scholarly journals Even More Effort Towards Improved Bounds and Fixed-Parameter Tractability for Multiwinner Rules

2021 ◽  
Author(s):  
Sushmita Gupta ◽  
Pallavi Jain ◽  
Saket Saurabh ◽  
Nimrod Talmon
Keyword(s):  
Weighted Average ◽  
Scoring Rules ◽  
Voting Rules ◽  
Voter Preferences ◽  
Voting Rule ◽  
The Family ◽  
Fixed Parameter ◽  
Real World Applications ◽  
Ordered Weighted Average ◽  
Fruitful Research

Multiwinner elections have proven to be a fruitful research topic with many real world applications. We contribute to this line of research by improving the state of the art regarding the computational complexity of computing good committees. More formally, given a set of candidates C, a set of voters V, each ranking the candidates according to their preferences, and an integer k; a multiwinner voting rule identifies a committee of size k, based on these given voter preferences. In this paper we consider several utilitarian and egailitarian OWA (ordered weighted average) scoring rules, which are an extensively researched family of rules (and a subfamily of the family of committee scoring rules). First, we improve the result of Betzler et al. [JAIR, 2013], which gave a O(n^n) algorithm for computing winner under the Chamberlin Courant rule (CC), where n is the number of voters; to a running time of O(2^n), which is optimal. Furthermore, we study the parameterized complexity of the Pessimist voting rule and describe a few tractable and intractable cases. Apart from such utilitarian voting rules, we extend our study and consider egalitarian median and egalitarian mean (both committee scoring rules), showing some tractable and intractable results, based on nontrivial structural observations.

scholarly journals Parameterized Algorithms for Finding a Collective Set of Items

2020 ◽  
Vol 34 (02) ◽  
pp. 1838-1845
Author(s):  
Robert Bredereck ◽  
Piotr Faliszewski ◽  
Andrzej Kaczmarczyk ◽  
Dušan Knop ◽  
Rolf Niedermeier
Keyword(s):  
Parameterized Complexity ◽  
Weighted Average ◽  
Fixed Parameter Tractability ◽  
Parameterized Algorithms ◽  
Utility Value ◽  
Average Operator ◽  
Fixed Parameter ◽  
Ordered Weighted Average ◽  
Integer Weight

We extend the work of Skowron et al. (AIJ, 2016) by considering the parameterized complexity of the following problem. We are given a set of items and a set of agents, where each agent assigns an integer utility value to each item. The goal is to find a set of k items that these agents would collectively use. For each such collective set of items, each agent provides a score that can be described using an OWA (ordered weighted average) operator and we seek a set with the highest total score. We focus on the parameterization by the number of agents and we find numerous fixed-parameter tractability results (however, we also find some W[1]-hardness results). It turns out that most of our algorithms even apply to the setting where each agent has an integer weight.

scholarly journals Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud

2020 ◽  
Vol 34 (02) ◽  
pp. 1870-1877
Author(s):  
Matteo Castiglioni ◽  
Andrea Celli ◽  
Nicola Gatti
Keyword(s):  
Utility Function ◽  
Natural Question ◽  
Voting Rules ◽  
Expected Return ◽  
Fixed Parameter Tractable ◽  
The Public ◽  
Voting Rule ◽  
Private Signals ◽  
Fixed Parameter ◽  
Public Signals

We focus on the following natural question: is it possible to influence the outcome of a voting process through the strategic provision of information to voters who update their beliefs rationally? We investigate whether it is computationally tractable to design a signaling scheme maximizing the probability with which the sender's preferred candidate is elected. We resort to the model recently introduced by Arieli and Babichenko (2019) (i.e., without inter-agent externalities), and focus on, as illustrative examples, k-voting rules and plurality voting. There is a sharp contrast between the case in which private signals are allowed and the more restrictive setting in which only public signals are allowed. In the former, we show that an optimal signaling scheme can be computed efficiently both under a k-voting rule and plurality voting. In establishing these results, we provide two contributions applicable to general settings beyond voting. Specifically, we extend a well-known result by Dughmi and Xu (2017) to more general settings and prove that, when the sender's utility function is anonymous, computing an optimal signaling scheme is fixed-parameter tractable in the number of receivers' actions. In the public signaling case, we show that the sender's optimal expected return cannot be approximated to within any factor under a k-voting rule. This negative result easily extends to plurality voting and problems where utility functions are anonymous.

scholarly journals Convergence of Iterative Scoring Rules

2016 ◽  
Vol 57 ◽  
pp. 573-591 ◽  
Author(s):  
Omer Lev ◽  
Jeffrey S. Rosenschein
Keyword(s):  
Linear Order ◽  
Scoring Rules ◽  
Voting Systems ◽  
Choice Functions ◽  
Stable States ◽  
Voting Rules ◽  
Voting Rule ◽  
Social Choice Functions ◽  
Breaking Mechanism ◽  
Iterative Voting

In multiagent systems, social choice functions can help aggregate the distinct preferences that agents have over alternatives, enabling them to settle on a single choice. Despite the basic manipulability of all reasonable voting systems, it would still be desirable to find ways to reach plausible outcomes, which are stable states, i.e., a situation where no agent would wish to change its vote. One possibility is an iterative process in which, after everyone initially votes, participants may change their votes, one voter at a time. This technique, explored in previous work, converges to a Nash equilibrium when Plurality voting is used, along with a tie-breaking rule that chooses a winner according to a linear order of preferences over candidates. In this paper, we both consider limitations of the iterative voting method, as well as expanding upon it. We demonstrate the significance of tie-breaking rules, showing that no iterative scoring rule converges for all tie-breaking. However, using a restricted tie-breaking rule (such as the linear order rule used in previous work) does not by itself ensure convergence. We prove that in addition to plurality, the veto voting rule converges as well using a linear order tie-breaking rule. However, we show that these two voting rules are the only scoring rules that converge, regardless of tie-breaking mechanism.

scholarly journals Determining Possible and Necessary Winners Given Partial Orders

2011 ◽  
Vol 41 ◽  
pp. 25-67 ◽  
Author(s):  
L. Xia ◽  
V. Conitzer
Keyword(s):  
Linear Order ◽  
Partial Orders ◽  
Scoring Rules ◽  
Linear Orders ◽  
Voting Rules ◽  
Voting Rule

Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial orders instead. Then, given a voting rule, a profile of partial orders, and an alternative (candidate) c, two important questions arise: first, is it still possible for c to win, and second, is c guaranteed to win? These are the possible winner and necessary winner problems, respectively. Each of these two problems is further divided into two sub-problems: determining whether c is a unique winner (that is, c is the only winner), or determining whether c is a co-winner (that is, c is in the set of winners). We consider the setting where the number of alternatives is unbounded and the votes are unweighted. We completely characterize the complexity of possible/necessary winner problems for the following common voting rules: a class of positional scoring rules (including Borda), Copeland, maximin, Bucklin, ranked pairs, voting trees, and plurality with runoff.

scholarly journals Can We Predict the Election Outcome from Sampled Votes?

2020 ◽  
Vol 34 (02) ◽  
pp. 2176-2183
Author(s):  
Evi Micha ◽  
Nisarg Shah
Keyword(s):  
Standard Model ◽  
Collective Decision ◽  
Scoring Rules ◽  
Election Outcome ◽  
Focus On The Family ◽  
Voting Rule ◽  
The Family ◽  
The Standard Model

In the standard model of voting, it is assumed that a voting rule observes the ranked preferences of each individual over a set of alternatives and makes a collective decision. In practice, however, not every individual votes. Is it possible to make a good collective decision for a group given the preferences of only a few of its members? We propose a framework in which we are given the ranked preferences of k out of n individuals sampled from a distribution, and the goal is to predict what a given voting rule would output if applied on the underlying preferences of all n individuals. We focus on the family of positional scoring rules, derive a strong negative result when the underlying preferences can be arbitrary, and discover interesting phenomena when they are generated from a known distribution.

scholarly journals Decision Making in Committees: Transparency, Reputation, and Voting Rules

2007 ◽  
Vol 97 (1) ◽  
pp. 150-168 ◽  
Author(s):  
Gilat Levy
Keyword(s):  
Decision Making ◽  
Career Concerns ◽  
Decision Making Process ◽  
Voting Rules ◽  
The Public ◽  
Voting Rule ◽  
The Right

In this paper I analyze the effect of transparency on decision making in committees. I focus on committees whose members are motivated by career concerns. The main result is that when the decision-making process is secretive (when individual votes are not revealed to the public), committee members comply with preexisting biases. For example, if the voting rule demands a supermajority to accept a reform, individuals vote more often against reforms. Transparent committees are therefore more likely to accept reforms. I also find that coupled with the right voting rule, a secretive procedure may induce better decisions than a transparent one. (JEL D71, D72)

scholarly journals METHODS FOR PROBABILISTIC DECISION MAKING WITH LINGUISTIC INFORMATION

2014 ◽  
Vol 20 (2) ◽  
pp. 193-209 ◽  
Author(s):  
Guiwu Wei ◽  
Xiaofei Zhao
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Owa Operator ◽  
Linguistic Information ◽  
Probabilistic Information ◽  
Ordered Weighted Average ◽  
Linguistic Labels ◽  
Selection Of

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with linguistic labels, some new decision analysis are proposed. Firstly, we shall develop three new aggregation operators: generalized probabilistic 2-tuple weighted average (GP-2TWA) operator, generalized probabilistic 2-tuple ordered weighted average (GP-2TOWA) operator and generalized immediate probabilistic 2-tuple ordered weighted average (GIP-2TOWA) operator. These operators use the weighted average (WA) operator, the ordered weighted average (OWA) operator, linguistic information, probabilistic information and immediate probabilistic information. They are quite useful because they can assess the uncertain information within the problem by using both linguistic labels and the probabilistic information that considers the attitudinal character of the decision maker. In these approaches, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.

APPLICATION OF ORDERED WEIGHTED AVERAGE TO ADAPT CONTINUOUS ASSESSMENT IN AN ENGINEERING PHYSICS COURSE DUE TO COVID-19

2021 ◽  
Author(s):  
José Manuel Brotons-Martínez ◽  
Francisca Martínez-Perez ◽  
José Solano-Jimenez ◽  
Jose María Cámara-Zapata
Keyword(s):  
Weighted Average ◽  
Continuous Assessment ◽  
Ordered Weighted Average ◽  
Physics Course ◽  
Engineering Physics
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