Objectively, the global population is about 8 billion. But subjectively?
Let p_i be the probability I’ll meet person i in the next year, and let μ = Σ p_i be the expected number of people I meet. Then the subjective population is
N = exp( -Σ (p_i/μ) log(p_i/μ) )
This is the perplexity of the conditional distribution “given I meet someone, who is it?”. For example, if there’s a pool of 100,000 people who I’ll meet with 3% chance each (everyone else is 0%) then I’ll meet 3000 people next year, and my subjective population is 100,000.
My guess is that my subjective population is around 30,000–100,000, but I might be way off.
Objectively, the global population is about 8 billion. But subjectively?
Let p_i be the probability I’ll meet person i in the next year, and let μ = Σ p_i be the expected number of people I meet. Then the subjective population is
N = exp( -Σ (p_i/μ) log(p_i/μ) )
This is the perplexity of the conditional distribution “given I meet someone, who is it?”. For example, if there’s a pool of 100,000 people who I’ll meet with 3% chance each (everyone else is 0%) then I’ll meet 3000 people next year, and my subjective population is 100,000.
My guess is that my subjective population is around 30,000–100,000, but I might be way off.