Results 1 
8 of
8
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.
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.
The Computational Rise and Fall of Fairness
"... The fair division of indivisible goods has long been an important topic in economics and, more recently, computer science. We investigate the existence of envyfree allocations of indivisible goods, that is, allocations where each player values her own allocated set of goods at least as highly as an ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The fair division of indivisible goods has long been an important topic in economics and, more recently, computer science. We investigate the existence of envyfree allocations of indivisible goods, that is, allocations where each player values her own allocated set of goods at least as highly as any other player’s allocated set of goods. Under additive valuations, we show that even when the number of goods is larger than the number of agents by a linear fraction, envyfree allocations are unlikely to exist. We then show that when the number of goods is larger by a logarithmic factor, such allocations exist with high probability. We support these results experimentally and show that the asymptotic behavior of the theory holds even when the number of goods and agents is quite small. We demonstrate that there is a sharp phase transition from nonexistence to existence of envyfree allocations, and that on average the computational problem is hardest at that transition.
Generalized Decision Scoring Rules: Statistical, Computational, and Axiomatic Properties
"... We pursue a design by social choice, evaluation by statistics and computer science paradigm to build a principled framework for discovering new social choice mechanisms with desirable statistical, computational, and social choice axiomatic properties. Our new framework is called generalized decisio ..."
Abstract
 Add to MetaCart
We pursue a design by social choice, evaluation by statistics and computer science paradigm to build a principled framework for discovering new social choice mechanisms with desirable statistical, computational, and social choice axiomatic properties. Our new framework is called generalized decision scoring rules (GDSRs), which naturally extend generalized scoring rules [Xia and Conitzer 2008] to arbitrary preference space and decision space, including sets of alternatives with fixed or unfixed size, rankings, and sets of rankings. We show that GDSRs cover a wide range of existing mechanisms including MLEs, Chamberlin and Courant rule, and resolute, irresolute, and preference function versions of many commonly studied voting rules. We provide a characterization of statistical consistency for any GDSR w.r.t. any statistical model and asymptotically tight bounds on the convergence rate. We investigate the complexity of winner determination and a wide range of strategic behavior called vote operations for all GDSRs, and prove a general phase transition theorem on the minimum number of vote operations for the strategic entity to succeed. We also characterize GDSRs by two social choice normative properties: anonymity and finite local consistency.