康尼島（英語：），又译科尼島，是位於美國紐約市布魯克林區的半島，原本為一座海島，其面向大西洋的海灘是美國知名的休閒娛樂區域。居民大多集中位於半島的西側，約有六萬人左右，範圍西至希捷社區，東至布萊登海灘和曼哈頓海灘，而北至葛瑞福山德社區。 二十世紀前葉在美國極為知名的太空星際樂園即是以康尼島作為主要的腹地，該樂園在二次大戰後開始衰退，並持續荒廢了許久。在最近幾年，康尼島因為凱斯班公園的開幕而重新繁榮起來，凱斯班公園是職棒小聯盟球隊布魯克林旋風的主要球場。旋風隊在當地十分受到歡迎，每季開賽時都會吸引許多球迷到場觀戰。 ..

Anjos da guarda são os anjos que segundo as crenças cristãs, Deus envia no nosso nascimento para nos proteger durante toda a nossa vida. Argumenta-se que a Bíblia sustenta em algumas ocasiões a crença do anjo da guarda: "Vou enviar um anjo adiante de ti para ..

Altay Cumhuriyeti (Rusça: Респу́блика Алта́й / Respublika Altay; Altay Türkçesi: Алтай Республика / Altay Respublika), Rusya'nın en güneyinde yer alan, federasyona bağlı bir özerk cumhuriyet. Orta Asya'da Asya kıtasının coğrafî merkezinin hemen kuzeyinde ve ..

沙羅週期長度為18年11天，本週期包含70次日食，其中公元3000年以前有49次。 註：下表各項數據均為食分最大地點的情況。寬度指該地點食甚時刻月球的本影（全食時）或偽本影（環食時）落在地表的寬度，持續時間指該地點食既到生光的時間，即全食或環食的持續時間，全環食（亦稱混合食）發生時，食分最大處為全食。最後兩項參數不適用於偏食。 本周期最終結束於3378年6月17日。

希西家王 (希伯來語：，英語：）是猶大末年的君主，也是猶大國歷史中極尊重上帝的君王，在位29年。終年54歲。他在位的年份有兩種說法：其一是前715年-前687年；另一種是前716年-前687年。他的德行在其前後的猶大列王中，没有一個能及他。其希伯來名字的意思是“被神加力量”。 希西家的父親亞哈斯是一個背逆上帝的君王。因此在希西家當政之初的猶大國，無論政治，宗教上都极其黑暗。根據《聖經》記載，因为北國以色列被亞述攻滅，亞述王可以趁勢来攻打猶大國；又猶大的先王亞哈斯曾封鎖了聖殿之路，引導舉國崇拜偶像，大大得罪上帝。若非上帝的憐憫，為了堅定向大衛家所說的應許，猶大國的暫得幸存。希西家在二十五歲就登基作王，且正在國家危急之秋，由於行耶和華上帝眼中看為正的事，因而得上帝的憐憫，得以成功脫離亞述大軍的攻擊和一場致死的大病。他樂於聽從當代先知以賽亞的指導，使他為上帝大發熱心。 ..

The OnePlus 2 (also abbreviated as OP2) is a smartphone designed by OnePlus. It is the successor to the OnePlus One. OnePlus revealed the phone on 28 July 2015 via virtual reality, using Google's Cardboard visor and their own app. OnePlus sold out 30,000 units ..

兴隆街镇，是中华人民共和国四川省内江市资中县下辖的一个乡镇级行政单位。 兴隆街镇下辖以下地区： 兴隆街社区、兴松村、玄天观村、三元村、金星村、三皇庙村、双桥村、红庙子村、华光村、高峰村、芦茅湾村、篮家坝村、五马村和解放村。

Национальная и университетская библиотека (словен. Narodna in univerzitetna knjižnica, NUK), основанная в 1774 году, — один из важнейших образовательных и культурных учреждений Словении. Она располагается в центре столицы Любляна, между улицами Турьяшка (Turjaška ..

Mauser M1924 (или M24) — серия винтовок компании Mauser, использовавшихся в армиях Бельгии и Югославии. Внешне напоминают чехословацкие винтовки vz. 24, в которых использовались стандартный открытый прицел, патроны калибра 7,92×57 мм (или 8×57 мм), укороченные ..

第三条道路（英語：），又称新中间路线（Middle Way），是一种走在自由放任资本主义和传统社会主义中间的一种政治经济理念的概称。它由中间派所倡导，是社会民主主义的一个流派，英国工党称其为「现代化的社会民主主义」。它的中心思想是既不主张纯粹的自由市场，也不主张纯粹的社會主義，主张在两者之间取折衷方案。 第三条道路不只单单是走在中间，或只是一种妥协或混合出来的东西，第三条道路的提倡者看到了社会主义和资本主义互有不足之处，所以偏向某一极端也不是一件好事，第三条道路正正是揉合了双方主义的优点，互补不足而成的政治哲学。 ..

**Pareto efficiency** or **Pareto optimality** is a situation where no individual or preference criterion can be better off without making at least one individual or preference criterion worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related:

- Given an initial situation, a
**Pareto improvement**is a new situation where some agents will gain, and no agents will lose. - A situation is called
**Pareto dominated**if it has a Pareto improvement. - A situation is called
**Pareto optimal**or**Pareto efficient**if no change could lead to improved satisfaction for all parties.

The **Pareto frontier** is the set of all Pareto efficient allocations, conventionally shown graphically. It also is variously known as the **Pareto front** or **Pareto set**.^{[1]}

"Pareto efficiency" is considered as a minimal notion of efficiency that does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society.^{[2]}^{[3]}^{:46–49} It is a necessary, but not sufficient, condition of efficiency.

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 goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.^{[4]}^{:459}

Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in engineering and biology. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of multi-objective optimization (also termed **Pareto optimization**).

"Pareto optimality" is a formally defined concept used to describe when an allocation is optimal. An allocation is *not* Pareto optimal if there is an alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a transfer that satisfies this condition, the reallocation is called a "Pareto improvement". When no further Pareto improvements are possible, the allocation is a "Pareto optimum".

The formal presentation of the concept in an economy is as follows: Consider an economy with agents and goods. Then an allocation , where for all *i*, is *Pareto optimal* if there is no other feasible allocation such that, for utility function for each agent , for all with for some .^{[5]} Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.

In principle, a change from a generally inefficient economic allocation to an efficient one is not necessarily considered to be a Pareto improvement. Even when there are overall gains in the economy, if a single agent is disadvantaged by the reallocation, the allocation is not Pareto optimal. For instance, if a change in economic policy eliminates a monopoly and that market subsequently becomes competitive, the gain to others may be large. However, since the monopolist is disadvantaged, this is not a Pareto improvement. In theory, if the gains to the economy are larger than the loss to the monopolist, the monopolist could be compensated for its loss while still leaving a net gain for others in the economy, allowing for a Pareto improvement. Thus, in practice, to ensure that nobody is disadvantaged by a change aimed at achieving Pareto efficiency, compensation of one or more parties may be required. It is acknowledged, in the real world, that such compensations may have unintended consequences leading to incentive distortions over time, as agents supposedly anticipate such compensations and change their actions accordingly.^{[6]}

Under the idealized conditions of the first welfare theorem, a system of free markets, also called a "competitive equilibrium", leads to a Pareto-efficient outcome. It was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu.

However, the result only holds under the restrictive assumptions necessary for the proof: markets exist for all possible goods, so there are no externalities; all markets are in full equilibrium; markets are perfectly competitive; transaction costs are negligible; and market participants have perfect information.

In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the Greenwald-Stiglitz theorem.^{[7]}

The second welfare theorem is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some competitive equilibrium, or free market system, although it may also require a lump-sum transfer of wealth.^{[5]}

**Weak Pareto optimality** is a situation that cannot be strictly improved for *every* individual.^{[8]}

Formally, we define a **strong pareto improvement** as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is **weak Pareto-optimal** if it has no strong Pareto-improvements.

Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0).

- It is a weak-PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements).
- But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5).

A market doesn't require local nonsatiation to get to a weak Pareto-optimum.^{[9]}

**Constrained Pareto optimality** is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.^{[10]}^{:104}

An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in moral hazard or an adverse selection and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see Lindahl prices). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".

The concept of constrained Pareto optimality assumes benevolence on the part of the planner and hence is distinct from the concept of government failure, which occurs when the policy making politicians fail to achieve an optimal outcome simply because they are not necessarily acting in the public's best interest.

**Fractional Pareto optimality** is a strengthening of Pareto-optimality in the context of fair item allocation. An allocation of indivisible items is **fractionally Pareto-optimal (fPO)** if it is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto-optimality, which only considers domination by feasible (discrete) allocations.^{[11]}

As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1).

- It is Pareto-optimal, since any other discrete allocation (without splitting items) makes someone worse-off.
- However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2).

Suppose each agent *i* is assigned a positive weight *a _{i}*. For every allocation

.

Let *x _{a}* be an allocation that maximizes the welfare over all allocations, i.e.:

.

It is easy to show that the allocation *x _{a}* is Pareto-efficient: since all weights are positive, any Pareto-improvement would increase the sum, contradicting the definition of

Japanese neo-Walrasian economist Takashi Negishi proved^{[12]} that, under certain assumptions, the opposite is also true: for *every* Pareto-efficient allocation *x*, there exists a positive vector *a* such that *x* maximizes *W*_{a}. A shorter proof is provided by Hal Varian.^{[13]}

The notion of Pareto efficiency has been used in engineering.^{[14]}^{:111–148} Given a set of choices and a way of valuing them, the **Pareto frontier** or **Pareto set** or **Pareto front** is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter.^{[15]}^{:63–65}

For a given system, the **Pareto frontier** or **Pareto set** is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters.^{[16]}^{:399–412}

The Pareto frontier, *P*(*Y*), may be more formally described as follows. Consider a system with function , where *X* is a compact set of feasible decisions in the metric space , and *Y* is the feasible set of criterion vectors in , such that .

We assume that the preferred directions of criteria values are known. A point is preferred to (strictly dominates) another point , written as . The Pareto frontier is thus written as:

A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the marginal rate of substitution is the same for all consumers. A formal statement can be derived by considering a system with *m* consumers and *n* goods, and a utility function of each consumer as where is the vector of goods, both for all *i*. The feasibility constraint is for . To find the Pareto optimal allocation, we maximize the Lagrangian:

where and are the vectors of multipliers. Taking the partial derivative of the Lagrangian with respect to each good for and and gives the following system of first-order conditions:

where denotes the partial derivative of with respect to . Now, fix any and . The above first-order condition imply that

Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.^{[17]}^{:114}

Algorithms for computing the Pareto frontier of a finite set of alternatives have been studied in computer science and power engineering.^{[18]} They include:

- "The maximum vector problem" or the skyline query.
^{[19]}^{[20]}^{[21]} - "The scalarization algorithm" or the method of weighted sums.
^{[22]}^{[23]}

- "The -constraints method".
^{[24]}^{[25]}

Pareto optimisation has also been studied in biological processes.^{[26]}^{:87–102} In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).^{[27]}

It would be incorrect to treat Pareto efficiency as equivalent to societal optimization,^{[28]}^{:358–364} as the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution.^{[29]}^{:10–15} An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.^{[30]}^{:95–132}

Pareto efficiency does not require a totally equitable distribution of wealth.^{[31]}^{:222} An economy in which a wealthy few hold the vast majority of resources can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; often the status quo is Pareto efficient regardless of the degree to which wealth is equitably distributed. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded.^{[32]}^{:18} The origin (and utility value) of the pie is conceived as immaterial in these examples. In such cases, whereby a "windfall" is gained that none of the potential distributees actually produced (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation. Wealth consolidation may exclude others from wealth accumulation because of bars to market entry, etc.

The liberal paradox elaborated by Amartya Sen shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.^{[33]}^{:92–94}

- Admissible decision rule, analog in decision theory
- Arrow's impossibility theorem
- Bayesian efficiency
- Fundamental theorems of welfare economics
- Deadweight loss
- Economic efficiency
- Highest and best use
- Kaldor–Hicks efficiency
- Market failure, when a market result is not Pareto optimal
- Maximal element, concept in order theory
- Maxima of a point set
- Multi-objective optimization
- Pareto-efficient envy-free division
*Social Choice and Individual Values*for the '(weak) Pareto principle'- TOTREP
- Welfare economics

- ↑ proximedia. "Pareto Front".
*www.cenaero.be*. Retrieved October 8, 2018. - ↑ Sen, A. (October 1993). "Markets and freedom: Achievements and limitations of the market mechanism in promoting individual freedoms" (PDF).
*Oxford Economic Papers*.**45**(4): 519–541. doi:10.1093/oxfordjournals.oep.a042106. JSTOR 2663703. - ↑ Barr, N. (2012). "3.2.2 The relevance of efficiency to different theories of society".
*Economics of the Welfare State*(5th ed.). Oxford University Press. pp. 46–49. ISBN 978-0-19-929781-8. - ↑ Black, J. D., Hashimzade, N., & Myles, G., eds.,
*A Dictionary of Economics*, 5th ed. (Oxford: Oxford University Press, 2017), p. 459. - 1 2 Mas-Colell, A.; Whinston, Michael D.; Green, Jerry R. (1995), "Chapter 16: Equilibrium and its Basic Welfare Properties",
*Microeconomic Theory*, Oxford University Press, ISBN 978-0-19-510268-0 - ↑ See Ricardian equivalence
- ↑ Greenwald, B.; Stiglitz, J. E. (1986). "Externalities in economies with imperfect information and incomplete markets".
*Quarterly Journal of Economics*.**101**(2): 229–64. doi:10.2307/1891114. JSTOR 1891114. - ↑ Mock, William B T. (2011). "Pareto Optimality".
*Encyclopedia of Global Justice*. pp. 808–809. doi:10.1007/978-1-4020-9160-5_341. ISBN 978-1-4020-9159-9. - ↑ Markey‐Towler, Brendan and John Foster. "Why economic theory has little to say about the causes and effects of inequality", School of Economics, University of Queensland, Australia, 21 February 2013, RePEc:qld:uq2004:476
- ↑ Magill, M., & Quinzii, M.,
*Theory of Incomplete Markets*, MIT Press, 2002, p. 104. - ↑ Barman, S., Krishnamurthy, S. K., & Vaish, R., "Finding Fair and Efficient Allocations",
*EC '18: Proceedings of the 2018 ACM Conference on Economics and Computation*, June 2018. - ↑ Negishi, Takashi (1960). "Welfare Economics and Existence of an Equilibrium for a Competitive Economy".
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*Journal of Public Economics*.**5**(3–4): 249–260. doi:10.1016/0047-2727(76)90018-9. hdl:1721.1/64180. - ↑ Goodarzi, E., Ziaei, M., & Hosseinipour, E. Z.,
*Introduction to Optimization Analysis in Hydrosystem Engineering*(Berlin/Heidelberg: Springer, 2014), pp. 111–148. - ↑ Jahan, A., Edwards, K. L., & Bahraminasab, M.,
*Multi-criteria Decision Analysis*, 2nd ed. (Amsterdam: Elsevier, 2013), pp. 63–65. - ↑ Costa, N. R., & Lourenço, J. A., "Exploring Pareto Frontiers in the Response Surface Methodology", in G.-C. Yang, S.-I. Ao, & L. Gelman, eds.,
*Transactions on Engineering Technologies: World Congress on Engineering 2014*(Berlin/Heidelberg: Springer, 2015), pp. 399–412. - ↑ Wilkerson, T.,
*Advanced Economic Theory*(Waltham Abbey: Edtech Press, 2018), p. 114. - ↑ Tomoiagă, Bogdan; Chindriş, Mircea; Sumper, Andreas; Sudria-Andreu, Antoni; Villafafila-Robles, Roberto (2013). "Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II".
*Energies*.**6**(3): 1439–55. doi:10.3390/en6031439. - ↑ Nielsen, Frank (1996). "Output-sensitive peeling of convex and maximal layers".
*Information Processing Letters*.**59**(5): 255–9. CiteSeerX 10.1.1.259.1042. doi:10.1016/0020-0190(96)00116-0. - ↑ Kung, H. T.; Luccio, F.; Preparata, F.P. (1975). "On finding the maxima of a set of vectors".
*Journal of the ACM*.**22**(4): 469–76. doi:10.1145/321906.321910. - ↑ Godfrey, P.; Shipley, R.; Gryz, J. (2006). "Algorithms and Analyses for Maximal Vector Computation".
*VLDB Journal*.**16**: 5–28. CiteSeerX 10.1.1.73.6344. doi:10.1007/s00778-006-0029-7. - ↑ Kim, I. Y.; de Weck, O. L. (2005). "Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation".
*Structural and Multidisciplinary Optimization*.**31**(2): 105–116. doi:10.1007/s00158-005-0557-6. ISSN 1615-147X. - ↑ Marler, R. Timothy; Arora, Jasbir S. (2009). "The weighted sum method for multi-objective optimization: new insights".
*Structural and Multidisciplinary Optimization*.**41**(6): 853–862. doi:10.1007/s00158-009-0460-7. ISSN 1615-147X. - ↑ "On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization".
*IEEE Transactions on Systems, Man, and Cybernetics*. SMC-1 (3): 296–297. 1971. doi:10.1109/TSMC.1971.4308298. ISSN 0018-9472. - ↑ Mavrotas, George (2009). "Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems".
*Applied Mathematics and Computation*.**213**(2): 455–465. doi:10.1016/j.amc.2009.03.037. ISSN 0096-3003. - ↑ Moore, J. H., Hill, D. P., Sulovari, A., & Kidd, L. C., "Genetic Analysis of Prostate Cancer Using Computational Evolution, Pareto-Optimization and Post-processing", in R. Riolo, E. Vladislavleva, M. D. Ritchie, & J. H. Moore, eds.,
*Genetic Programming Theory and Practice X*(Berlin/Heidelberg: Springer, 2013), pp. 87–102. - ↑ Seward, E. A., & Kelly, S., "Selection-driven cost-efficiency optimization of transcripts modulates gene evolutionary rate in bacteria",
*Genome Biology*, Vol. 19, 2018. - ↑ Drèze, J.,
*Essays on Economic Decisions Under Uncertainty*(Cambridge: Cambridge University Press, 1987), pp. 358–364 - ↑ Backhaus, J. G.,
*The Elgar Companion to Law and Economics*(Cheltenham, UK / Northampton, MA: Edward Elgar, 2005), pp. 10–15. - ↑ Paulsen, M. B., "The Economics of the Public Sector: The Nature and Role of Public Policy in the Finance of Higher Education", in M. B. Paulsen, J. C. Smart, eds.
*The Finance of Higher Education: Theory, Research, Policy, and Practice*(New York: Agathon Press, 2001), pp. 95–132. - ↑ Bhushi, K., ed.,
*Farm to Fingers: The Culture and Politics of Food in Contemporary India*(Cambridge: Cambridge University Press, 2018), p. 222. - ↑ Wittman, D.,
*Economic Foundations of Law and Organization*(Cambridge: Cambridge University Press, 2006), p. 18. - ↑ Sen, A.,
*Rationality and Freedom*(Cambridge, MA / London: Belknep Press, 2004), pp. 92–94.

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