  A simple and quick general test to screen for numerical anomalies is
presented. It can be applied, for example, to electoral processes, both
electronic and manual. It uses vote counts in officially published voting
units, which are typically widely available and institutionally backed. The
test examines the frequencies of digits on voting counts and rests on the First
(NBL1) and Second Digit Newcomb--Benford Law (NBL2), and in a novel
generalization of the law under restrictions of the maximum number of voters
per unit (RNBL2). We apply the test to the 2004 USA presidential elections, the
Puerto Rico (1996, 2000 and 2004) governor elections, the 2004 Venezuelan
presidential recall referendum (RRP) and the previous 2000 Venezuelan
Presidential election. The NBL2 is compellingly rejected only in the Venezuelan
referendum and only for electronic voting units. Our original suggestion on the
RRP (Pericchi and Torres, 2004) was criticized by The Carter Center report
(2005). Acknowledging this, Mebane (2006) and The Economist (US) (2007)
presented voting models and case studies in favor of NBL2. Further evidence is
presented here. Moreover, under the RNBL2, Mebane's voting models are valid
under wider conditions. The adequacy of the law is assessed through Bayes
Factors (and corrections of $p$-values) instead of significance testing, since
for large sample sizes and fixed $\alpha$ levels the null hypothesis is over
rejected. Our tests are extremely simple and can become a standard screening
that a fair electoral process should pass.
