Mathematics of the commons

1.The commons とは何か

Donald M. Nonini (https://www.jstor.org/stable/23182116 2006) によれば,「コモンズ」とは過去,現在,未来の世代にわたり人類が共有する資源の全体であり,それらは生物学的,文化的,社会的な再生産に不可欠なものとある. :Assemblages and ensembles of resources that human beings hold in commons or in trust to use on behalf of themselves, other living human beings, and past and future generations of human beings, and which are essential to their biological, cultural, and social reproduction. (Nonini 2006)

むろんここでの資源は,化石燃料をはじめとする狭い意味の物質資源のみを意味するものではなく,文化的,社会的な共有財産すべてを包含するものである.

・Garrett Hardin からElinor Ostromへ:コモンズの悲劇

このようなコモンズを誰が,どのように管理し,育てていくかについては様々な議論がなされてきた.とくにGarrett Hardin による “The Tragedy of the Commons” Science 162, 1243 (1968) は大きな影響を与えたが,そこで提示された解決策:政府による管理あるいは私有化は現実には有効でなく,伝統的な group-property institutionに劣るものであることは,これまでのいくつかの事例で実証されてきた:A satellite image of northern China, Mongolia, and southern Siberia (8) shows marked degradation in the Russian part of the image, whereas the Mongolian half of the image shows much less degradation.

しかしながら昨今の人間活動の増大はそのような伝統的な手法だけでは難しくなってきている.例えば食料・水問題や漁業を含む海洋エコロジー問題を考えれば十分であろう.さらにより包括的な気候変動への対策は地球レベルでの期限が間近に迫った問題となっている.これらははるかに巨大で複雑な系であることが問題の解決を難しくしている.

Elinor Ostrom らによる’’Revisiting the Commons: Local Lessons, Global Challenges” (Science, 284 (1999), • DOI: 10.1126/science.284.5412.278) での論考におけるCPR(Common Pool Resources) の公平かつ有効な管理の提案は極めて示唆的であり,long-term benefits を確保し,コストはできる限り抑えるという困難な最適化問題への提案をしている.この論文の最後の部分をやや長くなるが以下に引用する.

Lessons from Local and Regional Common-Pool Resources

The empirical and theoretical research stimulated over the past 30 years by Garrett Hardin’s article has shown that tragedies of the commons are real, but not inevitable. Solving the dilemmas of sustainable use is neither easy nor error-free even for local resources. But a scholarly consensus is emerging regarding the conditions most likely to stimulate successful self-organized processes for local and regional CPRs (6, 26, 32). Attributes of resource systems and their users affect the benefits and costs that users perceive. For users to see major benefits, resource conditions must not have deteriorated to such an extent that the resource is useless, nor can the resource be so little used that few advantages result from organizing. Benefits are easier to assess when users have accurate knowledge of external boundaries and internal microenvironments and have reliable and valid indicators of resource conditions. When the flow of resources is relatively predictable, it is also easier to assess how diverse management regimes will affect long-term benefits and costs. Users who depend on a resource for a major portion of their livelihood, and who have some autonomy to make their own access and harvesting rules, are more likely than others to perceive benefits from their own restrictions, but they need to share an image of how the resource system operates and how their actions affect each other and the resource. Further, users must be interested in the sustainability of the particular resource so that expected joint benefits will outweigh current costs. If users have some initial trust in others to keep promises, low-cost methods of monitoring and sanctioning can be devised. Previous organizational experience and local leadership reduces the users’ costs of coming to agreement and finding effective solutions for a particular environment. In all cases, individuals must overcome their tendency to evaluate their own benefits and costs more intensely than the total benefits and costs for a group. Collective-choice rules affect who is involved in deciding about future rules and how preferences will be aggregated. Thus, these rules affect the breadth of interests represented and involved in making institutional changes, and they affect decisions about which policy instruments are adopted (33).

 

The Broader Social Setting

Whether people are able to self-organize and manage CPRs also depends on the broader social setting within which they work. National governments can help or hinder local self-organization. “Higher” levels of government can facilitate the assembly of users of a CPR in organizational meetings, provide information that helps identify the problem and possible solutions, and legitimize and help enforce agreements reached by local users. National governments can at times, however, hinder local self-organization by defending rights that lead to overuse or maintaining that the state has ultimate control over resources without actually monitoring and enforcing existing regulations. Participants are more likely to adopt effective rules in macro-regimes that facilitate their efforts than in regimes that ignore resource problems entirely or that presume that central authorities must make all decisions. If local authority is not formally recognized by larger regimes, it is difficult for users to establish enforceable rules. On the other hand, if rules are imposed by outsiders without consulting local participants, local users may engage in a game of “cops and robbers” with outside authorities. In many countries, two centuries of colonization followed by state-run development policy that affected some CPRs has produced great resistance to externally imposed institutions. The broader economic setting also affects the level and distribution of gains and costs of organizing the management of CPRs. Expectations of rising resource prices encourage better management, whereas falling, unstable, or uncertain resource prices reduce the incentive to organize and assure future availability (34). National policy also affects factors such as human migration rates, the flow of capital, technology policy, and hence the range of conditions local institutions must address to work effectively. Finally, local institutions are only rarely able to cope with the ramifications of civil or international war.

 

Challenges of Global Commons

The lessons from local and regional CPRs are encouraging, yet humanity now faces new challenges to establish global institutions to manage biodiversity, climate change, and other ecosystem services (35). These new challenges will be especially difficult for at least the following reasons. Scaling-up problem. Having larger numbers of participants in a CPR increases the difficulty of organizing, agreeing on rules, and enforcing rules. Global environmental resources now involve 6 billion inhabitants of the globe. Organization at national and local levels can help, but it can also get in the way of finding solutions. Cultural diversity challenge. Along with economic globalization, we are in a period of reculturalization. Increasing cultural diversification offers increased hope that the diversity of ways in which people have organized locally around CPRs will not be quickly lost, and that diverse new ways will continue to evolve at the local level. However, cultural diversity can decrease the likelihood of finding shared interests and understandings. The problem of cultural diversity is exacerbated by “north-south” conflicts stemming from economic differences between industrialized and less-industrialized countries. Complications of interlinked CPRs. Although the links between grassland and forest management are complex, they are not so complex as those between maintaining biodiversity and ameliorating climate change. As we address global issues, we face greater interactions between global systems. Similarly, with increased specialization, people have become more interdependent. Thus, we all share one another’s common interests, but in more complex ways than the users of a forest or grassland. While we have become more complexly interrelated, we have also become more “distant” from each other and our environmental problems. From our increasingly specialized understandings and particular points on the globe, it is difficult to comprehend the significance of global CPRs and how we need to work together to govern these resources successfully. And given these complexities, finding fair solutions is even more challenging. Accelerating rates of change. Previous generations complained that change occurred faster and faster, and the acceleration continues. Population growth, economic develop ment, capital and labor mobility, and technological change push us past environmental thresholds before we know it. “Learning by doing” is increasingly difficult, as past lessons are less and less applicable to current problems. Requirement of unanimous agreement as a collective-choice rule. The basic collectivechoice rule for global resource management is voluntary assent to negotiated treaties (36). This allows some national governments to hold out for special privileges before they join others in order to achieve regulation, thus strongly affecting the kinds of resource management policies that can be adopted at this level. We have only one globe with which to experiment. Historically, people could migrate to other resources if they made a major error in managing a local CPR. Today, we have less leeway for mistakes at the local level, while at the global level there is no place to move. These new challenges clearly erode the confidence with which we can build from past and current examples of successful management to tackle the CPR problems of the future. Still, the lessons from successful examples of CPR management provide starting points for addressing future challenges. Some of these will be institutional, such as multilevel institutions that build on and complement local and regional institutions to focus on truly global problems. Others will build from improved technology. For example, more accurate long-range weather forecasts could facilitate improvements in irrigation management, or advances in fish tracking could allow more accurate population estimates and harvest management. And broad dissemination of widely believed data could be a major contributor to the trust that is so central to effective CPR management. In the end, building from the lessons of past successes will require forms of communication, information, and trust that are broad and deep beyond precedent, but not beyond possibility. Protecting institutional diversity related to how diverse peoples cope with CPRs may be as important for our long-run survival as the protection of biological diversity. There is much to learn from successful efforts as well as from failures.

2.コモンズの悲劇から複合危機の時代へ

このようなコモンズを誰が,どのように管理し,育てていくかについては様々な議論がなされてきた.とくにGarrett Hardin による 「コモンズの悲劇」(Science 162 (1968))は大きな影響を与えたが,そこで提示された解決策,すなわち政府による管理あるいは私有化が提案されたが,それらが実は伝統的な group-property institutionに劣るものであることは,これまでのいくつかの事例で実証されてきた.しかしながら昨今の人間活動の増大はそのような伝統的な手法だけでは難しくなってきている.例えば食料・水問題,エネルギー,感染症問題等を考えれば十分であろう.さらにより包括的な気候変動への対策は地球レベルでの緊急対応が迫った問題となっている.これらは多くの国や組織,さらに利害関係者が関与し,はるかに巨大で複雑な系であることが問題の解決を難しくしている.

それに対し,Elinor Ostrom らによる’’Revisiting the Commons: Local Lessons, Global Challenges”(Science, 284 (1999), • DOI: 10.1126/science.284.5412.278) での論考はCPR(Common Pool Resources) の公平かつ有効な管理の提案は極めて示唆的であり,long-term benefits を確保し,コストはできる限り抑えるという困難な最適化問題解決を目指した.さらにこの数十年の世界の情勢は大きく変化し,デジタル化の大幅な加速と共に社会の格差拡大は不安定感,不安感,不信感を増大させている.一方で地球温暖化は徐々に進行し,様々な激甚災害の増加を生み出している.多くの要素が関与する複合危機という状況に進展しているのが現在である.

3.「コモンズの数学」を必要とする背景

このように様々な兆候のシグナルが発せられているにも関わらず,上記の問題群に対し,個人から国のレベルをつなぐ大きなムーブメントが(少なくとも日本では)十分に形成されていないのはなぜであろうか.これはある種の楽観論,すなわち環境悪化を抑えつつ経済成長は可能:デカップリングは可能で原発・炭素回収等の最新技術により成長可能とするもの.あるいは再生エネルギーの大幅導入により「低エネルギー社会」の構築を目指す脱成長論が盛んに議論され,一定の説得力を持ちつつあることなどが背景にあると思われる.しかしながらそれでもなお bottom up から危機感を意識的あるいは無意識的に共有できる基盤はかなり脆弱と思われる.おそらくその理由の一つは,気候変動を含め人間は非常にゆっくりとした変化を感じとることは不得手である.また放射能,感染症など目に見えないものに対しても冷静な対処は難しい.さらに現状は大きく変化せず,このまま続くであろう,という認知バイアスも背後にあると考えられる.

4.数理モデルの社会的役割

このような状況を打破するために数学はどのような役割を果たすことができるであろうか.とくに数理モデルに焦点を当て,その役割を明確にすると同時に「コモンズの数学」という観点から今後具体的な発信を試みたい.一言でいうと前段に述べた状況は,ある種の想像力の欠如あるいはそれを喚起するための共有すべきストーリーが不足していることに由来するのではないかと考えられる.単純化すれば,自分毎として理解できるきっかけが足りないと思われる.そのために人間の時空間スケールを超えて,複合危機を理解できる物語として「数理モデル」は大きなポテンシャルをもっていると考えられる.それにより「そうなってしまうのか」という実感が共有できる「概念モデル」(conceptual model)をいくつか提示し,発展させ,そして前述の共通認識にまで深める先鞭としたい.それらは定性的メタファーと言えるが,その背後では極めて精緻な数学・数理科学,さらに最新のデータ科学の成果に支えられており,定量的モデルや現場での検証と相補的役割を果たすものである.今後具体的なテーマについて少しずつ述べていきたい.

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