I have about 350 online petitions, each of which has between 250 and 25,000 signatures. For any two petitions, I can easily measure how many individual signatories have signed both of them.
I want to analyze the commonality between two petitions based on the number of common signatures, but I don't know the best way to weight total signatures. The most obvious way is:
# a and b are sets of signature UIDs for two petitions len(a.intersect(b)) / (len(a) + len(b))
But this does not seem to work well for comparing the petitions when one has a small number and one has a large number. Is there a better way to weight the denominator? Maybe sum of the log of the lens? I don't care about the absolute value of the measurement, just that it's relative to all others.