Given that there are competing incentives (altruism vs. egoism and others) it is clear that some trade-off is needed.
An optimum solution might be too complex to be understood and accepted as fair by everyone.
Thus we have to look for simple approximations.
The simplest are
1 give nothing: g(x)=0
2 give a fixed amount: g(x)=c
3 give a fixed fraction: g(x)=fx
4 give everything above a treshold: g(x)=x>c?x-c:0
5 give a fixed fraction above a treshold: g(x)=x>c?f(x-c):0
6 give a by second order polynomial: g(x)=ax^2+bx+c
7 give a by second order polynomial with treshold: g(x)=x>c?ax^2+bx+d:0
Actually 4) is more complicated than
give/​receive above a treshold: g(x)=x-c
which implies that I should take if I have less than the treshold.
What other simple functions are there and what do they imply?
Given that there are competing incentives (altruism vs. egoism and others) it is clear that some trade-off is needed. An optimum solution might be too complex to be understood and accepted as fair by everyone. Thus we have to look for simple approximations.
The simplest are
1 give nothing: g(x)=0
2 give a fixed amount: g(x)=c
3 give a fixed fraction: g(x)=fx
4 give everything above a treshold: g(x)=x>c?x-c:0
5 give a fixed fraction above a treshold: g(x)=x>c?f(x-c):0
6 give a by second order polynomial: g(x)=ax^2+bx+c
7 give a by second order polynomial with treshold: g(x)=x>c?ax^2+bx+d:0
Actually 4) is more complicated than
give/​receive above a treshold: g(x)=x-c
which implies that I should take if I have less than the treshold.
What other simple functions are there and what do they imply?