{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T13:44:12Z","timestamp":1792676652569,"version":"4.5.0"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2017,1,4]],"date-time":"2017-01-04T00:00:00Z","timestamp":1483488000000},"content-version":"unspecified","delay-in-days":2195,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polit. anal."],"published-print":{"date-parts":[[2011]]},"abstract":"<jats:p>The proliferation of elections in even those states that are arguably anything but democratic has given rise to a focused interest on developing methods for detecting fraud in the official statistics of a state's election returns. Among these efforts are those that employ Benford's Law, with the most common application being an attempt to proclaim some election or another fraud free or replete with fraud. This essay, however, argues that, despite its apparent utility in looking at other phenomena, Benford's Law is problematical at best as a forensic tool when applied to elections. Looking at simulations designed to model both fair and fraudulent contests as well as data drawn from elections we know, on the basis of other investigations, were either permeated by fraud or unlikely to have experienced any measurable malfeasance, we find that conformity with and deviations from Benford's Law follow no pattern. It is not simply that the Law occasionally judges a fraudulent election fair or a fair election fraudulent. Its \u201csuccess rate\u201d either way is essentially equivalent to a toss of a coin, thereby rendering it problematical at best as a forensic tool and wholly misleading at worst.<\/jats:p>","DOI":"10.1093\/pan\/mpr014","type":"journal-article","created":{"date-parts":[[2011,8,17]],"date-time":"2011-08-17T03:28:41Z","timestamp":1313551721000},"page":"245-268","source":"Crossref","is-referenced-by-count":120,"title":["Benford's Law and the Detection of Election Fraud"],"prefix":"10.1017","volume":"19","author":[{"given":"Joseph","family":"Deckert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikhail","family":"Myagkov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter C.","family":"Ordeshook","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2017,1,4]]},"reference":[{"key":"S1047198700012808_fn4076","unstructured":"In 2004, Tatarstan and Bashkortostan reported turnout of 83.0% and 89%, respectively, whereas in 2008 those numbers were little changed at 83.0% and 90%. In 2004, Putin was awarded 86.55% and 91.8% of the vote in these two republics, respectively, whereas Medvedev's reported totals declined slightly to 79.2% and 88.0%."},{"key":"S1047198700012808_ref9897","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/10889388.1999.10641122","article-title":"The urban rural divide in the Russian electorate and the effects of distance from urban centers","volume":"40","author":"Berezkin","year":"1999","journal-title":"Post-Soviet Geography and Economics"},{"key":"S1047198700012808_fn4077","unstructured":"Putin was credited with 71.31% of the vote in 2004 versus Medvedev's 71.25% in 2008."},{"key":"S1047198700012808_ref9903","unstructured":"Chaing Lichun , and Ordeshook Peter C. 2009. Fraud, elections and the American gene in Taiwan's democracy. Unpublished manuscript, California Institute of Technology."},{"key":"S1047198700012808_ref9902","volume-title":"Behavioral game theory: Experiments in strategic interaction","author":"Camerer","year":"2003"},{"key":"S1047198700012808_ref9900","unstructured":"Buttorf Gail . 2008. Detecting fraud in America's gilded age. Unpublished manuscript, University of Iowa."},{"key":"S1047198700012808_fn4072","unstructured":"We report here on a total of 136 simulated elections with each set of parameter values simulated several times. Because of the high number of voters and districts, each simulation run takes a significant amount of computing time and running more simulations than already included would require a significant cost in terms of computer time at a negligible benefit in terms of increased confidence levels. However, the degrees of freedom when testing the second-digit mean in these simulations is derived from the number of districts in each election, which is 1000 in every case. Thus, we can achieve high levels of confidence about the second-digit mean in each scenario without running more simulations. So although N = 136 may seem small for simulated data, we are actually working with N = 1000 for each of the statistical tests performed."},{"key":"S1047198700012808_ref9898","article-title":"Location and political influence: A further elaboration of their effects on voting in recent Russian elections","volume":"44","author":"Berezkin","year":"2003","journal-title":"Post-Soviet Geography and Economics"},{"key":"S1047198700012808_fn4073","unstructured":"This evidence merely confirms what two of this essay's authors were told before the October vote by a Putin advisors sent to Kyiv to facilitate Yanukovich's campaign, namely that \u201cif necessary we can fudge 3% of the vote; 10% would be more difficult. \u201c"},{"key":"S1047198700012808_ref9908","unstructured":"Levin Ines , Cohn Gabe A. , Michael Alvarez R. , and Ordeshook Peter C. 2009. Detecting voter fraud in an electronic voting context: An analysis of the unlimited reelection vote in Venezuela. Electronic Voting Technology Workshop\/Workshop on Trustworthy Elections. Online Proceedings."},{"key":"S1047198700012808_ref9896","unstructured":"Berber Bernd , and Scacco Alexandra . 2008. What the numbers say: A digit based test for election fraud using new data from Nigeria. Paper presented at the Annual Meeting of the Am. Political Science Association, Boston, MA, August 28-31."},{"key":"S1047198700012808_ref9915","unstructured":"Sobyanin Alexandar , and Suchovolsky V. 1993. Elections and the referendum December 11, 1993, in Russia. Unpublished report to the Administration of the President of the RF, Moscow."},{"key":"S1047198700012808_fn4079","unstructured":"Despite its attempt at diplomatic language, the OSCE's official report on the 2004 election (ODIHR June 2, 2004), singled out Dagestan, Mordovia, Bashkortostan, Ingushetia, Tatarstan, and Chechnya in an Appendix titled \u201cSample of Implausible Turnout and Result Figures. \u201c"},{"key":"S1047198700012808_ref9914","volume-title":"Bloodlands: Europe between Hitler and Stalin","author":"Snyder","year":"2010"},{"key":"S1047198700012808_ref9901","volume-title":"Crime without punishment","author":"Buzin","year":"2008"},{"key":"S1047198700012808_ref9907","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1101840566"},{"key":"S1047198700012808_ref9904","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139174954"},{"key":"S1047198700012808_fn4078","unstructured":"Although turnover characterizes governments in Chechnya and Ingushetia owing to assassinations and the Kremlin's search for leaders loyal to Moscow, M. Shaymiyev has led Tatarstan since 1991, M. Rakhimov has held the position of president of Bashkortostan since 1993, M. Merkushkin has held the same post in Moldovia since 1995, and recent Putin appointee M. Aliyev heads Dagestan after replacing M. Magomedov, who ruled from 1982 to 2006."},{"key":"S1047198700012808_fn4074","unstructured":"Although the media noted these discrepancies and even anticipated them, little was made officially of things by either side. Yanukovich was hardly going to admit to fraud in his home region. Yushchenko's coalition, on the other hand, actually gained a net of two or three seats from the fraud\u2014enough to form a new governing coalition that deposed Yanukovich as Prime Minister in favor of Yulia Tymoshenko. Neither side, then, had any incentive to challenge the vote count in Donetsk."},{"key":"S1047198700012808_ref9910","unstructured":"Mebane Walter . 2007. Election forensics: Statistics, recounts and fraud Paper presented at the 2007 Annual Meeting of the Midwest Political Science Association. Chicago, IL, April 12-16."},{"key":"S1047198700012808_ref9906","volume-title":"Skew distributions and the sizes of business firms","author":"Ijiri","year":"1977"},{"key":"S1047198700012808_fn4075","unstructured":"One might conjecture that the low mean for Regions derives from peculiarities in the size of precincts. That is true in a complex way. If we isolate those 1841 smaller districts in which Regions' vote lies between 100 and 1000, the mean second digit shoots up to 4.43 whereas for the remaining 530 larger precincts, its second-digit score drops to 1.00 (a comparable reanalysis for the Socialists changes nothing since it secured 1000 or more votes in only 11 of the 353 districts in which it won more than 100 votes)."},{"key":"S1047198700012808_ref9909","unstructured":"Mebane Walter . 2006. Election forensics: Vote counts and Benford's Law. Paper prepared for the 2006 Summer Meeting of the Political Methodology Society, University of California, Davis, July 20-22."},{"key":"S1047198700012808_ref9911","volume-title":"Election fraud","author":"Mebane","year":"2008"},{"key":"S1047198700012808_ref9912","unstructured":"Mebane Walter , and Kalinin Kirill . 2009. Electoral falsifications in Russia: Complex diagnostics selections 2003-2004, 2007-8. Electoral Policy REO, 57\u201370 (in Russian)."},{"key":"S1047198700012808_fn4070","unstructured":"We note again that the various mean and variance parameter values of 2, 0.15, and \u22121 merely dictate the spread of ideal points and thus dictate the positions of the candidates we must choose to achieve specific splits in the candidates' vote shares. They do not, of themselves, determine second-digit frequencies. Moreover, in this model, turnout is not a function of candidate positions, second-digit frequencies are also invariant with the specifics of those positions except insofar as they determine vote shares. Joseph Deckert et al."},{"key":"S1047198700012808_ref9899","volume-title":"Comments on Benfords Law and the Venezuelan election","author":"Brady","year":"2005"},{"key":"S1047198700012808_ref9913","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626807"},{"key":"S1047198700012808_ref9905","unstructured":"Diekmann Andreas . 2010. Not the first digit: Using Benford's Law to detect fraudlent data. Unpublished paper, Swiss Federal Institute of Technology, Zurich. Paper presented at the 2010 Conference on Plagiarism, 21-23 June, Newcastle, UK."},{"key":"S1047198700012808_fn4071","unstructured":"The software employed in these simulations along with instructions for their implementation are available upon request."}],"container-title":["Political Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1047198700012808","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T03:41:39Z","timestamp":1556336499000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1047198700012808\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011]]}},"alternative-id":["S1047198700012808"],"URL":"https:\/\/doi.org\/10.1093\/pan\/mpr014","relation":{},"ISSN":["1047-1987","1476-4989"],"issn-type":[{"value":"1047-1987","type":"print"},{"value":"1476-4989","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}