Results 1  10
of
22
Preference Functions That Score Rankings and Maximum Likelihood Estimation
"... A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging ..."
Abstract

Cited by 60 (20 self)
 Add to MetaCart
(Show Context)
A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging rankings (of, say, webpages) into a single ranking. The key issue is choosing a PF to use. One natural and previously studied approach is to assume that there is an unobserved “correct ” ranking, and the votes are noisy estimates of this. Then, we can use the PF that always chooses the maximum likelihood estimate (MLE) of the correct ranking. In this paper, we define simple ranking scoring functions (SRSFs) and show that the class of neutral SRSFs is exactly the class of neutral PFs that are MLEs for some noise model. We also define extended ranking scoring functions (ERSFs) and show a condition under which these coincide with SRSFs. We study key properties such as consistency and continuity, and consider some example PFs. In particular, we study Single Transferable Vote (STV), a commonly used PF, showing that it is an ERSF but not an SRSF, thereby clarifying the extent to which it is an MLE function. This also gives a new perspective on how ties should be broken under STV. We leave some open questions. 1
AI’s war on manipulation: Are we winning?
 AI MAGAZINE
"... We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections. ..."
Abstract

Cited by 54 (8 self)
 Add to MetaCart
We provide an overview of more than two decades of work, mostly in AI, that studies computational complexity as a barrier against manipulation in elections.
Computing the Margin of Victory for Various Voting Rules
, 2012
"... 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 postelection audits, which has been wi ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
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 postelection audits, which has been widely used in the United States to detect errors or fraud caused by malfunctions of electronic voting machines. In this paper, we investigate the computational complexity and (in)approximability of computing the margin of victory for various voting rules, including approval voting, all positional scoring rules (which include Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also prove a dichotomy theorem, which states that for all continuous generalized scoring rules, including all voting rules studied in this paper, either with high probability the margin of victory is Θ ( √ n), or with high probability the margin of victory is Θ(n), wherenis the number of voters. Most of our results are quite positive, suggesting that the margin of victory can be efficiently computed. This sheds some light on designing efficient postelection audits for voting rules beyond the plurality rule.
A smooth transition from powerlessness to absolute power. http://www.cs.cmu.edu/˜arielpro/papers/ phase.pdf
, 2012
"... We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is o ( √ n), where n is the number of voters, then the probability that a random ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
(Show Context)
We study the phase transition of the coalitional manipulation problem for generalized scoring rules. Previously it has been shown that, under some conditions on the distribution of votes, if the number of manipulators is o ( √ n), where n is the number of voters, then the probability that a random profile is manipulable by the coalition goes to zero as the number of voters goes to infinity, whereas if the number of manipulators is ω ( √ n), then the probability that a random profile is manipulable goes to one. Here we consider the critical window, where a coalition has size c √ n, and we show that as c goes from zero to infinity, the limiting probability that a random profile is manipulable goes from zero to one in a smooth fashion, i.e., there is a smooth phase transition between the two regimes. This result analytically validates recent empirical results, and suggests that deciding the coalitional manipulation problem may not be computationally hard in practice. 1
How Many Vote Operations Are Needed to Manipulate a Voting System?
, 2012
"... In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate n votes i.i.d. according to a distribution π, and let n go to infinity, then for any ɛ > 0, ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate n votes i.i.d. according to a distribution π, and let n go to infinity, then for any ɛ > 0, with probability at least 1 − ɛ, the minimum number of operations that are needed for the strategic individual to achieve her goal falls into one of the following four categories: (1) 0, (2) Θ ( √ n), (3) Θ(n), and (4) ∞. This theorem holds for any set of vote operations, any individual vote distribution π, and any integer generalized scoring rule, which includes (but is not limited to) almost all commonly studied voting rules, e.g., approval voting, all positional scoring rules (including Borda, plurality, and veto), plurality with runoff, Bucklin, Copeland, maximin, STV, and ranked pairs. We also show that many wellstudied types of strategic behavior fall under our framework, including (but not limited to) constructive/destructive manipulation, bribery, and control by adding/deleting votes, margin of victory, and minimum manipulation coalition size. Therefore, our main theorem naturally applies to these problems.
Modal ranking: A uniquely robust voting rule
 In Proc. of 28th AAAI
, 2014
"... Motivated by applications to crowdsourcing, we study voting rules that output a correct ranking of alternatives by quality from a large collection of noisy input rankings. We seek voting rules that are supremely robust to noise, in the sense of being correct in the face of any “reasonable ” type of ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Motivated by applications to crowdsourcing, we study voting rules that output a correct ranking of alternatives by quality from a large collection of noisy input rankings. We seek voting rules that are supremely robust to noise, in the sense of being correct in the face of any “reasonable ” type of noise. We show that there is such a voting rule, which we call the modal ranking rule. Moreover, we establish that the modal ranking rule is the unique rule with the preceding robustness property within a large family of voting rules, which includes a slew of wellstudied rules.
Voting with Rank Dependent Scoring Rules
"... Positional scoring rules in voting compute the score of an alternative by summing the scores for the alternative induced by every vote. This summation principle ensures that all votes contribute equally to the score of an alternative. We relax this assumption and, instead, aggregate scores by takin ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
Positional scoring rules in voting compute the score of an alternative by summing the scores for the alternative induced by every vote. This summation principle ensures that all votes contribute equally to the score of an alternative. We relax this assumption and, instead, aggregate scores by taking into account the rank of a score in the ordered list of scores obtained from the votes. This defines a new family of voting rules, rankdependent scoring rules (RDSRs), based on ordered weighted average (OWA) operators, which, include all scoring rules, and many others, most of which of new. We study some properties of these rules, and show, empirically, that certain RDSRs are less manipulable than Borda voting, across a variety of statistical cultures.
Generalized Scoring Rules: A Framework That Reconciles Borda and Condorcet
"... Generalized scoring rules [Xia and Conitzer 08] are a relatively new class of social choice mechanisms. In this paper, we survey developments in generalized scoring rules, showing that they provide a fruitful framework to obtain general results, and also reconcile the Borda approach and Condorcet ap ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Generalized scoring rules [Xia and Conitzer 08] are a relatively new class of social choice mechanisms. In this paper, we survey developments in generalized scoring rules, showing that they provide a fruitful framework to obtain general results, and also reconcile the Borda approach and Condorcet approach via a new social choice axiom. We comment on some highlevel ideas behind GSRs and their connection to Machine Learning, and point out some ongoing work and future directions.
Designing Social Choice Mechanisms Using Machine Learning
"... Social choice studies ordinal preference and information aggregation with applications in highstakes political elections as well as lowstakes movie rating websites. Recently, computational aspects of classical social choice mechanisms have been extensively investigated, yet not much has been done ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Social choice studies ordinal preference and information aggregation with applications in highstakes political elections as well as lowstakes movie rating websites. Recently, computational aspects of classical social choice mechanisms have been extensively investigated, yet not much has been done in designing new mechanisms with the help of computational techniques. In this paper, we outline a workflow to formalize a principled approach towards designing novel social choice mechanisms using machine learning. In the workflow, we clearly separate the following two goals of social choice (1) reaching a compromise among agents ’ subjective preferences, and (2) revealing the ground truth. For each of the two goals, we discuss criteria for evaluation, main challenges, possible solutions, and future directions.
Computational Social Choice: Strategic and Combinatorial Aspects
"... When agents have conflicting preferences over a set of alternatives and they want to make a joint decision, a natural way to do so is by voting. How to design and analyze desirable voting rules has been studied by economists for centuries. In recent decades, technological advances, especially those ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
When agents have conflicting preferences over a set of alternatives and they want to make a joint decision, a natural way to do so is by voting. How to design and analyze desirable voting rules has been studied by economists for centuries. In recent decades, technological advances, especially those in internet economy, have introduced many new applications for voting theory. For example, we can rate movies based on people’s preferences, as done on many movie recommendation sites. However, in such new applications, we always encounter a large number of alternatives or an overwhelming amount of information, which makes computation in voting process a big challenge. Such challenges have led to a burgeoning area—computational social choice, aiming to address problems in computational aspects of preference representation and aggregation in a multiagent scenario.