The Inverse Shapley Value Problem

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice theory as a measure of the "influence" of voters. The \emph{Inverse Shapley Value Problem} is the problem of designing a weighted voting scheme which (approximately) achieves a desired input vector of values for the Shapley-Shubik indices. Despite much interest in this problem no provably correct and efficient algorithm was known prior to our work. We give the first efficient algorithm with provable performance guarantees for the Inverse Shapley Value Problem. For any constant \eps > 0 our algorithm runs in fixed poly$(n)$ time (the degree of the polynomial is independent of \eps) and has the following performance guarantee: given as input a vector of desired Shapley values, if any "reasonable" weighted voting scheme (roughly, one in which the threshold is not too skewed) approximately matches the desired vector of values to within some small error, then our algorithm explicitly outputs a weighted voting scheme that achieves this vector of Shapley values to within error \eps. If there is a "reasonable" voting scheme in which all voting weights are integers at most \poly(n) that approximately achieves the desired Shapley values, then our algorithm runs in time \poly(n) and outputs a weighted voting scheme that achieves the target vector of Shapley values to within error $\eps=n^{-1/8}.

Impact of gameplay vs. reading on mental models of social-ecological systems: a fuzzy cognitive mapping approach

Climate change is a highly complex social-ecological problem characterized by system-type dynamics that are important to communicate in a variety of settings, ranging from formal education to decision makers to informal education of the general public. Educational games are one approach that may enhance systems thinking skills. This study used a randomized controlled experiment to compare the impact on the mental models of participants of an educational card game vs. an illustrated article about the Arctic social-ecological system. A total of 41 participants (game: n = 20; reading: n = 21) created pre- and post-intervention mental models of the system, based on a "fuzzy cognitive mapping" approach. Maps were analyzed using network statistics. Both reading the article and playing the game resulted in measurable increases in systems understanding. The group reading the article perceived a more complex system after the intervention, with overall learning gains approximately twice those of the game players. However, game players demonstrated similar learning gains as article readers regarding the climate system, actions both causing environmental problems and protecting the Arctic, as well as the importance of the base- and mid-levels of the food chain. These findings contribute to the growing evidence showing that games are important resources to include as strategies for building capacity to understand and steward sustainable social-ecological systems, in both formal and informal education

“Stickier” learning through gameplay: an effective approach to climate change education

As the impacts of climate change grow, we need better ways to raise awareness and motivate action. Here we assess the effectiveness of an Arctic climate change card game in comparison with the more conventional approach of reading an illustrated article. In-person assessments with control/reading and treatment/game groups (N = 41), were followed four weeks later with a survey. The game was found to be as effective as the article in teaching content of the impacts of climate change over the short term, and was more effective than the article in long-term retention of new information. Game players also had higher levels of engagement and perceptions that they knew ways to help protect Arctic ecosystems. They were also more likely to recommend the game to friends or family than those in the control group were likely to recommend the article to friends or family. As we consider ways to broaden engagement with climate change, we should include games in our portfolio of approaches

False-Name Manipulation in Weighted Voting Games is Hard for Probabilistic Polynomial Time

False-name manipulation refers to the question of whether a player in a weighted voting game can increase her power by splitting into several players and distributing her weight among these false identities. Analogously to this splitting problem, the beneficial merging problem asks whether a coalition of players can increase their power in a weighted voting game by merging their weights. Aziz et al. [ABEP11] analyze the problem of whether merging or splitting players in weighted voting games is beneficial in terms of the Shapley-Shubik and the normalized Banzhaf index, and so do Rey and Rothe [RR10] for the probabilistic Banzhaf index. All these results provide merely NP-hardness lower bounds for these problems, leaving the question about their exact complexity open. For the Shapley--Shubik and the probabilistic Banzhaf index, we raise these lower bounds to hardness for PP, "probabilistic polynomial time", and provide matching upper bounds for beneficial merging and, whenever the number of false identities is fixed, also for beneficial splitting, thus resolving previous conjectures in the affirmative. It follows from our results that beneficial merging and splitting for these two power indices cannot be solved in NP, unless the polynomial hierarchy collapses, which is considered highly unlikely

Limitations of Majority Agreement in Crowdsourced Image Interpretation

Crowdsourcing can efficiently complete tasks that are difficult to automate, but the quality of crowdsourced data is tricky to evaluate. Algorithms to grade volunteer work often assume that all tasks are similarly difficult, an assumption that is frequently false. We use a cropland identification game with over 2,600 participants and 165,000 unique tasks to investigate how best to evaluate the difficulty of crowdsourced tasks and to what extent this is possible based on volunteer responses alone. Inter-volunteer agreement exceeded 90% for about 80% of the images and was negatively correlated with volunteer-expressed uncertainty about image classification. A total of 343 relatively difficult images were independently classified as cropland, non-cropland or impossible by two experts. The experts disagreed weakly (one said impossible while the other rated as cropland or non-cropland) on 27% of the images, but disagreed strongly (cropland vs. non-cropland) on only 7%. Inter-volunteer disagreement increased significantly with inter-expert disagreement. While volunteers agreed with expert classifications for most images, over 20% would have been mis-categorized if only the volunteers’ majority vote was used. We end with a series of recommendations for managing the challenges posed by heterogeneous tasks in crowdsourcing campaigns

Developing a framework for the analysis of power through depotentia

Stakeholder participation in tourism policy-making is usually perceived as providing a means of empowerment. However participatory processes drawing upon stakeholders from traditionally empowered backgrounds may provide the means of removing empowerment from stakeholders. Such an outcome would be in contradiction to the claims that participatory processes improve both inclusivity and sustainability. In order to form an understanding of the sources through which empowerment may be removed, an analytical perspective has been developed deriving from Lukes�s views of power dating from 1974. This perspective considers the concept of depotentia as the removal of �power to� without speculating upon the underlying intent and also provides for the multidimensionality of power to be examined within a single study. The application of this analytical perspective has been tested upon findings of the government-commissioned report of the Countryside and Community Research Unit in 2005. The survey and report investigated the progress of Local Access Forums in England created in response to the Countryside and Rights of Way Act 2000. Consideration of the data from this perspective permits the classification of individual sources of depotentia which can each be addressed and potentially enable stakeholder groups to reverse loss of empowerment where it has occurred

Understanding pregnancy planning in a low-income country setting: validation of the London measure of unplanned pregnancy in Malawi

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: The London Measure of Unplanned Pregnancy (LMUP) is a new and psychometrically valid measure of pregnancy intention that was developed in the United Kingdom. An improved understanding of pregnancy intention in low-income countries, where unintended pregnancies are common and maternal and neonatal deaths are high, is necessary to inform policies to address the unmet need for family planning. To this end this research aimed to validate the LMUP for use in the Chichewa language in Malawi.Methods: Three Chichewa speakers translated the LMUP and one translation was agreed which was back-translated and pre-tested on five pregnant women using cognitive interviews. The measure was field tested with pregnant women who were recruited at antenatal clinics and data were analysed using classical test theory and hypothesis testing.Results: 125 women aged 15-43 (median 23), with parities of 1-8 (median 2) completed the Chichewa LMUP. There were no missing data. The full range of LMUP scores was captured. In terms of reliability, the scale was internally consistent (Cronbach's alpha = 0.78) and test-retest data from 70 women showed good stability (weighted Kappa 0.80). In terms of validity, hypothesis testing confirmed that unmarried women (p = 0.003), women who had four or more children alive (p = 0.0051) and women who were below 20 or over 29 (p = 0.0115) were all more likely to have unintended pregnancies. Principal component analysis showed that five of the six items loaded onto one factor, with a further item borderline. A sensitivity analysis to assess the effect of the removal of the weakest item of the scale showed slightly improved performance but as the LMUP was not significantly adversely affected by its inclusion we recommend retaining the six-item score.Conclusion: The Chichewa LMUP is a valid and reliable measure of pregnancy intention in Malawi and can now be used in research and/or surveillance. This is the first validation of this tool in a low-income country, helping to demonstrate that the concept of pregnancy planning is applicable in such a setting. Use of the Chichewa LMUP can enhance our understanding of pregnancy intention in Malawi, giving insight into the family planning services that are required to better meet women's needs and save lives. © 2013 Hall et al.; licensee BioMed Central Ltd.Dr Hall’s Wellcome Trust Research Training Fellowship, grant number 097268/Z/11/Z

Novel diffusion mechanism on the GaAs(001) surface: the role of adatom-dimer interaction

Employing first principles total energy calculations we have studied the behavior of Ga and Al adatoms on the GaAs(001)-beta2 surface. The adsorption site and two relevant diffusion channels are identified. The channels are characterized by different adatom-surface dimer interaction. Both affect in a novel way the adatom migration: in one channel the diffusing adatom jumps across the surface dimers and leaves the dimer bonds intact, in the other one the surface dimer bonds are broken. The two channels are taken into account to derive effective adatom diffusion barriers. From the diffusion barriers we conclude a strong diffusion anisotropy for both Al and Ga adatoms with the direction of fastest diffusion parallel to the surface dimers. In agreement with experimental observations we find higher diffusion barriers for Al than for Ga.Comment: 4 pages, 2 figures, Phys. Rev. Lett. 79 (1997). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Superconductivity in Cu_xTiSe_2

Charge density waves (CDWs) are periodic modulations of the conduction electron density in solids. They are collective states that arise from intrinsic instabilities often present in low dimensional electronic systems. The layered dichalcogenides are the most well-studied examples, with TiSe_2 one of the first CDW-bearing materials known. The competition between CDW and superconducting collective electronic states at low temperatures has long been held and explored, and yet no chemical system has been previously reported where finely controlled chemical tuning allows this competition to be studied in detail. Here we report how, upon controlled intercalation of TiSe_2 with Cu to yield Cu_xTiSe_2, the CDW transition is continuously suppressed, and a new superconducting state emerges near x = 0.04, with a maximum T_c of 4.15 K found at x = 0.08. Cu_xTiSe_2 thus provides the first opportunity to study the CDW to Superconductivity transition in detail through an easily-controllable chemical parameter, and will provide new insights into the behavior of correlated electron systems.Comment: Accepted to Nature Physic

Estimation, planning, and mapping for autonomous flight using an RGB-D camera in GPS-denied environments

RGB-D cameras provide both color images and per-pixel depth estimates. The richness of this data and the recent development of low-cost sensors have combined to present an attractive opportunity for mobile robotics research. In this paper, we describe a system for visual odometry and mapping using an RGB-D camera, and its application to autonomous flight. By leveraging results from recent state-of-the-art algorithms and hardware, our system enables 3D flight in cluttered environments using only onboard sensor data. All computation and sensing required for local position control are performed onboard the vehicle, reducing the dependence on an unreliable wireless link to a ground station. However, even with accurate 3D sensing and position estimation, some parts of the environment have more perceptual structure than others, leading to state estimates that vary in accuracy across the environment. If the vehicle plans a path without regard to how well it can localize itself along that path, it runs the risk of becoming lost or worse. We show how the belief roadmap algorithm prentice2009belief, a belief space extension of the probabilistic roadmap algorithm, can be used to plan vehicle trajectories that incorporate the sensing model of the RGB-D camera. We evaluate the effectiveness of our system for controlling a quadrotor micro air vehicle, demonstrate its use for constructing detailed 3D maps of an indoor environment, and discuss its limitations.United States. Office of Naval Research (Grant MURI N00014-07-1-0749)United States. Office of Naval Research (Science of Autonomy Program N00014-09-1-0641)United States. Army Research Office (MAST CTA)United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1052)National Science Foundation (U.S.) (Contract IIS-0812671)United States. Army Research Office (Robotics Consortium Agreement W911NF-10-2-0016)National Science Foundation (U.S.). Division of Information, Robotics, and Intelligent Systems (Grant 0546467