Statistical mechanics of voting

Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We formulate natural political/social questions about the expected complexity of a voting rule and degree of cohesion/diversity among agents in terms of random matrix models---ensembles of statistical mechanics models---and compute quantitative answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context

Design and evaluation of a voting tool in a collaborative environment

This dissertation researchdesigned, implemented, and evaluated a Web-based Dynamic Voting Toolfor small group decision-making in a collaborative environment. In this dissertation, theliterature on voting tools in current GDSS research is presented. Variousvoting theories and methods are analyzed, and the advantages and weaknessesare compared, so as to gain a better understanding of how to apply thesedifferent voting methods to diverse decision-making situations. A briefoverview of scaling theories is also given, with an emphasis on Thurstone\u27sLaw. The basic features of someweb-based voting tool implementations are reviewed along with a discussionof the pros and cons of Intemet voting. A discussion of Human DynamicVoting (HDV) follows; HDV allows multiple voting and continuous feedbackin a group process. The Dynamic Voting Tool designed and developed bythe author (i.e., Zheng Li) integrated multiple scaling and voting methods,and supported dynamic voting. Its features, user feedback, and futureimprovements are further discussed. A controlled experiment wasconducted to evaluate the effects of the Dynamic Voting Tool (alongwith the List Gathering Tool by Yuanqiong Wang) interacting with smallgroup process. The design and procedures of the experiment, and thedata analysis results extracted from 187 student subjects from New JerseyInstitute of Technology are reported. While the System Survey yieldedvery positive feedback on the voting tool, the hypotheses tested bythe Post-Questionnaire and expert judgments showed no major positivesignificant results. This was probably due to the complexity of thetask and procedures, lack of motivation of the subjects, bad timing,insufficient training, and uneven distribution of subjects, etc. Several field studies usingthe Social Decision Support System (SDSS) Toolkit (List Gathering Tool+ Dynamic Voting Tool) are presented. The SDSS system worked well whenthe subjects were motivated. The field studies show that the toolkitcan be used in course evaluations, or other practical applications. Finally, it is suggestedthat future research can focus on improving the voting tool with truedynamic features, exploring more issues on SDSS systems design and experimentation,and exploring the relationship of voting and GSS

Parliamentary Voting Procedures: Agenda Control, Manipulation, and Uncertainty

We study computational problems for two popular parliamentary voting procedures: the amendment procedure and the successive procedure. While finding successful manipulations or agenda controls is tractable for both procedures, our real-world experimental results indicate that most elections cannot be manipulated by a few voters and agenda control is typically impossible. If the voter preferences are incomplete, then finding which alternatives can possibly win is NP-hard for both procedures. Whilst deciding if an alternative necessarily wins is coNP-hard for the amendment procedure, it is polynomial-time solvable for the successive one

Aggregating Dependency Graphs into Voting Agendas in Multi-Issue Elections

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections

Computational Aspects of Multi-Winner Approval Voting

We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots from the other agents

Ethics of e-voting: an essay on requirements and values in Internet elections

In this paper, we investigate ethical issues involved in the development and implementation of Internet voting technology. From a phenomenological perspective, we describe how voting via the Internet mediates the relation between people and democracy. In this relation, trust plays a major role. The dynamics of trust in the relation between people and their world forms the basis for our analysis of the ethical issues involved. First, we consider established principles of voting, confirming the identity of our democracy, which function as expectations in current experiments with online voting in the Netherlands. We investigate whether and how Internet voting can meet these expectations and thereby earn trust, based on the experiments in the Netherlands. We identify major challenges, and provide a basis for ethical and political discussion on these issues, especially the changed relation between public and private. If we decide that we want to vote via the Internet, more practical matters come into play in the implementation of the technology. The choices involved here are discussed in relation to the mediating role of concrete voting technologies in the relation between citizen and state