Voting with Rank Dependent Scoring Rules

This article examines strategic elements of voter behaviour in parliamentary elections where the voting method is a scoring rule other than plurality: the Borda Count, which is used for the election of ethnic minorities in Slovenia, and the Dowdall rule, which is used in the Pacific island state of Nauru in multi-seat districts. After first examining the general properties of scoring rules, and generating theoretical differences between the two rules, we look at empirical evidence from Nauru and Slovenia. This casts a doubt on predictions based simply on a voting rule's mathematical properties and on the accuracy of assumptions of sincere rank ordering.本文研究了议会选举投票者行为的策略因素。议会选举中的投票方法是一个有别于多数法的计分法则：斯洛文尼亚少数族群选举使用的波达计数法；太平洋岛屿国家瑙鲁多席位选区使用的斗多尔法则。作者首先分析了计分法则的一般属性，并对两种法则做了理论区分。然后研究了瑙鲁和斯洛文尼亚的实证资料。作者对仅仅基于投票规则数学属性的预测以及有关纯粹排行假设的精确性表示了质疑。

The margin of victory of an election, defined as the smallest number k such that k voters can change the winner by voting differently, is an important measurement for robustness of the election outcome. It also plays an important role in implementing efficient post-election audits, which has been widely used in the United States to detect errors or fraud caused by malfunctions of electronic voting machines.

When scheduling public works or events in a shared facility one needs to accommodate preferences of a population. We formalize this problem by introducing the notion of a collective schedule. We show how to extend fundamental tools from social choice theory - positional scoring rules, the Kemeny rule and the Condorcet principle - to collective scheduling. We study the computational complexity of finding collective schedules. We also experimentally demonstrate that optimal collective schedules can be found for instances with realistic sizes.

Election databases are the main elements of a recently introduced framework that aims to create bridges between the computational social choice and the data management communities. An election database consists of incomplete information about the preferences of voters, in the form of partial orders, alongside with standard database relations that provide contextual information. Earlier work in computational social choice focused on the computation of possible winners and necessary winners that are determined by the available incomplete information and the voting rule at hand. The presence of the relational context, however, permits the formulation of sophisticated queries about voting rules, candidates, potential winners, issues, and positions on issues. Such queries can be given possible answer semantics and necessary answer semantics on an election database, where the former means that the query is true on some completion of the given partial orders and the latter means that the query is true on every such completion. %In this paper, łooseness = -1 We carry out a systematic investigation of query evaluation on election databases by analyzing how the interaction between the partial preferences, the voting rules and the relational context impacts on the complexity of query evaluation. To this effect, we focus on positional scoring rules and unions of conjunctive queries. We establish a number of results that delineate the complexity of the possible answers and of the necessary answers for different positional scoring rules and for various classes of unions of conjunctive queries. Furthermore, we show that query evaluation is fixed-parameter tractable, where the parameter is the number of candidates in the election.

We study the complexity of estimating the probability of an outcome in an election over probabilistic votes. The focus is on voting rules expressed as positional scoring rules, and two models of probabilistic voters: the uniform distribution over the completions of a partial voting profile (consisting of a partial ordering of the candidates by each voter), and the Repeated Insertion Model (RIM) over the candidates, including the special case of the Mallows distribution. Past research has established that, while exact inference of the probability of winning is computationally hard (#P-hard), an additive polynomial-time approximation (additive FPRAS) is attained by sampling and averaging. There is often, though, a need for multiplicative approximation guarantees that are crucial for important measures such as conditional probabilities. Unfortunately, a multiplicative approximation of the probability of winning cannot be efficient (under conventional complexity assumptions) since it is already NP-complete to determine whether this probability is nonzero. Contrastingly, we devise multiplicative polynomial-time approximations (multiplicative FPRAS) for the probability of the complement event, namely, losing the election.

Committee scoring voting rules are multiwinner analogues of positional scoring rules, which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top- k -counting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k -Approval Chamberlin--Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.