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?