But I can't figure out how to favor those with the least popularity

There are several ways to do that. Which one is the most appropriate is very dependent on your final problem.

Anyway, I have not seen anybody propose an exponential solution, so let me do it. The idea is that every subject start with the same score, 1.0, for instance, and every time one of them gets a vote, you reduce its score multiplying it by a factor c such that 0 < c < 1.

As in your particular case, you have already done a draw, you can calculate the current scores as $score{$k} = $c ** $votes{$k}.

The only issue remaining is how to pick c. The key here is how much you want to penalize the popular ones.

In reply to Re: Randomly choosing from a set of alternatives with varying popularity by salva
in thread Randomly choosing from a set of alternatives with varying popularity by ibm1620

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