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@TheBrick(Tommy)
If
responsibility_to_me ~ 1/power for all positive power, which I understand is what we are talking about as negative power is impossible.
then
r_t_m has a minimum of zero and a maximum of one (multiplied by a positive constant).
your responsibility_to_others looks like it goes something like ~ (1-1/power)
so has a minimum of one and minimum of zero (multiplied by a positive constant).
So the sum of these two parts tends to one (multiplied by a positive constant).
Also there is the possibility to consider that fact that this "power responsibility" is a one on one relationship. If we are in a one on one situation the the limit of one holds. However given that we are operating within a city of population N individuals we need to multiply the responsibility to others by N. This results in a responsibility to power relationship which tends towards N (multiplied by a positive constant).