Noise Stability of Weighted Majority

A Law of Large Numbers for Weighted Majority

Consider an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is $p>1/2$. Condorcet's Jury Theorem which he derived from the weak law of large numbers asserts that if the number of voters tends to infinity then the probability that the first candidate will be elected tends to one. The notion of influence of a voter or its voting power is relevant for extensions of the weak law of large numbers for voting rules which are more general than simple majority. In this paper we point out two different wa…

Consistency of weighted majority votes

We revisit the classical decision-theoretic problem of weighted expert voting from a statistical learning perspective. In particular, we examine the consistency (both asymptotic and finitary) of the optimal Nitzan-Paroush weighted majority and related rules. In the case of known expert competence levels, we give sharp error estimates for the optimal rule. When the competence levels are unknown, they must be empirically estimated. We provide frequentist and Bayesian analyses for this situation. Some of our proof techniques are non-standard and may be of independent interest. The bounds we deriv…

Error Rate Bounds and Iterative Weighted Majority Voting for Crowdsourcing

Crowdsourcing has become an effective and popular tool for human-powered computation to label large datasets. Since the workers can be unreliable, it is common in crowdsourcing to assign multiple workers to one task, and to aggregate the labels in order to obtain results of high quality. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of general aggregation rules under the Dawid-Skene crowdsourcing model. The bounds are derived for multi-class labeling, and can be used to analyze many aggregation methods, including majority votin…

线性抛物型方程指数稳定性的加权半群方法

A weighted semigroup approach to exponential stability in linear parabolic equations

本文采用加权半群方法，证明了带一般漂移项和零阶系数的线性抛物型方程初边值问题解的指数L²稳定性，该结果对漂移项具有鲁棒性。

Network stability under max--min fair bandwidth sharing

There has recently been considerable interest in the stability of different fair bandwidth sharing policies for models that arise in the context of Internet congestion control. Here, we consider a connection level model, introduced by Massoulié and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. The weighted $α$-fair and weighted max-min fair bandwidth sharing policies are among important policies that have been studied for this model. Stability results are known in both cases when the interarrival times and ser…

Hölder正则性与加权泛函不等式的稳定性

Stability of Hölder regularity and weighted functional inequalities

本文研究度量测度空间上的对称Dirichlet形式，引入跳跃测度尾部条件和加权泛函不等式的新表述，建立了caloric和harmonic函数Hölder正则性的稳定等价刻画，并应用于证明具有边界爆炸行为的对称Markov过程的caloric函数的Hölder连续性。