Single-Peaked Choice

Single-peaked preferences have played an important role in the literature ever since they were used by Black (1948) to formulate a domain restriction that is sufficient for the exclusion of cycles according to the majority rule. In this paper, we approach single-peakedness from a choice-theoretic perspective. We show that the well-known axiom independence of irrelevant alternatives (a form of contraction consistency) and a weak continuity requirement characterize a class of single-peaked choice functions. Moreover, we examine the rationalizability and the rationalizability-representability of these choice functions.

Multiple Public Goods and Lexicographic Preferences Replacement Principle.

We study the problem of locating two public goods for a group of agents with single-peaked preferences over an interval. An alternative specifies a location for each public good. In Miyagawa (1998), each agent consumes only his most preferred public good without rivalry. We extend preferences lexicographically and characterize the class of single-peaked preference rules by Pareto-optimality and replacement-domination. This result is considerably different from the corresponding characterization by Miyagawa (2001a).

Single-Plateaued Choice

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of singleplateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed. Journal of Economic Literature Classification Nos.: D11, D71.

Single-plateaued choice

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-plateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed. Journal of Economic Literature Classification Nos.: D11, D71.

On Fixed-Path Rationing Methods.

Moulin (1999) characterizes the fixed-path rationing methods by efficiency, strategy-proofness, consistency, and resource-monotonicity. In this note, we give a straightforward proof of his result.

Probabilistic Assignments of Identical Indivisible Objects and Uniform Probabilistic Rules.

We consider a probabilistic approach to the problem of assigning k indivisible identical objects to a set of agents with single-peaked preferences. Using the ordinal extension of preferences, we characterize the class of uniform probabilistic rules by Pareto efficiency, strategy-proofness, and no-envy. We also show that in this characterization no-envy cannot be replaced by anonymity. When agents are strictly risk averse von-Neumann-Morgenstern utility maximizers, then we reduce the problem of assigning k identical objects to a problem of allocating the amount k of an infinitely divisible commodity.

Priorities in the Location of Multiple Public Facilities

A collective decision problem is described by a set of agents, a profile of single-peaked preferences over the real line and a number k of public facilities to be located. We consider public facilities that do not su¤er from congestion and are non-excludable. We provide a characterization of the class of rules satisfying Pareto-efficiency, object-population monotonicity and sovereignty. Each rule in the class is a priority rule that selects locations according to a predetermined priority ordering among interest groups. We characterize each of the subclasses of priority rules that respectively satisfy anonymity, hiding-proofness and strategy-proofness. In particular, we prove that a priority rule is strategy-proof if and only if it partitions the set of agents into a fixed hierarchy. Alternatively, any such rule can be viewed as a collection of fixed-populations generalized peak-selection median rules (Moulin, 1980), that are linked across populations, in a way that we describe.

Allocation rules on networks

When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and an agent depicts the possibility of a transfer from the source to the agent. Given the supplies at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that for each pair of citizens in the network, the extension is robust with respect to the fairness principle. We call this condition pairwise robustness with respect to the fairness principle. We provide an algorithm and show that each fairness principle has a unique extension which is pairwise robust with respect to the fairness principle. We give applications of the algorithm for three fairness principles: egalitarianism, proportionality and equal sacrifice.

Weighted Majoritarian Rules for the Location of Multiple Public Facilities

We consider collective decision problems given by a profile of single-peaked preferences defined over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on efficiency, object-population monotonicity and sovereignty. Each such rule is described by a fixed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically — anonymity — respects some form of coherence across collective decision problems — reinforcement — and only depends on peak information — peakonly — is a weighted majoritarian rule. Each such rule defines priorities based on the relative size of the interest groups and specific weights attached to locations. We give an explicit account of the richness of this class of rules.

Egalitarianism under Earmark Constraints

Agents with single-peaked preferences share a resource coming from different suppliers; each agent is connected to only a subset of suppliers. Examples include workload balancing, sharing earmarked funds, and rationing utilities after a storm. Unlike in the one supplier model, in a Pareto optimal allocation agents who get more than their peak from underdemanded suppliers, coexist with agents who get less from overdemanded suppliers. Our Egalitarian solution is the Lorenz dominant Pareto optimal allocation. It treats agents with equal demands as equally as the connectivity constraints allow. Together, Strategyproofness, Pareto Optimality, and Equal Treatment of Equals, characterize our solution.

Stochastic resonance for modulated gain in a single-mode laser

Stochastic resonance (SR) induced by the signal modulation is investigated, by introducing the signal-modulated gain into a single-mode laser system. Using the linear approximation method, we detailedly calculate the signal-to-noise ratio (SNR) of a gain-noise model of the single-mode laser, taking the cross-correlation between the quantum noise and pump noise into account. We find that, SR appears in the dependence of the SNR on the intensities of the quantum and the pump noises when the correlation coefficient between both the noises is negative; moreover, when the cross-correlation between the two noises is strongly negative, SR exhibits a resonance and a suppression versus the gain coefficient, meanwhile, the single-peaked SR and multi-peaked SR occur in the behaviors of the SNR as functions of the loss coefficient and the deterministic steady-state intensity. (c) 2005 Elsevier B.V. All rights reserved.

Solidarity in Choosing a Location on a Cycle

We study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Both conditions require that when circumstances change, the agents not responsible for the change should all be affected in the same direction: either they all gain or they all loose. The first condition, population-monotonicity, applies to arrival or departure of one agent. The second, replacement-domination, applies to changes in the preferences of one agent. Unfortunately, no Pareto-efficient solution satisfies any of these properties. However, if agents’ preferred points are restricted to the vertices of a small regular polygon inscribed in the circle, solutions exist. We characterize them as a class of efficient priority rules.

Single-basined choice

Single-basined preferences generalize single-dipped preferences by allowing for multiple worst elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-basinedness in a choice-theoretic setting. In conjunction with independence of irrelevant alternatives, single-basined choice implies a structure that conforms to the motivation underlying our definition. We also establish the consequenes of requiring single-basined choice correspondences to be upper semicontinuous, and of the revealed preference relation to be Suzumura consistent. Journal of Economic Literature.

Essays on robust mechanism design

Chapter 1: Under the average common value function, we select almost uniquely the mechanism that gives the seller the largest portion of the true value in the worst situation among all the direct mechanisms that are feasible, ex-post implementable and individually rational. Chapter 2: Strategy-proof, budget balanced, anonymous, envy-free linear mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of surplus loss to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss is uniquely achieved by the following simple allocation rule: assigns one object to each of the p−1 agents with the highest valuation, a large probability to the agent with the pth highest valuation, and the remaining probability to the agent with the (p+1)th highest valuation. When “envy freeness” is replaced by the weaker condition “voluntary participation”, the optimal mechanism differs only when p is much less than n. Chapter 3: One group is to be selected among a set of agents. Agents have preferences over the size of the group if they are selected; and preferences over size as well as the “stand-outside” option are single-peaked. We take a mechanism design approach and search for group selection mechanisms that are efficient, strategy-proof and individually rational. Two classes of such mechanisms are presented. The proposing mechanism allows agents to either maintain or shrink the group size following a fixed priority, and is characterized by group strategy-proofness. The voting mechanism enlarges the group size in each voting round, and achieves at least half of the maximum group size compatible with individual rationality.

松辽盆地南部大情字井地区CO2埋存体地质格架及储层建模

Increasing attentions have been paid to the subsurface geological storage for CO2 in view of the huge storage capacity of subsurface reservoirs. The basic requirement for subsurface CO2 storage is that the CO2 should be sequestrated as supercritical fluids (physical trapping), which may also interact with ambient reservoir rocks and formation waters, forming new minerals (chemical trapping). In order to the effective, durable and safe storage for CO2, enough storage space and stable sealing caprock with strong sealing capacity are necessitated, in an appropriate geological framework. Up till now, hydrocarbon reservoirs are to the most valid and appropriate CO2 storage container, which is well proven as the favorable compartment with huge storage capacity and sealing condition. The thesis focuses on two principal issues related to the storage and sealing capacity of storage compartment for the Qingshankou and Yaojia formations in the Daqingzijing block, Southern Songliao Basin, which was selected as the pilot well site for CO2-EOR storage. In the operation area, three facies, including deltaic plain, deltaic front and subdeep-deep lake facies associations, are recognized, in which 11 subfacies such as subaqueous distributary channel, river- mouth bar, interdistributary bay, sheet sandbody, crevasse splay and overflooding plain are further identified. These subfacies are the basic genetic units in the reservoir and sealing rocks. These facies further comprise the retrogradational and progradational depositional cycles, which were formed base- level rise and fall, respectively. During the regressive or lake lowstand stage, various sands including some turbidites and fans occurred mostly at the bottom of the hinged slope. During the progradation stage, these sands became smaller in size and episodically stepped backwards upon the slope, with greatly expanded and deeped lake. However, most of Cretaceous strata in the study area, localized in the basin centre under this stage, are mainly composed of grey or grizzly siltstones and grey or dark grey mudstones intercalated with minor fine sandstones and purple mudstones. On the base of borehole and core data, these siltstones are widespread, thin from 10 to 50 m thick, good grain sorting, and have relative mature sedimentary structures with graded bedding and cross- lamination or crossbeds such as ripples, which reflect strong hydrodynamic causes. Due to late diagenesis, pores are not widespread in the reservoirs, especially the first member of Qingshankou formation. There are two types of pores: primary pore and secondary cores. The primary pores include intergranular pores and micropores, and the secondary pores include emposieus and fracture pores. Throat channels related to pores is also small and the radius of throat in the first, second and third member of Qingshankou formation is only 0.757 μm, 0.802 μm and 0.631 μm respectively. In addition, based on analyzing the probability plot according to frequency of occurrence of porosity and permeability, they appear single- peaked distribution, which reflects strong hetero- geneity. All these facts indicate that the conditions of physical property of reservoirs are not better. One reason may be provided to interpret this question is that physical property of reservoirs in the study area is strong controlled by the depositional microfacies. From the statistics, the average porosity and permeability of microfacies such as subaqueous distributary channel, channel mouth bar, turbidites, is more than 9 percent and 1md respectively. On the contrary, the average porosity and permeability of microfacies including sand sheet, flagstone and crevasse splay are less than 9 percent and 0.2md respectively. Basically, different hydrodynamic environment under different microfacies can decide different physical property. According to the reservoir models of the first member of Qingshankou formation in the No. well Hei47 block, the character of sedimentary according to the facies models is accord to regional disposition evolution. Meantime, the parameter models of physical property of reservoir indicate that low porosity and low permeability reservoirs widespread widely in the study area, but the sand reservoirs located in the channels are better than other places and they are the main sand reservoirs. The distribution and sealing ability of fault- fractures and caprock are the key aspects to evaluate the stable conditions of compartments to store CO2 in the study area. Based on the core observation, the fractures widespread in the study area, especially around the wells, and most of them are located in the first and second member of Qingshankou formation, almost very few in the third member of Qingshankou formation and Yaojia formation instead. In addition, analyzing the sealing ability of eleven faults in the three-dimensional area in the study area demonstrates that most of faults have strong sealing ability, especially in the No. well Hei56 and Qing90-27. To some extent, the sealing ability of faults in the No. well Hei49, Qing4-6 and Qing84-29 are worse than others. Besides, the deposition environment of most of formations in the study area belongs to moderately deep and deep lake facies, which undoubtedly take advantage to caprocks composed of mudstones widespread and large scale under this deposition environment. In the study area, these mudstones distribute widely in the third member of Qingshankou formation, Yaojia and Nenjiang formation. The effective thickness of mudstone is nearly ~550m on an average with few or simple faults and fractures. In addition, there are many reservoir beds with widely- developed insulated interbeds consist of mudstones or silty mudstone, which can be the valid barrier to CO2 upper movement or leakage through diffusion, dispersion and convection. Above all, the closed thick mud caprock with underdeveloped fractures and reservoir beds can be taken regard as the favorable caprocks to provide stable conditions to avoid CO2 leakage.