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Donor Coordination
Donor coordination is a problem in social choice. There are several donors, each of whom wants to donate some money. Each donor supports a different set of targets. The goal is to distribute the total donated amount among the various targets in a way that respects the donors' preferences. As an example, consider a town with three recreational facilities that require funding: theater, chess club, and basketball field. There are two donors: Alice and George, each of whom wants to donate 3000. Alice wants to donate to indoor activities (theater or chess), whereas George prefers to donate to competitive activities (chess or basketball). Suppose further that the donors consider the facilities substitute goods, so that the utility of a donor is the sum of money distributed to a facility he likes. Consider the following possible distributions: * In the ''uncoordinated distribution'', Alice gives 1500 to each indoor activity, while George gives 1500 to each competitive activity. The resulti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures ( social welfare functions) used to combine individual preferences into a coherent whole.Amartya Sen (2008). "Social Choice". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> It contrasts with political science in that it is a normative field that studies how a society can make good decisions, whereas political science is a descriptive field that observes how societies actually do make decisions. While social choice began as a branch of economics and decision theory, it has since received substantial contributions from mathematics, philosophy, political science, and game theory. Real-world examples of social choice rules include constitutions and parliamentary procedures for voting on laws, as well as electoral systems; as such, the field is occasionall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utilitarian Rule
In social choice theory, social choice and operations research, the utilitarian rule (also called the max-sum rule) is a Social welfare function, 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 Utilitarianism, utilitarian philosophy, and is often justified by reference to Harsanyi's utilitarian theorem or the Von Neumann–Morgenstern utility theorem, Von Neumann–Morgenstern theorem. 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, utilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Altruism
Effective altruism (EA) is a 21st-century philosophical and social movement that advocates impartially calculating benefits and prioritizing causes to provide the greatest good. It is motivated by "using evidence and reason to figure out how to benefit others as much as possible, and taking action on that basis". People who pursue the goals of effective altruism, who are sometimes called , follow a variety of approaches proposed by the movement, such as donating to selected charities and choosing careers with the aim of maximizing positive impact. The movement gained popularity outside academia, spurring the creation of research centers, advisory organizations, and charities, which collectively have donated several hundred million dollars. Effective altruists emphasize impartiality and the global equal consideration of interests when choosing beneficiaries. Popular cause priorities within effective altruism include global health and development, social and economic inequality ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crowdfunding
Crowdfunding is the practice of funding a project or venture by raising money from a large number of people, typically via the internet. Crowdfunding is a form of crowdsourcing and Alternative Finance, alternative finance, to fund projects "without standard financial intermediaries". Mollick, E. (2014). ''The dynamics of crowdfunding: An exploratory study.'' Journal of Business Venturing. Vol. 29, pp. 1–16. In 2015, over was raised worldwide by crowdfunding. Although similar concepts can also be executed through mail-order subscriptions, benefit events, and other methods, the term crowdfunding refers to internet-mediated registries. This modern crowdfunding model is generally based on three types of actors – the project initiator who proposes the idea or project to be funded, individuals or groups who support the idea, and a moderating organization (the "platform") that brings the parties together to launch the idea. The term crowdfunding was coined in 2006 by entrepreneur an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zambia
Zambia, officially the Republic of Zambia, is a landlocked country at the crossroads of Central Africa, Central, Southern Africa, Southern and East Africa. It is typically referred to being in South-Central Africa or Southern Africa. It is bordered to the north by the Democratic Republic of the Congo, Tanzania to the north-east, Malawi to the east, Mozambique to the southeast, Zimbabwe and Botswana to the south, Namibia to the southwest, and Angola to the west. The capital city of Zambia is Lusaka, located in the south-central part of Zambia. The population is concentrated mainly around Lusaka in the south and the Copperbelt Province to the north, the core economic hubs of the country. Originally inhabited by Khoisan peoples, the region was affected by the Bantu expansion of the thirteenth century. Following European colonization of Africa, European colonisers in the 18th century, the British colonised the region into the British protectorates of Barotziland–North-Western Rho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigma2p
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP. Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing machines. It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH. Classes within the hierarchy have complete problems (with respect to polynomial-time reductions) that ask if quantified Boolean formulae hold, for formulae with restrictions on the quantifier order. It is known that equality between classes on the same level or consecutive levels in the hierarchy would imply a "collapse" of the hierarchy to that level. Definitions There are multiple equivalent definitions of the classes of the polynomial hierarchy. Oracle definition For the oracle def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FPTAS
A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems. An FPTAS takes as input an instance of the problem and a parameter ε > 0. It returns as output a value which is at least 1-\varepsilon times the correct value, and at most 1 + \varepsilon times the correct value. In the context of optimization problems, the correct value is understood to be the value of the optimal solution, and it is often implied that an FPTAS should produce a valid solution (and not just the value of the solution). Returning a value and finding a solution with that value are equivalent assuming that the problem possesses self reducibility. Importantly, the run-time of an FPTAS is polynomial in the problem size and in 1/ε. This is in contrast to a general polynomial-time approximation scheme (PTAS). The run-time of a general PTAS is polynomial in the problem size for each specific ε, but might ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Of Fairness
In the theory of fair division, the price of fairness (POF) is the ratio of the largest economic welfare attainable by a division to the economic welfare attained by a ''fair'' division. The POF is a quantitative measure of the loss of welfare that society has to take in order to guarantee fairness. In general, the POF is defined by the following formula:POF=\frac The exact price varies greatly based on the kind of division, the kind of fairness and the kind of social welfare we are interested in. The most well-studied type of social welfare is '' utilitarian social welfare'', defined as the sum of the (normalized) utilities of all agents. Another type is '' egalitarian social welfare'', defined as the minimum (normalized) utility per agent. Numeric example In this example we focus on the ''utilitarian price of proportionality'', or UPOP. Consider a heterogeneous land-estate that has to be divided among 100 partners, all of whom value it as 100 (or the value is normalized to 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egalitarian Equivalence
Egalitarian equivalence (EE) is a criterion of fair division. In an egalitarian-equivalent division, there exists a certain "reference bundle" Z such that each agent feels that his/her share is equivalent to Z. The EE fairness principle is usually combined with Pareto efficiency. A PEEEA is an allocation that is both Pareto efficient and egalitarian-equivalent. Definition A set of resources are divided among several agents such that every agent i receives a bundle X_i. Every agent i has a subjective preference relation \succeq_i which is a total order over bundle. These preference relations induce an equivalence relation in the usual way: X \sim_i Y iff X \succeq_i Y \succeq_i X. An allocation is called ''egalitarian-equivalent'' if there exists a bundle Z such that, for all i: :::X_i \sim_i Z An allocation is called ''PEEEA'' if it is both Pareto-efficient and egalitarian-equivalent. Motivation The EE criterion was introduced by Elisha Pazner and David Schmeidler in 1978. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategyproofness
In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly- dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private information (e.g. their type or their value to some item), and the strategy space of each player consists of the possible information values (e.g. possible types or values), a truthful mechanism is a game in which revealing the true information is a weakly-dominant strategy for each player. An SP mechanism is also called dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. A SP mechanism is immune to manipulations by individual players (but not by coalitions). In contrast, in a group strategyproof mechanism, no group of people can collude to misreport their preferences in a way that makes every member better off. In a strong group strategyproof mechanism, no group of people can c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto-optimality
In welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse off than they were before. A situation is called Pareto efficient or Pareto optimal if all possible Pareto improvements have already been made; in other words, there are no longer any ways left to make one person better off without making some other person worse-off. In social choice theory, the same concept is sometimes called the unanimity principle, which says that if ''everyone'' in a society ( non-strictly) prefers A to B, society as a whole also non-strictly prefers A to B. The Pareto front consists of all Pareto-efficient situations. In addition to the context of efficiency in ''allocation'', the concept of Pareto efficiency also arises in the context of ''efficiency in production'' vs. ''x-inefficiency'': a set of outputs of good ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Participatory Budgeting
Combinatorial participatory budgeting, also called indivisible participatory budgeting or budgeted social choice, is a problem in social choice. There are several candidate ''projects'', each of which has a fixed costs. There is a fixed ''budget'', that cannot cover all these projects. Each voter has different ''preferences'' regarding these projects. The goal is to find a ''budget-allocation'' - a subset of the projects, with total cost at most the budget, that will be funded. Combinatorial participatory budgeting is the most common form of participatory budgeting. Combinatorial PB can be seen as a generalization of committee voting: committee voting is a special case of PB in which the "cost" of each candidate is 1, and the "budget" is the committee size. This assumption is often called the ''unit-cost assumption''. The setting in which the projects are divisible (can receive any amount of money) is called portioning, fractional social choice, or budget-proposal aggregation. P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
