Lirong Xia

Profit-Maximizing Incentive for Participatory Sensing

We design an incentive mechanism based on all-pay auctions for participatory sensing. The organizer (principal) aims to attract a high amount of contribution from participating users (agents) while at the same time lowering his payout, which we formulate as a profit-maximization problem. We use a contribution-dependent prize function in an environment that is specifically tailored to participatory sensing, namely incomplete information (with information asymmetry), risk-averse agents, and stochastic population. We derive the optimal prize function that induces the maximum profit for the principal, while satisfying strict individual rationality (i.e., strictly have incentive to participate at equilibrium) for both risk-neutral and weakly risk-averse agents. The thus induced profit is demonstrated to be higher than the maximum profit induced by constant (yet optimized) prize. We also show that our results are readily extensible to cases of risk-neutral agents and deterministic populations.

Generalized scoring rules and the frequency of coalitional manipulability

We introduce a class of voting rules called <i>generalized scoring rules</i>. Under such a rule, each vote generates a vector of <i>k</i> scores, and the outcome of the voting rule is based only on the sum of these vectors---more specifically, only on the order (in terms of score) of the sums components. This class is extremely general: we do not know of any commonly studied rule that is not a generalized scoring rule. We then study the coalitional manipulation problem for generalized scoring rules. We prove that under certain natural assumptions, if the number of manipulators is <i>O</i>(<i>n^p</i>) (for any <i>p</i>< 1/2), then the probability that a random profile is manipulable is <i>O</i>(<i>n^p--1/2</i>), where <i>n</i> is the number of voters. We also prove that under another set of natural assumptions, if the number of manipulators is Ω(<i>n^p</i>) (for any <i>p</i>> 1/2) and <i>o</i>(<i>n</i>), then the probability that a random profile is manipulable (to any possible winner under the voting rule) is 1--<i>O</i>(<i>e</i>^{--Ω(<i>n</i>^{2<i>p</i>--1)}}). We also show that common voting rules satisfy these conditions (for the uniform distribution). These results generalize earlier results by Procaccia and Rosenschein as well as even earlier results on the probability of an election being tied.

A sufficient condition for voting rules to be frequently manipulable

The Gibbard-Satterthwaite Theorem states that (in unrestricted settings) any reasonable voting rule is manipulable. Recently, a quantitative version of this theorem was proved by Ehud Friedgut, Gil Kalai, and Noam Nisan: when the number of alternatives is three, for any neutral voting rule that is far from any dictatorship, there exists a voter such that a random manipulation---that is, the true preferences and the strategic vote are all drawn i.i.d., uniformly at random---will succeed with a probability of Ω(1/n), where n is the number of voters. However, it seems that the techniques used to prove this theorem can not be fully extended to more than three alternatives. In this paper, we give a more limited result that does apply to four or more alternatives. We give a sufficient condition for a voting rule to be randomly manipulable with a probability of Ω(1/n) for at least one voter, when the number of alternatives is held fixed. Specifically, our theorem states that if a voting rule r satisfies 1. homogeneity, 2. anonymity, 3. non-imposition, 4. a canceling-out condition, and 5. there exists a stable profile that is still stable after one given alternative is uniformly moved to different positions; then there exists a voter such that a random manipulation for that voter will succeed with a probability of Ω(1/n). We show that many common voting rules satisfy these conditions, for example any positional scoring rule, Copeland, STV, maximin, and ranked pairs.

Computing the margin of victory for various voting rules

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. 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), where n is 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 post-election audits for voting rules beyond the plurality rule.

New candidates welcome! Possible winners with respect to the addition of new candidates☆

In voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number k of new candidates will be added. We give a computational study of this problem, focusing on scoring rules, and we provide a formal comparison with related problems such as control via adding candidates or cloning.

Sequential voting rules and multiple elections paradoxes

Multiple election paradoxes arise when voting separately on each issue from a set of related issues results in an obviously undesirable outcome. Several authors have argued that a sufficient condition for avoiding multiple election paradoxes is the assumption that voters have separable preferences. We show that this extremely demanding restriction can be relaxed into the much more reasonable one: there exists a linear order <b>x</b>₁ > … > <b>x</b>_<i>p</i> on the set of issues such that for each voter, every issue <b>x</b>_<i>i</i> is preferentially independent of <b>x</b>_<i>i+1</i>, …, <b>x</b>_<i>p</i> given <b>x</b>₁, …, <b>x</b>_<i>i</i>-1. This leads us to define a family of sequential voting rules, defined as the sequential composition of local voting rules. These rules relate to the setting of conditional preference networks (CP-nets) recently developed in the Artificial Intelligence literature. We study in detail how these sequential rules inherit, or do not inherit, the properties of their local components. We focus on the case of multiple referenda, corresponding to multiple elections with binary issues.

Image orientation detection with integrated human perception cues (or which way is up)

In this paper, we propose a set of human perceptual cues used jointly to automatically detect image orientation. The cues used are: orientation of faces, position of the sky, brighter regions, and textured objects, and symmetry. We combine these cues in a Bayesian framework, and the photo acquiring model has been considered carefully as the prior knowledge of the image orientation. Results on more than a thousand different images provide a compelling argument that our approach is a viable one.

Incentive Mechanism Design for Crowdsourcing: An All-Pay Auction Approach

Crowdsourcing can be modeled as a principal-agent problem in which the principal (crowdsourcer) desires to solicit a maximal contribution from a group of agents (participants) while agents are only motivated to act according to their own respective advantages. To reconcile this tension, we propose an all-pay auction approach to incentivize agents to act in the principal’s interest, i.e., maximizing profit, while allowing agents to reap strictly positive utility. Our rationale for advocating all-pay auctions is based on two merits that we identify, namely all-pay auctions (i) compress the common, two-stage “bid-contribute” crowdsourcing process into a single “bid-cum-contribute” stage, and (ii) eliminate the risk of task nonfulfillment. In our proposed approach, we enhance all-pay auctions with two additional features: an adaptive prize and a general crowdsourcing environment. The prize or reward adapts itself as per a function of the unknown winning agent’s contribution, and the environment or setting generally accommodates incomplete and asymmetric information, risk-averse (and risk-neutral) agents, and a stochastic (and deterministic) population. We analytically derive this all-pay auction-based mechanism and extensively evaluate it in comparison to classic and optimized mechanisms. The results demonstrate that our proposed approach remarkably outperforms its counterparts in terms of the principal’s profit, agent’s utility, and social welfare.

Complexity of and algorithms for the manipulation of Borda, Nanson's and Baldwin's voting rules

We investigate manipulation of the Borda voting rule, as well as two elimination style voting rules, Nansons and Baldwins voting rules, which are based on Borda voting. We argue that these rules have a number of desirable computational properties. For unweighted Borda voting, we prove that it is NP-hard for a coalition of two manipulators to compute a manipulation. This resolves a long-standing open problem in the computational complexity of manipulating common voting rules. We prove that manipulation of Baldwins and Nansons rules is computationally more difficult than manipulation of Borda, as it is NP-hard for a single manipulator to compute a manipulation. In addition, for Baldwins and Nansons rules with weighted votes, we prove that it is NP-hard for a coalition of manipulators to compute a manipulation with a small number of candidates.Because of these NP-hardness results, we compute manipulations using heuristic algorithms that attempt to minimise the number of manipulators. We propose several new heuristic methods. Experiments show that these methods significantly outperform the previously best known heuristic method for the Borda rule. Our results suggest that, whilst computing a manipulation of the Borda rule is NP-hard, computational complexity may provide only a weak barrier against manipulation in practice. In contrast to the Borda rule, our experiments with Baldwins and Nansons rules demonstrate that both of them are often more difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.

Efficient Algorithms for Reconstructing Zero-Recombinant Haplotypes on a Pedigree Based on Fast Elimination of Redundant Linear Equations

Computational inference of haplotypes from genotypes has attracted a great deal of attention in the computational biology community recently, partially driven by the international HapMap project. In this paper, we study the question of how to efficiently infer haplotypes from genotypes of individuals related by a pedigree, assuming that the hereditary process was free of mutations (i.e., the Mendelian law of inheritance) and recombinants. The problem has recently been formulated as a system of linear equations over the finite field of