We provide a simple $(1-O(\frac{1}{\sqrt{k}}))$-selectable Online Contention Resolution Scheme for $k$-uniform matroids against a fixed-order adversary. If $A_i$ and $G_i$ denote the set of selected elements and the set of realized active elements among the first $i$ (respectively), our algorithm selects with probability $1-\frac{1}{\sqrt{k}}$ any active element $i$ such that $|A_{i-1}| + 1 \leq (1-\frac{1}{\sqrt{k}})\cdot \mathbb{E}[|G_i|]+\sqrt{k}$. This implies a $(1-O(\frac{1}{\sqrt{k}}))$ prophet inequality against fixed-order adversaries for $k$-uniform matroids that is considerably simpler than previous algorithms [Ala14, AKW14, JMZ22]. We also prove that no OCRS can be $(1-Ω(\sqrt{\frac{\log k}{k}}))$-selectable for $k$-uniform matroids against an almighty adversary. This guarantee is matched by the (known) simple greedy algorithm that accepts every active element with probability $1-Θ(\sqrt{\frac{\log k}{k}})$ [HKS07].

The use of product reviews in online platforms is ubiquitous and it is well established that reviews play a significant role on customer purchase decisions. The process in which reviews impact product purchases can be seen as a problem of social learning, which generically studies how agents update their beliefs for an unknown quantity of interest (e.g., product quality) based on observing actions of past agents (e.g., reading reviews by past customers). The typical assumption in the literature of social learning with reviews is that, when deciding whether to purchase a product, customers consider either all reviews provided by previous customers or a summary statistic such as their average rating. However, in practice, a common scenario may be somewhere "in between" the above two assumptions: customers read a small number of reviews in detail.