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Proportional-fair Rule
In operations research and social choice, the proportional-fair (PF) rule is a rule saying that, among all possible alternatives, one should pick an alternative that cannot be improved, where "improvement" is measured by the sum of relative improvements possible for each individual agent. It aims to provide a compromise between the utilitarian rule - which emphasizes overall system efficiency, and the egalitarian rule - which emphasizes individual fairness. The rule was first presented in the context of rate control in communication networks. However, it is a general social choice rule and can also be used, for example, in resource allocation. Definition Let X be a set of possible `states of the world' or `alternatives'. Society wishes to choose a single state from X. For example, in a single-winner election, X may represent the set of candidates; in a resource allocation setting, X may represent all possible allocations of the resource. Let I be a finite set, representing a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice Theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Social Choice,". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences. Social choice blends elements of welfare economics and public choice theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utilitarian Rule
In social choice and operations research, the utilitarian rule (also called the max-sum rule) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the ''sum of the utilities'' of all individuals in society. It is a formal mathematical representation of the utilitarian philosophy. Definition Let X be a set of possible `states of the world' or `alternatives'. Society wishes to choose a single state from X. For example, in a single-winner election, X may represent the set of candidates; in a resource allocation setting, X may represent all possible allocations of the resource. Let I be a finite set, representing a collection of individuals. For each i \in I, let u_i:X\longrightarrow\mathbb be a ''utility function'', describing the amount of happiness an individual ''i'' derives from each possible state. A '' social choice rule'' is a mechanism which uses the data (u_i)_ to select some element(s) from X which are `best' for s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egalitarian Rule
In social choice and operations research, the egalitarian rule (also called the max-min rule or the Rawlsian rule) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the ''minimum utility'' of all individuals in society. It is a formal mathematical representation of the egalitarian philosophy. It also corresponds to John Rawls' principle of maximizing the welfare of the worst-off individual. Definition Let X be a set of possible `states of the world' or `alternatives'. Society wishes to choose a single state from X. For example, in a single-winner election, X may represent the set of candidates; in a resource allocation setting, X may represent all possible allocations. Let I be a finite set, representing a collection of individuals. For each i \in I, let u_i:X\longrightarrow\mathbb be a ''utility function'', describing the amount of happiness an individual ''i'' derives from each possible state. A '' social choice rule' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-winner Election
A single-member district is an electoral district represented by a single officeholder. It contrasts with a multi-member district, which is represented by multiple officeholders. Single-member districts are also sometimes called single-winner voting, winner-takes-all, or single-member constituencies. A number of electoral systems use single-member districts, including plurality voting (first-past-the-post), two-round systems, instant-runoff voting (IRV), approval voting, range voting, Borda count, and Condorcet methods (such as the Minimax Condorcet, Schulze method, and Ranked Pairs). Of these, plurality and runoff voting are the most common. In some countries, such as Australia and India, members of the lower house of parliament are elected from single-member districts; and members of the upper house are elected from multi-member districts. In some other countries like Singapore, members of parliament can be elected from both single-member districts as well as multi-member ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resource Allocation
In economics, resource allocation is the assignment of available resources to various uses. In the context of an entire economy, resources can be allocated by various means, such as markets, or planning. In project management, resource allocation or resource management is the scheduling of activities and the resources required by those activities while taking into consideration both the resource availability and the project time. Economics In economics, the field of public finance deals with three broad areas: macroeconomic stabilization, the distribution of income and wealth, and the allocation of resources. Much of the study of the allocation of resources is devoted to finding the conditions under which particular mechanisms of resource allocation lead to Pareto efficient outcomes, in which no party's situation can be improved without hurting that of another party. Strategic planning In strategic planning, resource allocation is a plan for using available resources, for exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a single consumer's preference ordering over a choice set but is not comparable across consumers. This concept of utility is personal and based on choice rather than on pleasure received, and so is specified more rigorously than the original concept but makes it less useful (and controversial) for ethical decisions. Utility function Consider a set of alternatives among which a person can make a preference ordering. The utility obtained from these alternatives is an unknown function of the utilities obtained from each alternative, not the sum o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice Theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Social Choice,". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences. Social choice blends elements of welfare economics and public choice theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional-fair Scheduling
Proportional-fair scheduling is a compromise-based scheduling algorithm. It is based upon maintaining a balance between two competing interests: Trying to maximize total throughput of the network (wired or not) while at the same time allowing all users at least a minimal level of service. This is done by assigning each data flow a data rate or a scheduling priority (depending on the implementation) that is inversely proportional to its anticipated resource consumption.Guowang Miao, Jens Zander, Ki Won Sung, and Ben Slimane, Fundamentals of Mobile Data Networks, Cambridge University Press, , 2016. Weighted fair queuing Proportionally fair scheduling can be achieved by means of weighted fair queuing (WFQ), by setting the scheduling weights for data flow i to w_i = 1 / c_i, where the cost c_i is the amount of consumed resources per data bit. For instance: * In CDMA spread spectrum cellular networks, the cost may be the required energy per bit in the transmit power control (the incre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Subset Sum Problem
The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem. The input to the problem is a multiset S of ''n'' integers and a positive integer ''m'' representing the number of subsets. The goal is to construct, from the input integers, some ''m'' subsets. The problem has several variants: * ''Max-sum MSSP'': for each subset ''j'' in 1,...,''m'', there is a capacity ''Cj''. The goal is to make the ''sum'' of all subsets as large as possible, such that the sum in each subset j is at most ''Cj''. * ''Max-min MSSP'' (also called ''bottleneck MSSP'' or ''BMSSP''): again each subset has a capacity, but now the goal is to make the ''smallest'' subset sum as large as possible. * ''Fair SSP'': the subsets have no fixed capacities, but each subset belongs to a different person. The utility of each person is the sum of items in his/her subsets. The goal is to construct subsets that satisfy a given crit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
