{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T20:11:35Z","timestamp":1779912695971,"version":"3.53.1"},"reference-count":11,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2014,4,4]],"date-time":"2014-04-04T00:00:00Z","timestamp":1396569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of \u201cthe same information\u201d two or more random variables specify about a target random variable. As of yet, none is wholly satisfactory. A palatable measure of intersection information would provide a principled way to quantify slippery concepts, such as synergy. Here, we introduce an intersection information measure based on the G\u00e1cs-K\u00f6rner common random variable that is the first to satisfy the coveted target monotonicity property. Our measure is imperfect, too, and we suggest directions for improvement.<\/jats:p>","DOI":"10.3390\/e16041985","type":"journal-article","created":{"date-parts":[[2014,4,4]],"date-time":"2014-04-04T11:11:12Z","timestamp":1396609872000},"page":"1985-2000","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":69,"title":["Intersection Information Based on Common Randomness"],"prefix":"10.3390","volume":"16","author":[{"given":"Virgil","family":"Griffith","sequence":"first","affiliation":[{"name":"Computation and Neural Systems, Caltech, Pasadena, CA 91125, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edwin","family":"Chong","sequence":"additional","affiliation":[{"name":"Dept. of Electrical & Computer Engineering, Colorado State University, Fort Collins, CO 80523, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ryan","family":"James","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Colorado, Boulder, CO 80309, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher","family":"Ellison","sequence":"additional","affiliation":[{"name":"Center for Complexity and Collective Computation, Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI 53715, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Crutchfield","sequence":"additional","affiliation":[{"name":"Complexity Sciences Center and Physics Dept, University of California Davis, Davis, CA 95616, USA"},{"name":"Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2014,4,4]]},"reference":[{"key":"ref_1","unstructured":"Williams, P.L., and Beer, R.D. (2010). Nonnegative Decomposition of Multivariate Information. arXiv:1004.2515 [cs.IT]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Prokopenko, M. (2014). Guided Self-Organization: Inception, Springer.","DOI":"10.1007\/978-3-642-53734-9"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"012130","DOI":"10.1103\/PhysRevE.87.012130","article-title":"Bivariate measure of redundant information","volume":"87","author":"Harder","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_4","unstructured":"Gilbert, T., Kirkilionis, M., and Nicolis, G. (2012, January 3\u20137). Shared Information\u2014New Insights and Problems in Decomposing Information in Complex Systems. Brussels, Belgium."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lizier, J., Flecker, B., and Williams, P. (2013, January 16\u201317). Towards a synergy-based approach to measuring information modification. Singapore.","DOI":"10.1109\/ALIFE.2013.6602430"},{"key":"ref_6","first-page":"149","article-title":"Common information is far less than mutual information","volume":"2","year":"1973","journal-title":"Probl. Control Inform. Theor"},{"key":"ref_7","first-page":"1","article-title":"Zero-error information and applications in cryptography","volume":"4","author":"Wolf","year":"2004","journal-title":"Proc. IEEE Inform. Theor. Workshop"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"683","DOI":"10.3390\/e13030683","article-title":"On a Connection between Information and Group Lattices","volume":"13","author":"Li","year":"2011","journal-title":"Entropy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1109\/TIT.1975.1055346","article-title":"The common information of two dependent random variables","volume":"21","author":"Wyner","year":"1975","journal-title":"IEEE Trans. Inform. Theor"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5194","DOI":"10.1103\/PhysRevLett.79.5194","article-title":"Negative Entropy and Information in Quantum Mechanics","volume":"79","author":"Cerf","year":"1997","journal-title":"Phys. Rev. Lett"},{"key":"ref_11","unstructured":"Cover, T.M., and Thomas, J.A. (1991). Elements of Information Theory, John Wiley."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/4\/1985\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:09:58Z","timestamp":1760216998000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/4\/1985"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,4]]},"references-count":11,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,4]]}},"alternative-id":["e16041985"],"URL":"https:\/\/doi.org\/10.3390\/e16041985","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,4]]}}}