  The Honduran incumbent president and his administration recently declared
victory in an election riddled with irregularities and indicators of fraud.
Perhaps most curious, however, was a numerical anomaly: the primary challenger
carried a very significant lead of five percentage points more than half way
through the election but was ultimately defeated by the incumbent. The
incumbent (Hernandez) offered a plausible explanation for the surprising
turnaround in the ballots: his popularity is greater in remote areas of the
country but votes from remote areas were not counted until later in the
election. Here, we mathematically formalize this argument, which we will call
the Hernandez conjecture, and employ the resulting formulae together with
geodemographic data from Honduras to quantitatively assess the conjectures
veracity. When the departamentos were analyzed individually, three
sparsely-populated departamentos (of 18 total) showed small but non-negligible
probability of the conjectures veracity; however, when the country was analyzed
as a whole, the overall probability of the conjectures veracity was calculated
to be less than 0.0001 under a wide range of different assumptions. Results of
our three-pronged analysis, taken together, indicate a negligible probability
of a fair win by the incumbent.
