  We present a method and software for ballot-polling risk-limiting audits
(RLAs) based on Bernoulli sampling: ballots are included in the sample with
probability $p$, independently. Bernoulli sampling has several advantages: (1)
it does not require a ballot manifest; (2) it can be conducted independently at
different locations, rather than requiring a central authority to select the
sample from the whole population of cast ballots or requiring stratified
sampling; (3) it can start in polling places on election night, before margins
are known. If the reported margins for the 2016 U.S. Presidential election are
correct, a Bernoulli ballot-polling audit with a risk limit of 5% and a
sampling rate of $p_0 = 1\%$ would have had at least a 99% probability of
confirming the outcome in 42 states. (The other states were more likely to have
needed to examine additional ballots.) Logistical and security advantages that
auditing in the polling place affords may outweigh the cost of examining more
ballots than some other methods might require.
