These problems illustrate that vote counting, like any other measurement
process, has a certain amount of inherent uncertainty.
Naively we would suppose that the question of which candidate a certain
ballot indicates is a question with a certain answer. In fact though
there is always a probabilistic element. In well designed ballots the
vast majority will have a clean answer. But in any system there will
be a gray area.
Some fraction of the ballots will be ambiguous to some degree or another.
Your counting system will have to draw a conceptual line to separate
the ballots that can be counted for one or another candidate from those
which can't. And the location of this line will be arbitrary.
Several years ago I reported on a local election which would tip the
balance on the local board of county supervisors. It was extremely close
and went through several recounts, getting a different winner each time.
In the end a judge had to manually inspect dozens of partially spoiled
ballots and try to ascertain the likely intention of the voters.
This eventually decided the election.
The Florida count currently separates the candidates by less than .005%.
Their votes are the same to four significant figures. Measuring any
physical phenomenon reliably to five significant figures is a challenge.
It is no wonder that there is uncertainty in the ballot counts.
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