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Chatani, Satoru, Hikari Shimadera, Syuichi Itahashi, and Kazuyo Yamaji. "Comprehensive analyses of source sensitivities and apportionments of PM<sub>2.5</sub> and ozone over Japan via multiple numerical techniques." Atmospheric Chemistry and Physics 20, no. 17 (September 4, 2020): 10311–29. http://dx.doi.org/10.5194/acp-20-10311-2020.
Abstract. Source sensitivity and source apportionment are two major indicators representing source–receptor relationships, which serve as essential information when considering effective strategies to accomplish improved air quality. This study evaluated source sensitivities and apportionments of ambient ozone and PM2.5 concentrations over Japan with multiple numerical techniques embedded in regional chemical transport models, including a brute-force method (BFM), a high-order decoupled direct method (HDDM), and an integrated source apportionment method (ISAM), to update the source–receptor relationships considering stringent emission controls recently implemented in Japan and surrounding countries. We also attempted to understand the differences among source sensitivities and source apportionments calculated by multiple techniques. While a part of ozone concentrations was apportioned to domestic sources, their sensitivities were small or even negative; ozone concentrations were exclusively sensitive to transport from outside Japan. Although the simulated PM2.5 concentrations were significantly lower than those reported by previous studies, their sensitivity to transport from outside Japan was still relatively large, implying that there has been a reduction in Japanese emissions, similar to surrounding countries including China, due to implementation of stringent emission controls. HDDM allowed us to understand the importance of the non-linear responses of PM2.5 concentrations to precursor emissions. Apportionments derived by ISAM were useful in distinguishing various direct and indirect influences on ozone and PM2.5 concentrations by combining with sensitivities. The results indicate that ozone transported from outside Japan plays a key role in exerting various indirect influences on the formation of ozone and secondary PM2.5 components. While the sensitivities come closer to the apportionments when perturbations in emissions are larger in highly non-linear relationships – including those between NH3 emissions and NH4+ concentrations, NOx emissions and NO3- concentrations, and NOx emissions and ozone concentrations – the sensitivities did not reach the apportionments because there were various indirect influences including other sectors, complex photochemical reactions, and gas–aerosol partitioning. It is essential to consider non-linear influences to derive strategies for effectively suppressing concentrations of secondary pollutants.
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Gari, Yared, Paul Block, Tammo S. Steenhuis, Muluneh Mekonnen, Getachew Assefa, Abebe Kidus Ephrem, Yared Bayissa, and Seifu A. Tilahun. "Developing an Approach for Equitable and Reasonable Utilization of International Rivers: The Nile River." Water 15, no. 24 (December 18, 2023): 4312. http://dx.doi.org/10.3390/w15244312.
The absence of a basin-wide apportionment agreement on using the Nile River equitably has been a long-standing source of disagreement among Nile riparian states. This study introduces a new approach that the riparian states can consider that quantifies the Nile River’s apportionment. The approach includes (1) developing a basin-wide database of indicators representative of the United Nations Watercourse Convention (UNWC) relevant factors and circumstances, (2) developing an ensemble of indicator weighting scenarios using various weighting methods, and (3) developing six water-sharing methods to obtain a range of apportionments for Egypt, Sudan, Ethiopia and the group of the White Nile Equatorial States for each weighting scenarios. The results illustrate a relatively narrow range of country-level water apportionments, even though some individual factor weights vary from 3% to 26%. Considering the entire Nile River, the water apportionment for Ethiopia ranges from 32% to 38%, Sudan and South Sudan from 25% to 33%, Egypt from 26% to 35%, and the Equatorial States from 5% to 7%. We trust that the six proposed equitable water-sharing methods may aid in fostering basin-wide negotiations toward a mutual agreement and address the dispute over water sharing.
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Haman, Jacek. "THE CONCEPT OF DEGRESSIVE AND PROGRESSIVE PROPORTIONALITY AND ITS NORMATIVE AND DESCRIPTIVE APPLICATIONS." Studies in Logic, Grammar and Rhetoric 50, no. 1 (June 27, 2017): 67–91. http://dx.doi.org/10.1515/slgr-2017-0019.
Abstract The article discusses the concept of progressive and degressive proportionality of the distribution of parliamentary seats. In the first part are presented axiological sources of the principles of proportionality and progressive and degressive proportionality and the history of degressively proportional apportionments of seats in the European Parliament. The main part of the article is devoted to the formulation of proposals for strict formal definition of degressive and progressive proportionality, and a description of the method of apportionment of seats in the European Parliament based on the strict definition of degressive proportionality and maintaining maximum compatibility with former apportionments adopted in multilateral negotiations. The last part of the article consists of a discussion of the possibilities of adopting the concept of progressive proportionality in the analysis of the functioning of parliamentary electoral systems.
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Bolun, Ion. "Degree of favoring in apportionments." Computer Science Journal of Moldova 30, no. 2 (89) (July 2022): 187–213. http://dx.doi.org/10.56415/csjm.v30.11.
To quantitatively estimate the degree of favoring the beneficiaries in proportional apportionments of entities of the same kind (seats, PCs, etc.), five quantitative criteria were defined. By computer simulation, the degree of favoring the large or small beneficiaries by 6 apportionment methods is identified. Thus, favoring large beneficiaries by the d’Hondt method can overpass 10.7-12.1 entities (entities in excess) and that of small beneficiaries by the Huntington-Hill method -- 2.7-11.0 entities, and by the Adapted Sainte-Lagu\"{e} method -- 1.7-9.7 entities. The Huntington-Hill method favors small beneficiaries up to 5.70 times stronger than the Adapted Sainte-Laguë one does. Also, the d’Hondt method favors beneficiaries (the large ones) much stronger than the Adapted Sainte-Laguë one does (the small ones) -- for very many cases the respective ratio exceeds 10 times.
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Edelman, Paul H. "Voting power apportionments." Social Choice and Welfare 44, no. 4 (February 1, 2015): 911–25. http://dx.doi.org/10.1007/s00355-015-0869-4.
The inter-comparison of regional air quality models is an effective way to understand uncertainty in ambient pollutant concentrations simulated using various model configurations, as well as to find ways to improve model performance. Based on the outcomes and experiences of Japanese projects thus far, a new model inter-comparison project called Japan’s study for reference air quality modeling (J-STREAM) has begun. The objective of J-STREAM is to establish reference air quality modeling for source apportionment and effective strategy making to suppress secondary air pollutants including PM2.5 and photochemical ozone in Japan through model inter-comparison. The first phase focuses on understanding the ranges and limitations in ambient PM2.5 and ozone concentrations simulated by participants using common input datasets. The second phase focuses on issues revealed in previous studies in simulating secondary inorganic aerosols, as well as on the three-dimensional characteristics of photochemical ozone as a new target. The third phase focuses on comparing source apportionments and sensitivities under heavy air pollution episodes simulated by participating models. Detailed understanding of model performance, uncertainty, and possible improvements to urban-scale air pollution involving secondary pollutants, as well as detailed sector-wise source apportionments over megacities in Japan are expected.
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Yang, Zhiyi, Md Kamrul Islam, Tian Xia, and Stuart Batterman. "Apportionment of PM2.5 Sources across Sites and Time Periods: An Application and Update for Detroit, Michigan." Atmosphere 14, no. 3 (March 20, 2023): 592. http://dx.doi.org/10.3390/atmos14030592.
Identifying sources of air pollutants is essential for informing actions to reduce emissions, exposures, and adverse health impacts. This study updates and extends apportionments of particulate matter (PM2.5) in Detroit, MI, USA, an area with extensive industrial, vehicular, and construction activity interspersed among vulnerable communities. We demonstrate an approach that uses positive matrix factorization models with combined spatially and temporally diverse datasets to assess source contributions, trend seasonal levels, and examine pandemic-related effects. The approach consolidates measurements from 2016 to 2021 collected at three sites. Most PM2.5 was due to mobile sources, secondary sulfate, and secondary nitrate; smaller contributions arose from soil/dust, ferrous and non-ferrous metals, and road salt sources. Several sources varied significantly by season and site. Pandemic-related changes were generally modest. Results of the consolidated models were more consistent with respect to trends and known sources, and the larger sample size should improve representativeness and stability. Compared to earlier apportionments, contributions of secondary sulfate and nitrate were lower, and mobile sources now represent the dominant PM2.5 contributor. We show the growing contribution of mobile sources, the need to update apportionments performed just 5–10 years ago, and that apportionments at a single site may not apply elsewhere in the same urban area, especially for local sources.
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Batista, P. V. G., J. P. Laceby, and O. Evrard. "How to evaluate sediment fingerprinting source apportionments." Journal of Soils and Sediments 22, no. 4 (February 9, 2022): 1315–28. http://dx.doi.org/10.1007/s11368-022-03157-4.
Abstract Purpose Evaluating sediment fingerprinting source apportionments with artificial mixtures is crucial for supporting decision-making and advancing modeling approaches. However, artificial mixtures are rarely incorporated into fingerprinting research and guidelines for model testing are currently lacking. Here, we demonstrate how to test source apportionments using laboratory and virtual mixtures by comparing the results from Bayesian and bootstrapped modeling approaches. Materials and methods Laboratory and virtual mixtures (n = 79) with known source proportions were created with soil samples from two catchments in Fukushima Prefecture, Japan. Soil samples were sieved at 63 µm and analyzed for colorimetric and geochemical parameters. The MixSIAR Bayesian framework and a bootstrapped mixing model (BMM) were used to estimate source contributions to the artificial mixtures. In addition, we proposed and demonstrated the use of multiple evaluation metrics to report on model uncertainty, residual errors, performance, and contingency criteria. Results and discussion Overall, there were negligible differences between source apportionments for the laboratory and virtual mixtures, for both models. The comparison between MixSIAR and BMM illustrated a trade-off between accuracy and precision in the model results. The more certain MixSIAR solutions encompassed a lesser proportion of known source values, whereas the BMM apportionments were markedly less precise. Although model performance declined for mixtures with a single source contributing greater than 0.75 of the material, both models represented the general trends in the mixtures and identified their major sources. Conclusions Virtual mixtures are as robust as laboratory mixtures for assessing fingerprinting mixing models if analytical errors are negligible. We therefore recommend to always include virtual mixtures as part of the model testing process. Additionally, we highlight the value of using evaluation metrics that consider the accuracy and precision of model results, and the importance of reporting uncertainty when modeling source apportionments.
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Argersinger, Peter H. "All Politics Are Local: Another Look at the 1890s." Journal of the Gilded Age and Progressive Era 8, no. 1 (January 2009): 7–24. http://dx.doi.org/10.1017/s1537781400000979.
Although rarely considered by historians, legislative and congressional apportionments were among the most important, absorbing, and contentious political issues of the late nineteenth century. Local, state, and national party leaders struggled to shape apportionments and thereby secure disproportionate influence for the counties, districts, and states their followers controlled. Gerrymanders, in turn, not only distorted representation but often incited a furious opposition, which disrupted legislative bodies, transformed political campaigns, and ultimately produced unprecedented judicial intervention. In surveying these overlooked developments, this essay points to important questions that historians must hereafter address.
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Zhou, Chuanlong, Hao Zhou, Philip K. Hopke, and Thomas M. Holsen. "Overview of the Trajectory-Ensemble Potential Source Apportionment Web (TraPSA-Web) Toolkit for Atmospheric Pollutant Source Identification." Atmosphere 15, no. 2 (January 30, 2024): 176. http://dx.doi.org/10.3390/atmos15020176.
Trajectory ensemble receptor models (TERMs) were widely used to determine the likely source locations and apportionment of air pollutants. This paper describes the development and applications of the Trajectory-ensemble Potential Source Apportionment Web application (TraPSA-Web), a comprehensive toolkit for likely atmospheric pollutant source location apportionments using TERMs and back trajectories generated with the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model. The TERMs integrated within the TraPSA-web include Concentration Field Analysis (CFA), Concentration Weighted Trajectory (CWT), single-site and multiple-site Potential Source Contribution Function (PSCF), and Simplified Quantitative Transport Bias Analysis (SQBA). TraPSA-Web is designed as a web application with a user-friendly modern graphical user interface (GUI), which largely enhances the accessibility to the users. TraPSA-Web will provide the air quality research community with a sophisticated toolkit for (1) easy management of the research project and datasets, (2) efficient automatization for HYSPLIT configurations, calculations, and result aggregations, (3) flexible configurations for the research scenarios and TERM parameters, and (4) interactive visualizations for the pollutant pattern analysis and TERM result mapping.
Hajigholizadeh, Mohammad. "Water Quality Modelling Using Multivariate Statistical Analysis and Remote Sensing in South Florida." FIU Digital Commons, 2016. http://digitalcommons.fiu.edu/etd/2992.
The overall objective of this dissertation research is to understand the spatiotemporal dynamics of water quality parameters in different water bodies of South Florida. Two major approaches (multivariate statistical techniques and remote sensing) were used in this study. Multivariate statistical techniques include cluster analysis (CA), principal component analysis (PCA), factor analysis (FA), discriminant analysis (DA), absolute principal component score-multiple linear regression (APCS-MLR) and PMF receptor modeling techniques were used to assess the water quality and identify and quantify the potential pollution sources affecting the water quality of three major rivers of South Florida. For this purpose, a 15-year (2000–2014) data set of 12 water quality variables, and about 35,000 observations were used. Agglomerative hierarchical CA grouped 16 monitoring sites into three groups (low pollution, moderate pollution, and high pollution) based on their similarity of water quality characteristics. DA, as an important data reduction method, was used to assess the water pollution status and analysis of its spatiotemporal variation. PCA/FA identified potential pollution sources in wet and dry seasons, respectively, and the effective mechanisms, rules, and causes were explained. The APCS-MLR and PMF models apportioned their contributions to each water quality variable.
Also, the bio-physical parameters associated with the water quality of the two important water bodies of Lake Okeechobee and Florida Bay were investigated based on remotely sensed data. The principal objective of this part of the study is to monitor and assess the spatial and temporal changes of water quality using the application of integrated remote sensing, GIS data, and statistical techniques. The optical bands in the region from blue to near infrared and all the possible band ratios were used to explore the relation between the reflectance of a waterbody and observed data. The developed MLR models appeared to be promising for monitoring and predicting the spatiotemporal dynamics of optically active and inactive water quality characteristics in Lake Okeechobee and Florida Bay. It is believed that the results of this study could be very useful to local authorities for the control and management of pollution and better protection of water quality in the most important water bodies of South Florida.
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Crow, Mason W. "Multiple sensor credit apportionment." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2002. http://library.nps.navy.mil/uhtbin/hyperion-image/02Jun%5FCrow.pdf.
Wagener, Andreas. "Evolutionary Tax Competition with Formulary Apportionment." WU Vienna University of Economics and Business, Universität Wien, 2017. http://epub.wu.ac.at/5899/1/SSRN%2Did3078969.pdf.
Evolutionary stability is a necessary condition for imitative dynamics of policy learning
and innovation to come to a rest. We apply this concept to profit tax competition
in a regime where a common and consolidated profit tax base for multi-jurisdictional
firms is divided among governments by means of formulary apportionment. In evolutionary
play, governments exhibit aggregate-taking behavior: when comparing
their performance with others, they ignore their impact on the consolidated tax
base. Consequently, evolutionarily stable tax rates are less efficient than tax rates
in best-response tax competition. Series: WU International Taxation Research Paper Series
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Maier, Sebastian. "Biproportional apportionment methods : constraints, algorithms, and simulation /." München : Verl. Dr. Hut, 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=017317892&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
Carter-Brown, Clinton Geoffrey. "Voltage drop apportionment in Eskom's distribution networks." Master's thesis, University of Cape Town, 2002. http://hdl.handle.net/11427/5258.
Laurie, Elizabeth Helen. "Source apportionment of urban atmospheric polycyclic aromatic hydrocarbons." Thesis, University of Birmingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.273558.
Muir, David. "Source apportionment of PMâ‚â‚€ during pollution episodes." Thesis, University of the West of England, Bristol, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274699.
We describe a method to estimate pollution profiles and contribution levels for distinct prominent pollution sources in a region based on daily pollutant concentration measurements from multiple measurement stations over a period of time. In an extension of existing work, we will estimate common source profiles but distinct contribution levels based on measurements from each station. In addition, we will explore the possibility of extending existing work to allow adjustments for synoptic regimes—large scale weather patterns which may effect the amount of pollution measured from individual sources as well as for particular pollutants. For both extensions we propose Bayesian methods to estimate pollution source profiles and contributions.
Evans, Eric J. Tithes: Maps, apportionments and the 1836 Act : a guide for local historians. 3rd ed. Salisbury: British Association for Local History, 1997.
United States. Office of the Special Inspector General for Iraq Reconstruction. Iraq Relief and Reconstruction Fund 1: Report on apportionments, expenditures, and canceled funds. Arlington, VA: Office of the Special Inspector General for Iraq Reconstruction, 2011.
California. Legislature. Assembly. Committee on Transportation. Assembly Transportation Committee hearing on gas tax apportionments: Counties, October 17, 1985, Fresno, California. [Sacramento, Calif.]: The Committee, 1986.
North Yorkshire (England). County Record Office. Parish registers, census returns, land tax returns, tithe apportionments, enclosure awards in the North Yorkshire County Record Office. [Northallerton]: North Yorkshire County Council, 1988.
United States. Office of the Special Inspector General for Iraq Reconstruction. Iraq Relief and Reconstruction Fund 2: Report on apportionments, expenditures, and status at end of fiscal year 2010. Arlington, VA: Office of the Special Inspector General for Iraq Reconstruction, 2011.
North Yorkshire County Record Office. Parish registers, census returns, land tax returns, tithe apportionments, enclosure awards in the North Yorkshire County Record Office. Northallerton: North Yorkshire County Record Office, 2000.
Gambarelli, Gianfranco, and Arsen Palestini. "Minimax Multi-District Apportionments." In Power, Voting, and Voting Power: 30 Years After, 169–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35929-3_10.
Cegiełka, Katarzyna, Piotr Dniestrzański, Janusz Łyko, Arkadiusz Maciuk, and Radosław Rudek. "On Ordering a Set of Degressively Proportional Apportionments." In Transactions on Computational Collective Intelligence XXVII, 53–62. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70647-4_4.
Helgason, Thorkell, Kurt Jörnsten, and Athanasios Migdalas. "Maxmin Formulation of the Apportionments of Seats to a Parliament." In Nonconvex Optimization and Its Applications, 109–18. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4613-3557-3_7.
El-Helaly, Sherif. "Apportionment." In The Mathematics of Voting and Apportionment, 159–250. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14768-6_3.
Smith, Douglas. "Apportionment Politics, 1920-70." In A Companion to California History, 375–90. Oxford, UK: John Wiley & Sons, Ltd, 2013. http://dx.doi.org/10.1002/9781444305036.ch22.
Misra, Sanghamitra. "The Apportionment of Sovereignty." In The Long Conquest, 136–78. London: Routledge India, 2024. http://dx.doi.org/10.4324/9781032619163-5.
El-Helaly, Sherif. "Social Choice." In The Mathematics of Voting and Apportionment, 1–114. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14768-6_1.
El-Helaly, Sherif. "Yes-No Voting." In The Mathematics of Voting and Apportionment, 115–57. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14768-6_2.
Тези доповідей конференцій з теми "Apportionments":
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Bolun, Ion. "Generating of hamilton full favoring apportionments." In International Scientific Conference “30 Years of Economic Reforms in the Republic of Moldova: Economic Progress via Innovation and Competitiveness”. Academy of Economic Studies of Moldova, 2022. http://dx.doi.org/10.53486/9789975155663.22.
Aspects of full favoring of small beneficiaries in apportionments using Hamilton method are discussed. For this purpose, the requirements of full favoring Hamilton apportionments were defined and the AHS algorithm for determining such apportionments is described. Then, calculations which confirm the opportunity of using the AHS algorithm in this aim were performed.
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Konstantinov, M. M., G. B. Pelova, and K. D. Yanev. "Plain apportionments: History, paradoxes, generalizations, new methods." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'14). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902460.
Yang, Wenbo, Xiaodong Liu, and Fumin Lei. "Apportionment Game." In 2010 International Conference on E-Product E-Service and E-Entertainment (ICEEE 2010). IEEE, 2010. http://dx.doi.org/10.1109/iceee.2010.5660474.
Saruç, Naci Tolga, İsa Sağbaş, and Recep Yorulmaz. "The Impact of Tax Apportionment on Fiscal Equalization: A Case Study of Turkish Metropolitan Municipalities." In International Conference on Eurasian Economies. Eurasian Economists Association, 2017. http://dx.doi.org/10.36880/c09.01968.
As a monthly basis, 6% of tax revenues collected within provincial borders is allocated by central government as fiscal transfers to 30 metropolitan municipalities of Turkey. These transfers are the most important external revenue of the metropolitan municipalities. The fact that metropolitan cities have a different level of wealth causes the difference between the amounts of taxes collected in the provinces. The lack of tax apportionment policy further increases the disparity of fiscal transfers, since a significant part of major taxes are collected in a few metropolitan cities. In this study, a simulation of tax apportionment is carried out. Taxes and fiscal transfers before and after tax apportionment are compared. Inequality measures (e.g. Gini coefficient) show that fiscal equalization is promoted after tax apportionment.
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Hay, Simon, and Andrew Rice. "The case for apportionment." In the First ACM Workshop. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1810279.1810283.
Cembrano, Javier, José Correa, and Victor Verdugo. "Multidimensional Apportionment through Discrepancy Theory." In EC '21: The 22nd ACM Conference on Economics and Computation. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3465456.3467596.
Schäbe, H. "SIL apportionment and SIL allocation." In The 2nd International Conference on Engineering Sciences and Technologies. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742: CRC Press, 2017. http://dx.doi.org/10.1201/9781315210469-427.
Ilić, Danijela, and Vule Mizdraković. "Risks of Property Value Apportionment." In Finiz 2016. Belgrade, Serbia: Singidunum University, 2016. http://dx.doi.org/10.15308/finiz-2016-125-129.
Bredereck, Robert, Piotr Faliszewski, Michal Furdyna, Andrzej Kaczmarczyk, and Martin Lackner. "Strategic Campaign Management in Apportionment Elections." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/15.
In parliamentary elections, parties compete for a limited, typically fixed number of seats. We study the complexity of the following bribery-style problem: Given the distribution of votes among the parties, what is the smallest number of voters that need to be convinced to vote for our party, so that it gets a desired number of seats. We also run extensive experiments on real-world election data and measure the effectiveness of our method.
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Addabbo, Tommaso, Francesco Bertocci, Ada Fort, Marco Mugnaini, Valerio Vignoli, Santina Rocchi, and Luay Shahin. "HMM used for component parameters apportionment." In 2014 11th International Multi-Conference on Systems, Signals & Devices (SSD). IEEE, 2014. http://dx.doi.org/10.1109/ssd.2014.6808818.
Furbish, Glenn, David Childress, and George Salvatierra. Iraq Relief and Reconstruction Fund 2: Report on Apportionments, Expenditures, and Status at End of Fiscal Year 2010. Fort Belvoir, VA: Defense Technical Information Center, April 2011. http://dx.doi.org/10.21236/ada545424.
Day, Robert, George White, William Cook, M. Bryant, and Robert Miller. Joint Materiel Apportionment and Allocation. Fort Belvoir, VA: Defense Technical Information Center, July 1988. http://dx.doi.org/10.21236/ada199037.
Hines, James. Income Misattribution under Formula Apportionment. Cambridge, MA: National Bureau of Economic Research, July 2009. http://dx.doi.org/10.3386/w15185.
Stockton, R. C. Some Effects of Weapons Technology on Air Apportionment. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada392063.
Goolsbee, Austan, and Edward Maydew. Coveting Thy Neighbor's Manuafacturing: The Dilemma of State Income Apportionment. Cambridge, MA: National Bureau of Economic Research, June 1998. http://dx.doi.org/10.3386/w6614.
McLure, Charles, and Walter Hellerstein. Does Sales-only Apportionment of Corporate Income Violate the GATT? Cambridge, MA: National Bureau of Economic Research, July 2002. http://dx.doi.org/10.3386/w9060.
Harley, N. H. Measurement and apportionment of radon source terms for modeling indoor environments. Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/5983014.
Harley, N. H. Measurement and apportionment of radon source terms for modeling indoor environments. Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/6529453.
Harley, N. H. Measurement and apportionment of radon source terms for modeling indoor environments. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/6537543.
Williams, A. Apportionment of multiple aerosol size distributions modes using factor analysis techniques. Office of Scientific and Technical Information (OSTI), December 1990. http://dx.doi.org/10.2172/10127131.
