Repeated Sampling in the Presence of Publication Effects
研究了民意调查或调查结果公布后，人们态度或行为可能发生改变（如从众效应），并分析了重复抽样下估计量的统计性质，包括反应函数、不动点和不变分布，对预测选举等连续调查结果有参考价值。
Abstract The generation and public dissemination of information from surveys or polls may be expected to modify or condition the private attitudes or intentions it is hoped to measure. Thus the application of statistics to human affairs is often characterized by a reactivity or reflexivity that may even negate its findings or predictions. Bandwagon, funding, or floating voter effects arising from the publication of political polls are well known. Forecasts of expected visitor numbers for major events may exert a depressant effect on actual attendance, arising from fears of overcrowding or expensive accommodation, or alternatively a stimulatory effect from the generation of additional services or entertainment events. Likewise, the expression of certain psychological or sociological traits may be modified by knowledge of their social desirability. This article investigates the sampling theory of such reactions, concentrating in particular on the properties of a replication over time of polls or surveys. A Markovian framework is established, involving a reaction function (H) between a parameter of interest (θ) and the published statistic (e) estimating its current value. This reaction function is assumed to remain unknown but temporally stable. Such a sampling dynamics induces a second reaction (γ), representing the expectation of the underlying parameter in the next period, conditional on its value in the current period. Two different types of fixed points arise corresponding to either H or γ. In addition, under a replicated set of samples the distribution of the estimator e, tends under suitable conditions to an invariant distribution as the number of replications r becomes large. A different kind of fixed point arises, namely the mean of the invariant distribution. The relationships of the three fixed or invariant points are investigated, for various kinds of reaction function H. The mean of the invariant distribution may be estimated by the running mean [ebar]r = 1/r(e1 + e2 + … + er) of the sample statistics. This running mean may be useful as a predictor of the final outcome from a replicated series of sampled polls, such as those leading up to a presidential election. If people start reacting to the running mean [ebar]r, as predictor—instead of to the current assessments [ebar]r—then its predictive properties are greatly enhanced, for in this case all types of fixed points collapse to the same fixed point regardless of the nature of the reaction function H. Finally, if the published result of a survey or poll can influence attitudes or intentions, then considerations of social welfare arise from a decision to replicate—or even to conduct the survey in the first place. We discuss, without pretending to solve, such issues. Key Words: Random samplingReaction functionSufficient statisticMarkov processInvariant distributionLiapounov stochastic stability criterionFixed pointsMarkov central limit theoremPrediction