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In recent years, several philosophers have generalized this argument to less idealized circumstances. Some authors (Easwaran,\n                    <jats:italic>Thought: A Journal of Philosophy<\/jats:italic>\n                    , 2(1), 53\u201361 2013; Nielsen,\n                    <jats:italic>Statistics &amp; Probability Letters<\/jats:italic>\n                    , 185, 109412 2022) relax finiteness, while others (Carr,\n                    <jats:italic>Synthese<\/jats:italic>\n                    , 198(4), 3581\u20133601 2021; Gallow,\n                    <jats:italic>No\u00fbs<\/jats:italic>\n                    , 55(3), 487\u2013516 2021; Isaacs &amp; Russell, 2022; Schultheis, 2023) relax partitionality. In this paper, we show how to do both at once. We give novel philosophical justifications of the use of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\sigma $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03c3<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -algebras in the infinite setting, and argue for a different interpretation of the \u201csignals\u201d in the non-partitional setting. We show that the resulting update plan mitigates some problems that arise when only relaxing finiteness, but not partitionality, such as the Borel-Kolmogorov paradox.\n                  <\/jats:p>","DOI":"10.1007\/s10992-025-09814-6","type":"journal-article","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T10:50:36Z","timestamp":1759315836000},"page":"1095-1134","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Updating by Maximizing Expected Accuracy in Infinite Non-Partitional Settings"],"prefix":"10.1007","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2278-6257","authenticated-orcid":false,"given":"Kenny","family":"Easwaran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3161-6823","authenticated-orcid":false,"given":"Michael","family":"Nielsen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,1]]},"reference":[{"key":"9814_CR1","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198712060.003.0006","volume-title":"Vagueness and Thought","author":"A Bacon","year":"2018","unstructured":"Bacon, A. 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