In the context of depth-
pooling for constructing web search test collections, we compare two approaches to ordering pooled documents for relevance assessors: The prioritisation strategy (PRI) used widely at NTCIR, and the simple randomisation strategy (RND). In order to address research questions regarding PRI and RND, we have constructed and released the WWW3E8 dataset, which contains eight independent relevance labels for 32,375 topic-document pairs, i.e., a total of 259,000 labels. Four of the eight relevance labels were obtained from PRI-based pools; the other four were obtained from RND-based pools. Using WWW3E8, we compare PRI and RND in terms of inter-assessor agreement, system ranking agreement, and robustness to new systems that did not contribute to the pools. We also utilise an assessor activity log we obtained as a byproduct of WWW3E8 to compare the two strategies in terms of assessment efficiency. Our main findings are: (a) The presentation order has no substantial impact on assessment efficiency; (b) While the presentation order substantially affects which documents are judged (highly) relevant, the difference between the inter-assessor agreement under the PRI condition and that under the RND condition is of no practical significance; (c) Different system rankings under the PRI condition are substantially more similar to one another than those under the RND condition; and (d) PRI-based relevance assessment files (qrels) are substantially and statistically significantly more robust to new systems than RND-based ones. Finding (d) suggests that PRI helps the assessors identify relevant documents that affect the evaluation of many existing systems, including those that did not contribute to the pools. Hence, if researchers need to evaluate their current IR systems using legacy IR test collections, we recommend the use of those constructed using the PRI approach unless they have a good reason to believe that their systems retrieve relevant documents that are vastly different from the pooled documents. While this robustness of PRI may also mean that the PRI-based pools are biased against future systems that retrieve highly novel relevant documents, one should note that there is no evidence that RND is any better in this respect.