By comparing sampling with and without replacement, we present a scenario where more information does not necessarily lead to a decrease in (subjective) uncertainty. The reason is that under certain information-generating mechanisms, it is costly to obtain information. For sampling with replacement, repeated sampling provides more information and thus reduces ambiguity. However, this is not the case for sampling with no replacement. Using simulation experiments, we show that sampling without replacement affects not only subjective beliefs, but also the environment the decision-maker faces. The former has a positive effect on the decision-maker's knowledge of the true distribution, which we call the information effect. The latter changes the state probability to be estimated and thus adds ``noise'' to the decision-maker's belief update, which we call the scale effect. When the sample drawn from the population is small, the information effect dominates. When the number of samples observed becomes large, especially when it is close to the size of the population, the scale effect dominates. That is, although the improved knowledge of the population is favorable, the larger the sample, the less the decision-makers know about the data-generating mechanism for the remaining population. As a result, more information does not necessarily reduce the ambiguity confronted by decision-makers. When the two effects cancel each other, it is optimal to stop learning.
张顺明，中国人民大学财政金融学院教授，博士生导师，中国人民大学金融工程研究所所长。国家杰出青年科学基金获得者(2008)，“新世纪百千万人才工程”国家级人选(2009)，教育部“长江学者奖励计划”特聘教授(2015)。曾主持国家社会科学基金重点项目与国家自然科学基金面上项目多项，主要从事经济学与金融学的教学与研究，在数理经济学、金融经济学、经济理论和经济政策等方面发表学术论文80多篇，发表国内外期刊论文的杂志包括Journal of Financial Markets, Journal of Banking and Finance, Mathematical Finance, Journal of Development Economics, Journal of Mathematical Economics, Economic Theory, World Economy, Economics Letters, Economic Modelling, Journal of Mathematical Analysis and Applications, European Journal of Operational Research,经济研究，经济学季刊，管理科学学报，系统工程理论与实践等。