Given some information need, Large Language Models (LLMs) are increasingly used for candidate text relevance assessment, typically using a one-by-one pointwise (PW) strategy where each LLM call evaluates one candidate at a time. Meanwhile, it has been shown that LLM performance can be improved through self-consistency: prompting the LLM to do the same task multiple times (possibly in perturbed ways) and then aggregating the responses. To take advantage of self-consistency, we hypothesize that batched PW strategies, where multiple passages are judged in one LLM call, are better suited than one-by-one PW methods since a larger input context can induce more diverse LLM sampling across self-consistency calls. We first propose several candidate batching strategies to create prompt diversity across self-consistency calls through subset reselection and permutation. We then test our batched PW methods on relevance assessment and ranking tasks against one-by-one PW and listwise LLM ranking baselines with and without self-consistency, using three passage retrieval datasets and GPT-4o, Claude Sonnet 3, and Amazon Nova Pro. We find that batched PW methods outperform all baselines, and show that batching can greatly amplify the positive effects of self-consistency. For instance, on our legal search dataset, GPT-4o one-by-one PW ranking NDCG@10 improves only from 44.9% to 46.8% without self-consistency vs. with 15 self consistency calls, while batched PW ranking improves from 43.8% to 51.3%, respectively.