Counting Distinctions: On the Conceptual Foundations of Shannon's Information Theory

Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u') from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition p on U making a distinction, i.e., if u and u' were in different blocks of p. Subset logic leads to finite probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |UxU| from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions." (forthcoming in Synthese

Deductive and Analogical Reasoning on a Semantically Embedded Knowledge Graph

Representing knowledge as high-dimensional vectors in a continuous semantic vector space can help overcome the brittleness and incompleteness of traditional knowledge bases. We present a method for performing deductive reasoning directly in such a vector space, combining analogy, association, and deduction in a straightforward way at each step in a chain of reasoning, drawing on knowledge from diverse sources and ontologies.Comment: AGI 201

The effects on developing countries of the Kyoto Protocol and carbon dioxide emissions trading

The trading of rights to emit carbon dioxide has not officially been sanctioned by the United Nations Framework Convention on Climate Change, but it is of interest to investigate the consequences, both for industrial (Annex B) and developing countries, of allowing such trades. The authors examine the trading of caps assigned to Annex B countries under the Kyoto Protocol and compare the outcome with a world in which Annex B countries meet with their Kyoto targets without trading. Under the trading scenario the former Soviet Union is the main seller of carbon dioxide permits and Japan, the European Union, and the United States are the main buyers. Permit trading is estimated to reduce the aggregate cost of meeting the Kyoto targets by about 50 percent, compared with no trading. Developing countries, though they do not trade, are nonetheless affected by trading. For example, the price of oil and the demand for other developing country exports are higher with trading than without. The authors also consider what might happen if developing countries were to voluntarily accept caps equal to Business as Usual Emissions and were allowed to sell emission reductions below these caps to Annex B countries. The gains from emissions trading could be big enough to give buyers and sellers incentive to support the system. Indeed, a global market for rights to emit carbon dioxide could reduce the cost of meeting the Kyoto targets by almost 90 percent, if the market were to operate competitively. The division of trading gains, however, may make a competitive outcome unlikely: Under perfect competition, the vast majority of trading gains go to buyers of permits rather than to sellers. Even markets in which the supply of permits is restricted can, however, substantially reduce the cost to Annex B countries of meeting their Kyoto targets, while yielding profits to developing countries that elect to sell permits.Economic Theory&Research,Environmental Economics&Policies,Markets and Market Access,Montreal Protocol,Climate Change,Environmental Economics&Policies,Carbon Policy and Trading,Energy and Environment,Economic Theory&Research,Montreal Protocol

Short-term CO₂ abatement in the European power sector

This paper focuses on the possibilities for short term abatement in response to a CO2 price through fuel switching in the European power sector. The model E-Simulate is used to simulate the electricity generation in Europe as a means of both gaining insight into the process of fuel switching and estimating the abatement in the power sector during the first trading period of the European Union Emission Trading Scheme. Abatement is shown to depend not only on the price of allowances, but also and more importantly on the load level of the system and the ratio between natural gas and coal prices. Estimates of the amount of abatement through fuel switching are provided with a lower limit of 35 million metric tons in 2005 and 19 Mtons in 2006

Bringing Transportation into a Cap-and-Trade Regime

Abstract in HTML and technical report in PDF available on the Massachusetts Institute of Technology Joint Program on the Science and Policy of Global Change website (http://mit.edu/globalchange/www/).The U.S. may at some point adopt a national cap-and-trade system for greenhouse gases, and if and when that happens the system of CAFE regulation of vehicle design very likely could still be in place. Imposed independently these two systems can lead to economic waste. One way to avoid the inefficiency is to integrate the two systems by allowing emissions trading between them. Two possible approaches to potential linkage are explored here, along with a discussion of ways to guard against violation under such a trading regime of vehicle standards that may be justified by non-climate objectives. At a minimum, implementation of a U.S. cap-and-trade system is several years in the future, so we also suggest intermediate measures that would gain some of the advantages of an integrated system and smooth the way to ultimate interconnection.This study received funding from the MIT Joint Program on the Science and Policy of Global Change, which is supported by a consortium of government, industry and foundation sponsors

Green consumer markets in the fight against climate change

Climate change has become one of the greatest threats to environmental security, as attested by the growing frequency of severe flooding and storms, extreme temperatures and droughts. Accordingly, the European Union’s (EU) 6th Environment Action Programme (2010) lists tackling climate change as its first priority. A key aim of the EU has been to cut CO2 emissions, a major factor in climate change, by 8% until 2012 and 20% until 2020. The European Commission has proposed the encouragement of private consumer market for green products and services as one of several solutions to this problem. However, existing research suggests that the market share of these products has been only 3%, although 30% of individuals favour environmental and ethical goods. This article uses Public Goods Theory to explain why the contribution of the green consumer market to fighting climate change has been and possibly may remain limited without further public intervention

Climate Change Taxes and Energy Efficiency in Japan

Abstract in HTML and technical report in PDF available on the Massachusetts Institute of Technology Joint Program on the Science and Policy of Global Change website (http://mit.edu/globalchange/www/).In 2003 Japan proposed a Climate Change Tax to reduce its CO2 emissions to the level required by the Kyoto Protocol. If implemented, the tax would be levied on fossil fuel use and the revenue distributed to several sectors of the economy to encourage the purchase of energy efficient equipment. Analysis using the MIT Emissions Prediction and Policy Analysis (EPPA) model shows that this policy is unlikely to bring Japan into compliance with its Kyoto target unless the subsidy encourages improvement in energy intensity well beyond Japan’s recent historical experience. Similar demand-management programs in the U.S., where there has been extensive experience, have not been nearly as effective as they would need to be to achieve energy efficiency goals of the proposal. The Climate Change Tax proposal also calls for restricting Japan’s participation in the international emission trading. We consider the economic implications of limits on emissions trading and find that they are substantial. Full utilization of international emission trading by Japan reduces the carbon price, welfare loss, and impact on its energy-intensive exports substantially. The welfare loss with full emissions trading is one-sixth that when Japan meets its target though domestic actions only, but Japan can achieve substantial savings even under cases where, for example, the full amount of the Russian allowance is not available in international markets

The Allocation of European Union Allowances: Lessons, Unifying Themes and General Principles

A critical issue in dealing with climate change is deciding who has a right to emit carbon dioxide (CO 2 ), and under what conditions, when those emissions are limited. The European Union Emissions Trading Scheme (EU ETS) is the world’s first large experiment with an emission trading system for CO 2 and it is likely to be copied by others if there is to be a global regime for limiting greenhouse gas emissions. This paper provides the first in-depth description and analysis of the process by which rights to emit carbon dioxide were created and distributed in the EU ETS. The main objective of the paper is to distill the lessons and general principles to be learned from the allocation of allowances in the EU ETS, i.e. in the world’s first experience with allocating carbon allowances to sub-national entities. We discuss the lessons and unifying observations that emerge from this experience and provide some insights on what seem to be more general principles informing the allocation process and on what are the global implications of the EU ETS

Emissions trading to reduce greenhouse gas emissions in the United States : the McCain-Lieberman Proposal

Abstract in HTML and technical report in PDF available on the Massachusetts Institute of Technology Joint Program on the Science and Policy of Global Change website (http://mit.edu/globalchange/www/).The Climate Stewardship Act of 2003 (S. 139) is the most detailed effort to date to design an economy-wide cap-and-trade system for US greenhouse gas emissions reductions. The Act caps sectors at their 2000 emissions in Phase I of the program, running from 2010 to 2015, and then to their 1990 emissions in Phase II starting 2016. There is a strong incentive for banking of allowances, raising the costs in Phase I to achieve savings in Phase II. Use of credits from outside the capped sectors could significantly reduce the cost of the program, even though limited to 15% and 10% of Phase I and II allowances respectively. These credits may come from CO2 sequestration in soils and forests, reductions in emissions from uncapped sectors, allowances acquired from foreign emissions trading systems, and from a special incentive program for automobile manufacturers. The 15% and 10% limits increase the incentive for banking and could prevent full use of cost-effective reductions from the uncapped sectors. Moreover, some of the potential credits might contribute little or no real climate benefit, particularly if care is not taken in defining those from forest and soil CO2 sequestration. Analysis using the MIT Emissions Prediction and Policy Analysis model shows that costs over the two Phases of the program could vary substantially, depending on normal uncertainty in economic and emissions growth, and the details of credit system implementation