{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T19:03:29Z","timestamp":1779995009732,"version":"3.53.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2014,6,30]],"date-time":"2014-06-30T00:00:00Z","timestamp":1404086400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,6,30]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>\n                    In this article we formalize the Bertrand\u2019s Ballot Theorem based on [17]. Suppose that in an election we have two candidates:\n                    <jats:italic>A<\/jats:italic>\n                    that receives\n                    <jats:italic>n<\/jats:italic>\n                    votes and\n                    <jats:italic>B<\/jats:italic>\n                    that receives\n                    <jats:italic>k<\/jats:italic>\n                    votes, and additionally\n                    <jats:italic>n \u2265 k<\/jats:italic>\n                    . Then this theorem states that the probability of the situation where\n                    <jats:italic>A<\/jats:italic>\n                    maintains more votes than\n                    <jats:italic>B<\/jats:italic>\n                    throughout the counting of the ballots is equal to (\n                    <jats:italic>n \u2212 k<\/jats:italic>\n                    )\/(\n                    <jats:italic>n<\/jats:italic>\n                    +\n                    <jats:italic>k<\/jats:italic>\n                    ).\n                  <\/jats:p>\n                  <jats:p>This theorem is item #30 from the \u201cFormalizing 100 Theorems\u201d list maintained by Freek Wiedijk at http:\/\/www.cs.ru.nl\/F.Wiedijk\/100\/.<\/jats:p>","DOI":"10.2478\/forma-2014-0014","type":"journal-article","created":{"date-parts":[[2015,2,5]],"date-time":"2015-02-05T08:48:28Z","timestamp":1423126108000},"page":"119-123","source":"Crossref","is-referenced-by-count":0,"title":["Bertrand\u2019s Ballot Theorem"],"prefix":"10.2478","volume":"22","author":[{"given":"Karol","family":"P\u0105k","sequence":"first","affiliation":[{"name":"Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2014,6,30]]},"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/22\/2\/article-p119.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2014-0014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T18:50:13Z","timestamp":1779994213000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2014-0014"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,30]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,6,30]]},"published-print":{"date-parts":[[2014,6,30]]}},"alternative-id":["10.2478\/forma-2014-0014"],"URL":"https:\/\/doi.org\/10.2478\/forma-2014-0014","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,30]]}}}