> Unless done carefully this will almost certainly fail Benford’s Law.
IIRC Benford's law relies upon things that have power-law underpinnings, such as iterated growth% at different rates. In contrast, relative vote amounts at a given point in time don't have many ways to exhibit that, particularly when the total number of voters is fixed rather than having voters divide like bacteria during polling day.
However it might work if you were checking the growth in total eligible voters in different locations over time.
I like to imagine Benford's Law a bit like throwing randomly distributed darts through the air at a paper target, exept the target is graph paper with log-10 subdivisions. The "leading 1" zones are simply bigger targets. [0]
I think the concern is that precinct size tends to cluster in ways that mean results can cluster in ways that - for a large portion of the data - does not span a full order of magnitude.
To elaborate, if we imagine a polity with precincts that turn out 10,000 people each election, with two major party candidates that each get between 20% and 80% of the vote, we'd see precisely 0% precincts with a leading digit of 1, much less the ~30% predicted by Benford's law. Of course that doesn't exactly describe any real polity, but it doesn't seem surprising that real elections would be enough like that to screw with the pattern.
Manipulating statistics is harder than you think.