attractiveness results based on empirical data from Orange County, California, were compared with an independent survey with excellent match.     

On an optimal stopping problem of Gusein-Zade

We study the problem of selecting one of the r best of n rankable individuals arriving in random order, in which selection must be made with a stopping rule based only on the relative ranks of the successive arrivals. For each r up to r=25, we give the limiting (as n→∞) optimal risk (probability of not selecting one of the r best) and the limiting optimal proportion of individuals to let go by before being willing to stop. (The complete limiting form of the optimal stopping rule is presented for each r up to r=10, and for r=15, 20 and 25.) We show that, for large n and r, the optical risk is approximately (1−t^*)^r, where t^*≈0.2834 is obtained as the roof of a function which is the solution to a certain differential equation. The optimal stopping rule τ_r,n lets approximately t^*n arrivals go by and then stops ‘almost immediately’, in the sense that τ_r,n/n→t^* in probability as n→∞, r→∞     

Some properties of choice functions based on valued binary relations

Choice functions based on t-norms of valued binary relations are introduced. Strict preference is also specified with the use of a t-norm. Properties of the choice functions are investigated and rationality conditions are studied. Some classical particular cases are presented.     

Binariness and rational choice

The concept of numerical representability of preferences together with maximality is at the heart of the concept of rationality embodied in classical optimization models. The difficulty of representing social preferences arises from inherent intransitivities thrown up by democratic voting procedures and by non-binary choice rules which need to be adopted to cope with these intransitivities. An alternative (weaker) concept of representability is developed and it is shown that this concept can partially accommodate intransitivity and non-binariness. ‘Weak transitivity’ and ‘weak binaries’ conditions are provided and it is shown that these conditions are necessary and sufficient for ‘weak representability’. While the weak transitivity condition would be violated by social aggregation procedures, the non-binary functions used by social choice theorists do indeed satisfy the condition of ‘weak binariness’.