Fair river sharing is a kind of a fair division problem in which the waters of a river has to be divided among countries located along the river. It differs from other fair division problems in that the resource to be divided—the water—flows in one direction—from upstream countries to downstream countries. To attain any desired division, it may be required to limit the consumption of upstream countries, but this may require to give these countries some monetary compensation.
82-773: The Pamir River is a shared river located in the Badakhshan Province of Afghanistan and in the Gorno-Badakhshan in Tajikistan . It is a tributary of the Panj River , and forms the northern boundary of Afghanistan's Wakhan District . The river has its sources in the Pamir Mountains in the far eastern part of Gorno-Badakhshan, Tajikistan. It flows between the Alichur mountain range in
164-402: A . Japanese neo- Walrasian economist Takashi Negishi proved 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 . The notion of Pareto efficiency has been used in engineering. Given a set of choices and a way of valuing them,
246-561: A lump-sum transfer of wealth. An ineffective distribution of resources in a free market is known as market failure . Given that there is room for improvement, market failure implies Pareto inefficiency. For instance, excessive use of negative commodities (such as drugs and cigarettes) results in expenses to non-smokers as well as early mortality for smokers. Cigarette taxes may help individuals stop smoking while also raising money to address ailments brought on by smoking. A Pareto improvement may be seen, but this does not always imply that
328-416: A normal-form game , this concept of efficiency can be observed, in that the strategy profile ( Cooperate , Cooperate ) is more efficient than ( Defect , Defect ). Using the definition above, let s = (-2, -2) ( Both Defect ) and s' = (-1, -1) ( Both Cooperate ). Then u i (s') > u i (s) for all i . Thus Both Cooperate is a Pareto improvement over Both Defect , which means that Both Defect
410-617: A total order relation for n > 1 {\displaystyle n>1} which would not always prioritize one target over another target (like the lexicographical order ). In the multi-objective optimization setting, various solutions can be "incomparable" as there is no total order relation to facilitate the comparison f → ( x → ∗ ) ≥ f → ( x → ) {\displaystyle {\vec {f}}({\vec {x}}^{*})\geq {\vec {f}}({\vec {x}})} . Only
492-442: A , b , c , d , e ) and 6 voters. The voters' approval sets are ( ac , ad , ae , bc , bd , be ) . All five outcomes are PE, so every lottery is ex-post PE. But the lottery selecting c , d , e with probability 1/3 each is not ex-ante PE, since it gives an expected utility of 1/3 to each voter, while the lottery selecting a , b with probability 1/2 each gives an expected utility of 1/2 to each voter. Bayesian efficiency
574-1324: A different rule for cost-sharing, that does take into account the different pollution-production. The underlying idea is that each agent should pay for the pollution it emits. However, the emission levels are not known - only the cleaning-costs c i {\displaystyle c_{i}} are known. The emission levels could be calculated from the cleaning costs using the transfer rate t (a number in [0,1]), as follows: V i ( t , c 1 , … , c n ) = { c i 1 − t if i = 1 c i 1 − t − c i − 1 1 − t t if i = 2 , … , n − 1 c i − c i − 1 1 − t t if i = n {\displaystyle V_{i}(t,c_{1},\ldots ,c_{n})={\begin{cases}{c_{i} \over 1-t}&{\text{if }}i=1\\{c_{i} \over 1-t}-{c_{i-1} \over 1-t}t&{\text{if }}i=2,\ldots ,n-1\\c_{i}-{c_{i-1} \over 1-t}t&{\text{if }}i=n\end{cases}}} However, usually t
656-417: 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
738-629: A pie. The third person does not lose out (even if he does not partake in the pie), hence splitting it in half and giving it to two individuals would be considered Pareto efficient. On a frontier of production possibilities, Pareto efficiency will happen. It is impossible to raise the output of products without decreasing the output of services when an economy is functioning on a basic production potential frontier, such as at point A, B, or C. If multiple sub-goals f i {\displaystyle f_{i}} (with i > 1 {\displaystyle i>1} ) exist, combined into
820-454: A single "best" (optimal) outcome. Instead, it only identifies a set of outcomes that might be considered optimal, by at least one person. Formally, a state is Pareto-optimal if there is no alternative state where at least one participant's well-being is higher, and nobody else's well-being is lower. If there is a state change that satisfies this condition, the new state is called a "Pareto improvement". When no Pareto improvements are possible,
902-489: 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 goods is Pareto-efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while
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#1732765714887984-440: A society better-off (or at least as well-off as 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
1066-402: 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". Fractional Pareto efficiency is a strengthening of Pareto efficiency in the context of fair item allocation . An allocation of indivisible items is fractionally Pareto-efficient (fPE or fPO) if it
1148-413: A vector-valued objective function f → = ( f 1 , … f n ) T {\displaystyle {\vec {f}}=(f_{1},\dots f_{n})^{T}} , generally, finding a unique optimum x → ∗ {\displaystyle {\vec {x}}^{*}} becomes challenging. This is due to the absence of
1230-546: Is Q 1 = 2 , Q 2 = 0 {\displaystyle Q_{1}=2,Q_{2}=0} . Without cooperation, country 1 will consume 2 units and country 2 will have 0 units: q 1 = 2 , q 2 = 0 {\displaystyle q_{1}=2,q_{2}=0} . Then, the benefits will be u 1 = b 1 = 2 , u 2 = b 2 = 0 {\displaystyle u_{1}=b_{1}={\sqrt {2}},u_{2}=b_{2}=0} . This
1312-1002: Is Pareto-optimal if there is no other feasible allocation { x 1 ′ , … , x n ′ } {\displaystyle \{x_{1}',\dots ,x_{n}'\}} where, for utility function u i {\displaystyle u_{i}} for each agent i {\displaystyle i} , u i ( x i ′ ) ≥ u i ( x i ) {\displaystyle u_{i}(x_{i}')\geq u_{i}(x_{i})} for all i ∈ { 1 , … , n } {\displaystyle i\in \{1,\dots ,n\}} with u i ( x i ′ ) > u i ( x i ) {\displaystyle u_{i}(x_{i}')>u_{i}(x_{i})} for some i {\displaystyle i} . Here, in this simple economy, "feasibility" refers to an allocation where
1394-406: Is Pareto-efficient if-and-only-if it maximizes the sum of all agents' benefits and wastes no money. Under the assumption that benefit functions are strictly concave, there is a unique optimal allocation. It structure is simple. Intuitively, the optimal allocation should equalize the marginal benefits of all countries (as in the above example). However, this may be impossible because of the structure of
1476-666: Is a negative externality : when an upstream country pollutes a river, this creates external cleaning costs for downstream countries. This externality may result in over-pollution by the upstream countries. Theoretically, by the Coase theorem , we could expect the countries to negotiate and achieve a deal in which polluting countries will agree to reduce the level of pollution for an appropriate monetary compensation. However, in practice this does not always happen. Evidence from various international rivers shows that, at water quality monitoring stations immediately upstream of international borders,
1558-497: Is a linear combination of the emissions. The relation between e {\displaystyle e} and q {\displaystyle q} is given by a diffusion matrix H {\displaystyle H} , such that: q = H ⋅ e {\displaystyle q=H\cdot e} . In the special case of a linear river presented above, we have m = n {\displaystyle m=n} , and H {\displaystyle H}
1640-444: Is a matrix with a triangle of ones. Efficiency is attained by permitting free trade in licenses. Two kinds of licenses are studied: In both markets, free trade can lead to an efficient outcome. However, the market in pollution-licenses is more widely applicable than the market in emission-licenses. There are several difficulties with the market approach, such as: how should the initial allocation of licenses be determined? How should
1722-598: Is a pie and three persons; the most equitable way would be to divide the pie into three equal portions. However, if the pie is divided in half and shared between two people, it is considered Pareto efficient – meaning that the third person does not lose out (despite the fact that he does not receive a piece of the pie). When making judgments, it is critical to consider a variety of aspects, including social efficiency, overall welfare, and issues such as diminishing marginal value. In order to fully understand market failure, one must first comprehend market success, which
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#17327657148871804-436: Is a situation that cannot be strictly improved for every individual. Formally, a strong Pareto improvement is defined 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-efficient if it has no strong Pareto improvements. Any strong Pareto improvement
1886-414: Is a strict partial order , though it is not a product order (neither non-strict nor strict). If f → ( x → 1 ) ≺ f → ( x → 2 ) {\displaystyle {\vec {f}}({\vec {x}}_{1})\prec {\vec {f}}({\vec {x}}_{2})} , then this defines a preorder in
1968-410: 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. An example is of a setting where individuals have private information (for example,
2050-416: 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): A market does not require local nonsatiation to get to a weak Pareto optimum. Constrained Pareto efficiency
2132-421: Is an economic good , it is often required to share river pollution (or the cost of cleaning it), which is an economic bad . There are 148 rivers in the world flowing through two countries, 30 through three, nine through four and 13 through five or more. Some notable examples are: In the international law, there are several conflicting views on the property rights to the river waters. Kilgour and Dinar were
2214-405: Is an adaptation of Pareto efficiency to settings in which players have incomplete information regarding the types of other players. Ordinal Pareto efficiency is an adaptation of Pareto efficiency to settings in which players report only rankings on individual items, and we do not know for sure how they rank entire bundles. Although an outcome may be a Pareto improvement, this does not imply that
2296-414: Is assigned a positive weight a i . For every allocation x , define the welfare of x as the weighted sum of utilities of all agents in x : Let x a be an allocation that maximizes the welfare over all allocations: 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 x
2378-422: Is defined as an inefficient allocation of resources. Due to the fact that it is feasible to improve, market failure implies Pareto inefficiency. For example, excessive consumption of depreciating items (drugs/tobacco) results in external costs to non-smokers, as well as premature death for smokers who do not quit. An increase in the price of cigarettes could motivate people to quit smoking while also raising funds for
2460-427: Is defined as the ability of a set of idealized competitive markets to achieve an equilibrium allocation of resources that is Pareto-optimal in terms of resource allocation. According to the definition of market failure, it is a circumstance in which the conclusion of the first fundamental theorem of welfare is erroneous; that is, when the allocations made through markets are not efficient. In a free market, market failure
2542-420: Is helpful not only for the cooperating countries, but also for the non-cooperating countries! With satiable countries, each coalition has two different core-lower-bounds: As illustrated above, the cooperative core-lower-bound is higher than the non-cooperative core-lower-bound. The non-cooperative-core is non-empty. Moreover, the downstream-incremental-distribution is the unique solution that satisfies both
Pamir River - Misplaced Pages Continue
2624-469: Is mathematically represented when there is no other strategy profile s' such that u i (s') ≥ u i (s) for every player i and u j (s') > u j (s) for some player j . In this equation s represents the strategy profile, u represents the utility or benefit, and j represents the player. Efficiency is an important criterion for judging behavior in a game. In a notable and often analyzed game known as Prisoner's Dilemma , depicted below as
2706-401: Is non-satiable, then 1 cannot leave water to 3, since it will be entirely consumed by 2 along the way. So 1 must consume all its water. In contrast, if country 2 is satiable (and this fact is common knowledge), then it may be worthwhile for 1 to leave some water to 3, even if some of it will be consumed by 2. This increases the welfare of the coalition, but also the welfare of 2. Thus, cooperation
2788-547: Is not Pareto efficient : it is possible to allocate 1 unit of water to each country: q 1 = q 2 = 1 {\displaystyle q_{1}=q_{2}=1} , and transfer e.g. 0.5 {\displaystyle 0.5} units of money from country 2 to country 1. Then, the utilities will be u 1 = 1.5 , u 2 = 0.5 {\displaystyle u_{1}=1.5,u_{2}=0.5} which are better for both countries. Because preferences are quasi-linear, an allocation
2870-408: Is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto efficiency, which only considers domination by feasible (discrete) allocations. 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
2952-826: Is not Pareto-efficient. Furthermore, neither of the remaining strategy profiles, (0, -5) or (-5, 0) , is a Pareto improvement over Both Cooperate , since -5 < -1 . Thus Both Cooperate is Pareto-efficient. In zero-sum games , every outcome is Pareto-efficient. A special case of a state is an allocation of resources. The formal presentation of the concept in an economy is the following: Consider an economy with n {\displaystyle n} agents and k {\displaystyle k} goods. Then an allocation { x 1 , … , x n } {\displaystyle \{x_{1},\dots ,x_{n}\}} , where x i ∈ R k {\displaystyle x_{i}\in \mathbb {R} ^{k}} for all i ,
3034-486: Is not known accurately. Upper and lower bounds on t can be estimated from the vector of cleaning-costs. Based on these bounds, it is possible to calculate bounds on the responsibility of upstream agents. Their principles for cost-sharing are: The rule characterized by these principles is called the Upstream Responsibility (UR) rule: it estimates the responsibility of each agent using expected value of
3116-476: Is not true: ex-ante PE is stronger that ex-post PE. For example, suppose there are two objects – a car and a house. Alice values the car at 2 and the house at 3; George values the car at 2 and the house at 9. Consider the following two lotteries: While both lotteries are ex-post PE, the lottery 1 is not ex-ante PE, since it is Pareto-dominated by lottery 2. Another example involves dichotomous preferences . There are 5 possible outcomes (
3198-463: Is possible to adjust the quantities to the actual amount of water that flows through the river each year. The utility of such flexible agreements has been demonstrated by simulations based on historical of the Ganges flow. The social welfare when using the flexible agreement is always higher than when using the optimal fixed agreement, but the increase is especially significant in times of drought , when
3280-438: Is relevant for non-linear river trees, in which waters from various sources flow into a common lake. It means that the payments by agents in two different branches of the tree should be independent of each other's costs. In the above models, pollution levels are not specified. Hence, their methods do not reflect the different responsibility of each region in producing the pollution. 2. Alcalde-Unzu, Gomez-Rua and Molis suggest
3362-452: Is the Pareto order. This means that y → ( 1 ) {\displaystyle {\vec {y}}^{(1)}} is not worse than y → ( 2 ) {\displaystyle {\vec {y}}^{(2)}} in any goal but is better (since smaller) in at least one goal j {\displaystyle j} . The Pareto order
Pamir River - Misplaced Pages Continue
3444-556: The Pareto front (or Pareto set or Pareto frontier ) 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 trade-offs within this set, rather than considering the full range of every parameter. Modern microeconomic theory has drawn heavily upon the concept of Pareto efficiency for inspiration. Pareto and his successors have tended to describe this technical definition of optimal resource allocation in
3526-419: The first welfare theorem , a competitive market leads to a Pareto-efficient outcome. This result was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu . However, the result only holds under the assumptions of the theorem: markets exist for all possible goods, there are no externalities , markets are perfectly competitive, and market participants have perfect information . In
3608-473: The ATS doctrine, each country has full rights to the water in its region. Therefore, the monetary payments should guarantee to each country at least the utility-level that it could attain on its own. With non-satiable countries, this level is at least b i ( Q i ) {\displaystyle b_{i}(Q_{i})} . Moreover, we should guarantee to each coalition of countries, at least
3690-1351: The Pareto order is applicable: Consider a vector-valued minimization problem: y → ( 1 ) ∈ R n {\displaystyle {\vec {y}}^{(1)}\in \mathbb {R} ^{n}} Pareto dominates y → ( 2 ) ∈ R n {\displaystyle {\vec {y}}^{(2)}\in \mathbb {R} ^{n}} if and only if: : ∀ i ∈ 1 , … m : y → i ( 1 ) ≤ y → i ( 2 ) {\displaystyle \forall i\in {1,\dots m}:{\vec {y}}_{i}^{(1)}\leq {\vec {y}}_{i}^{(2)}} and ∃ j ∈ 1 , … m : y → j ( 1 ) < y → j ( 2 ) . {\displaystyle \exists j\in {1,\dots m}:{\vec {y}}_{j}^{(1)}<{\vec {y}}_{j}^{(2)}.} We then write y → ( 1 ) ≺ y → ( 2 ) {\displaystyle {\vec {y}}^{(1)}\prec {\vec {y}}^{(2)}} , where ≺ {\displaystyle \prec }
3772-462: The absence of perfect information or complete markets, outcomes will generally be Pareto-inefficient, per the Greenwald–Stiglitz theorem . 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
3854-409: The absence of the other countries. This implies an upper bound on the utility of each coalition, called the aspiration upper bound . There is at most one welfare-distribution that satisfies both the core-lower-bound and the aspiration-upper-bound: it is the downstream incremental distribution . The welfare of each country i {\displaystyle i} should be the stand-alone value of
3936-401: The coalition { 1 , … , i } {\displaystyle \{1,\ldots ,i\}} minus the stand-alone value of the coalition { 1 , … , i − 1 } {\displaystyle \{1,\ldots ,i-1\}} . When the benefit functions of all countries are non-satiable, the downstream-incremental-distribution indeed satisfies both
4018-600: The context of it being an equilibrium that can theoretically be achieved within an abstract model of market competition. It has therefore very often been treated as a corroboration of Adam Smith 's " invisible hand " notion. More specifically, it motivated the debate over " market socialism " in the 1930s. However, because the Pareto-efficient outcome is difficult to assess in the real world when issues including asymmetric information, signalling, adverse selection, and moral hazard are introduced, most people do not take
4100-467: The core-lower-bounds and the aspiration-upper-bounds. Hence, this allocation scheme can be seen as a reasonable compromise between the doctrines of ATS and UTI. When the benefit functions are satiable, new coalitional considerations come into play. These are best illustrated by an example. Suppose there are three countries. Countries 1 and 3 are in a coalition. Country 1 wants to sell water to country 3 in order to increase their group welfare. If country 2
4182-418: The efficient pollution level. Gengenbach and Weikard and Ansink focus on the stability of voluntary coalitions of countries, that cooperate for pollution-reduction. van-der-Laan and Moes focus on property rights and the distribution of the gain in social welfare that arises when countries along an international river switch from no cooperation on pollution levels to full cooperation: It is possible to attain
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#17327657148874264-434: The efficient pollution levels by monetary payments. The monetary payments depend on property rights: This model can be generalized to rivers that are not linear but have a tree-like topology. 1. Dong, Ni and Wang (extending a previous work by Ni and Wang ) assume each agent i {\displaystyle i} has an exogenously given cost c i {\displaystyle c_{i}} , caused by
4346-567: The emission best for it given the emissions of the others. The total amount of emission ∑ i e i {\displaystyle \sum _{i}e_{i}} in equilibrium is strictly higher than in the optimal situation, in accordance with the empirical findings of Sigman. For example, suppose there are two countries with the following benefit functions: The socially-optimal levels are e 1 = 0.1621 , e 2 = 0.2968 {\displaystyle e_{1}=0.1621,e_{2}=0.2968} , and
4428-423: The final allocation of licenses be enforced? See Emissions trading for more details. Laan and Moes (2012) describe the polluted-river situation as follows. Under the above assumptions, there exists a unique optimal emission-vector, in which the social welfare (the sum of benefits minus the sum of costs) is maximized. There also exists a unique Nash equilibrium emission-vector, in which each country produces
4510-401: The first to suggest a theoretical model for efficient water sharing. Without cooperation, each country maximizes its individual utility. So if a country is an insatiable agent (its benefit function is always increasing), it will consume all the water that enters its region. This may be inefficient. For example, suppose there are two countries with the following benefit functions: The inflow
4592-409: The flow is below the average. Calculating the efficient water allocation is only the first step in solving a river-sharing problem. The second step is calculating monetary transfers that will incentivize countries to cooperate with the efficient allocation. What monetary transfer vector should be chosen? Ambec and Sprumont study this question using axioms from cooperative game theory. According to
4674-400: The largest utility that a country can hope for. This is the utility it could get alone, if there were no other countries upstream: b i ( ∑ j = 1 i Q i ) {\displaystyle b_{i}(\sum _{j=1}^{i}Q_{i})} . Moreover, the aspiration level of each coalition of countries is the highest utility-level it could attain in
4756-467: 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 p 1 , but if of type B , they pay price p 2 " (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 p x , then they get
4838-423: The need to clean the river to match environmental standards. This cost is caused by the pollution of the agent itself and all agents upstream to it. The goal is to charge each agent i a vector of payments x i j {\displaystyle x_{ij}} such that c j = ∑ i x i j {\displaystyle c_{j}=\sum _{i}x_{ij}} , i.e.,
4920-468: The non-cooperative-core-lower-bounds and the aspiration-upper-bound. However, the cooperative-core may be empty: there might be no allocation that satisfies the cooperative-core-lower-bound. Intuitively, it is harder to attain stable agreements, since middle countries might "free-ride" agreements by downstream and upstream countries. A river carries not only water but also pollutants coming from agricultural, biological and industrial waste. River pollution
5002-697: The north and the Wakhan District in the south. It starts from the Lake Zorkul , at a height of 4,130 meters, and then flows west, and later southwest. Near the town of Langar , at 2,799 m, its confluences with the Wakhan River forms the Panj River . The Pamir forms the boundary between Afghanistan and Tajikistan along its entire length. Northwest of Langar is the 6,726 m (22,067 ft) high Karl Marx Peak and Friedrich Engels Peak (6,507 m (21,348 ft)). A road runs along
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#17327657148875084-426: The optimal allocation, the marginal benefits are weakly decreasing. The countries are divided to consecutive groups, from upstream to downstream. In each group, the marginal benefit is the same, and between groups, the marginal benefit is decreasing. The possibility of calculating an optimal allocation allows much more flexibility in water-sharing agreements. Instead of agreeing in advance on fixed water quantities, it
5166-412: The outcome is equitable. It is possible that inequality persists even after a Pareto improvement. Despite the fact that it is frequently used in conjunction with the idea of Pareto optimality, the term "efficiency" refers to the process of increasing societal productivity. It is possible for a society to have Pareto efficiency while also have high levels of inequality. Consider the following scenario: there
5248-485: The outputs of all other goods either increase or remain the same. Besides economics, the notion of Pareto efficiency has also been applied to selecting alternatives in engineering and biology . Each option is first assessed, under multiple criteria, and then a subset of options is 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
5330-509: The payments of all agents for region j cover the cost of cleaning it. They suggest three rules for dividing the total costs of pollution among the agents: Each of these methods can be characterized by some axioms: additivity , efficiency (the payments exactly cover the costs), no blind costs (an agent with zero costs should pay zero - since he does not pollute), independence of upstream/downstream costs , upstream/downstream symmetry , and independence of irrelevant costs . The latter axiom
5412-470: The pollution levels are more than 40% higher than the average levels at control stations. This may imply that countries do not cooperate for pollution reduction, and the reason for this may be the unclearness in property rights. See and and for other empirical studies. Dong, Ni, Wang and Meidan Sun discuss the Baiyang Lake , which was polluted by a tree of 13 counties and townships. To clean
5494-546: The problem. Emissions trading is a market-based approach to attain an efficient pollution allocation. It is applicable to general pollution settings; river pollution is a special case. As an example, Montgomery studies a model with n {\displaystyle n} agents each of which emits e i {\displaystyle e_{i}} pollutants, and m {\displaystyle m} locations each of which suffers pollution q i {\displaystyle q_{i}} which
5576-500: The responsibility is a non-linear function of t . In particular, the UR rule is better for upstream countries (it charges them less), and the EUR rule is better for downstream countries. Pareto efficient 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 everyone in
5658-421: The result is desirable or equitable. After a Pareto improvement, inequality could still exist. However, it does imply that any change will violate the "do no harm" principle, because at least one person will be worse off. A society may be Pareto efficient but have significant levels of inequality. The most equitable course of action would be to split the pie into three equal portions if there were three persons and
5740-1094: The river and its sources, 13 wastewater treatment plants were built in the region. The authors discuss different theoretic models for sharing the costs of these buildings among the townships and counties, but mention that at the end the costs were not shared but rather paid by the Baoding municipal government, since the polluters did not have an incentive to pay. Hophmayer-Tokich and Kliot present two case studies from Israel where municipalities who suffer from water pollution initiated cooperation on wastewater treatment with upstream polluters. The findings suggest that regional cooperation can be an efficient tool in promoting advanced wastewater treatment, and has several advantages: an efficient use of limited resources (financial and land); balancing disparities between municipalities (size, socio-economic features, consciousness and ability of local leaders); and reducing spillover effects. However, some problems were reported in both cases and should be addressed. Several theoretical models were proposed for
5822-646: The river on the Tajik side to Khargush where it turns north to join the Pamir Highway . A road of lower quality continues east past Zorkul, almost to the Chinese border. Scottish explorer John Wood was the first known European to try to find the source of the Oxus, or Pamir River. He made a pioneering journey in 1839 and reached Lake Zorkul . Fair river sharing In addition to sharing river water, which
5904-536: The river: the upstream countries do not have access to downstream waters. For example, in the above two-country example, if the inflow is Q 1 = 0.5 , Q 2 = 1.5 {\displaystyle Q_{1}=0.5,Q_{2}=1.5} , then it is not possible to equalize the marginal benefits, and the optimal allocation is to let each country consume its own water: q 1 = 0.5 , q 2 = 1.5 {\displaystyle q_{1}=0.5,q_{2}=1.5} . Therefore, in
5986-512: The search space and we say x → 1 {\displaystyle {\vec {x}}_{1}} Pareto dominates the alternative x → 2 {\displaystyle {\vec {x}}_{2}} and we write x → 1 ≺ f → x → 2 {\displaystyle {\vec {x}}_{1}\prec _{\vec {f}}{\vec {x}}_{2}} . Weak Pareto efficiency
6068-587: The second to George, where the utility profile is (3, 1): When the decision process is random, such as in fair random assignment or random social choice or fractional approval voting , there is a difference between ex-post and ex-ante Pareto efficiency : If some lottery L is ex-ante PE, then it is also ex-post PE. Proof : suppose that one of the ex-post outcomes x of L is Pareto-dominated by some other outcome y . Then, by moving some probability mass from x to y , one attains another lottery L ' that ex-ante Pareto-dominates L . The opposite
6150-412: The state is a "Pareto optimum". In other words, Pareto efficiency is when it is impossible to make one party better off without making another party worse off. This state indicates that resources can no longer be allocated in a way that makes one party better off without harming other parties. In a state of Pareto Efficiency, resources are allocated in the most efficient way possible. Pareto efficiency
6232-470: The subject of multi-objective optimization (also termed Pareto optimization ). The concept is named after Vilfredo Pareto (1848–1923), an Italian civil engineer and economist , who used the concept in his studies of economic efficiency and income distribution . Pareto originally used the word "optimal" for the concept, but this is somewhat of a misnomer : Pareto's concept more closely aligns with an idea of "efficiency", because it does not identify
6314-406: 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. Under the assumptions of
6396-495: The transfer-rate, and charges each agent according to its estimated responsibility. In a further study they present a different rule called the Expected Upstream Responsibility (EUR) rule: it estimate the expected responsibility of each agent taking the transfer-rate as a random variable, and charges each agent according to its estimated expected responsibility. The two rules are different because
6478-404: The treatment of smoking-related ailments. Given some ε > 0, an outcome is called ε -Pareto-efficient if no other outcome gives all agents at least the same utility, and one agent a utility at least (1 + ε ) higher. This captures the notion that improvements smaller than (1 + ε ) are negligible and should not be considered a breach of efficiency. Suppose each agent i
6560-447: The upstream country 1 over-pollutes; this improves its own utility but harms the utility of the downstream country 2. The main question of interest is: how to make countries reduce pollution to its optimal level? Several solutions have been proposed. The cooperative approach deals directly with pollution levels (rather than licenses). The goal is to find monetary transfers that will make it profitable to agents to cooperate and implement
6642-511: The utilities are u 1 = 0.376 , u 2 = 0.334 {\displaystyle u_{1}=0.376,u_{2}=0.334} . The Nash equilibrium levels are e 1 = 0.3969 , e 2 = 0.1847 {\displaystyle e_{1}=0.3969,e_{2}=0.1847} , and the utilities (benefit minus cost) are u 1 = 0.473 , u 2 = 0.092 {\displaystyle u_{1}=0.473,u_{2}=0.092} . In equilibrium,
6724-473: The utility-level that they could attain by the optimal allocation among the countries in the coalition. This implies a lower bound on the utility of each coalition, called the core lower bound . According to the UTI doctrine, each country has rights to all water in its region and upstream. These rights are not compatible since their sum is above the total amount of water. However, these rights define an upper bound -
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