36,814 research outputs found

    On the complexity of problems on simple games

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    Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes–no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand, each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games. This analysis as usual depends on the game representation used as input. We consider four natural explicit representations: winning, losing, minimal winning, and maximal losing. We first analyze the complexity of testing whether a game is simple and testing whether a game is weighted. We show that, for the four types of representations, both problems can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. We analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game. We finalize with some considerations on the possibility of representing a game in a more succinct representation showing a natural representation in which the recognition problem is hard.Preprin

    Network-Based Vertex Dissolution

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    We introduce a graph-theoretic vertex dissolution model that applies to a number of redistribution scenarios such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the deletion of certain vertices and the redistribution of their load to neighboring vertices in a completely balanced way. We investigate how the underlying graph structure, the knowledge of which vertices should be deleted, and the relation between old and new vertex loads influence the computational complexity of the underlying graph problems. Our results establish a clear borderline between tractable and intractable cases.Comment: Version accepted at SIAM Journal on Discrete Mathematic

    Universal Voting Protocol Tweaks to Make Manipulation Hard

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    Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. A number of recent papers study the complexity of manipulating existing protocols. This paper is the first work to take the next step of designing new protocols that are especially hard to manipulate. Rather than designing these new protocols from scratch, we instead show how to tweak existing protocols to make manipulation hard, while leaving much of the original nature of the protocol intact. The tweak studied consists of adding one elimination preround to the election. Surprisingly, this extremely simple and universal tweak makes typical protocols hard to manipulate! The protocols become NP-hard, #P-hard, or PSPACE-hard to manipulate, depending on whether the schedule of the preround is determined before the votes are collected, after the votes are collected, or the scheduling and the vote collecting are interleaved, respectively. We prove general sufficient conditions on the protocols for this tweak to introduce the hardness, and show that the most common voting protocols satisfy those conditions. These are the first results in voting settings where manipulation is in a higher complexity class than NP (presuming PSPACE \neq NP)

    Approval-Based Shortlisting

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    Shortlisting is the task of reducing a long list of alternatives to a (smaller) set of best or most suitable alternatives from which a final winner will be chosen. Shortlisting is often used in the nomination process of awards or in recommender systems to display featured objects. In this paper, we analyze shortlisting methods that are based on approval data, a common type of preferences. Furthermore, we assume that the size of the shortlist, i.e., the number of best or most suitable alternatives, is not fixed but determined by the shortlisting method. We axiomatically analyze established and new shortlisting methods and complement this analysis with an experimental evaluation based on biased voters and noisy quality estimates. Our results lead to recommendations which shortlisting methods to use, depending on the desired properties

    Manipulating Tournaments in Cup and Round Robin Competitions

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    In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal number of games that need to be thrown to manipulate the result can also be determined in polynomial time. Finally, we show that there are several different variations of standard cup competitions where manipulation remains polynomial.Comment: Proceedings of Algorithmic Decision Theory, First International Conference, ADT 2009, Venice, Italy, October 20-23, 200

    The Importance of Parties and Party System Institutionalization in New Democracies

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    This paper discusses the importance of parties and party systems in new democracies. Scholars have long touted the importance of political parties and stable party system for new democracies, which are in the process of consolidating their regimes. Robert Dix writes that ?institutionalization of parties and party systems is crucial in the maintenance of the tenuous new democracies.? (1992, p. 490). Recently, anti-system politicians have been on the rise, political parties have been heavily attacked and associated with ?old politics? and party fragmentation has increased. Scholars have asked whether or not you can have democracy without political parties. This paper focuses on how important parties are to functioning democracies, and also highlights the importance of stable party systems to new democracies

    The effective number of relevant parties : how voting power improves Laakso-Taagepera’s index

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    This paper proposes a new method to evaluate the number of rel- evant parties in an assembly. The most widespread indicator of frag- mentation used in comparative politics is the ‘Effective Number of Par- ties’(ENP), designed by Laakso and Taagepera (1979). Taking both the number of parties and their relative weights into account, the ENP is arguably a good parsimonious operationalization of the number of ‘relevant’ parties. This index however produces misleading results in single-party ma jority situations as it still indicates that more than one party is relevant in terms of government formation. We propose to modify the ENP formula by replacing proportions of seats by voting power measures. This improved index behaves more in line with Sar- tori’s definition of relevance, without requiring additional information in its construction.Voting power indices; Effective Number of Parties; Party system fragmentation; Relevance; Coalition Formation
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