1
$\begingroup$

I hope you guys find this an interesting question. Imagine you want to implement a system that rewards people for their contributions (regardless of quality or any external assessment). What is a good model, considering the following conditions:

  • It shouldn't reward people that contributes "excessively" only to gain whatever you're giving as reward. For example, if you're giving an award for 5 contributions, then you can't give that award again because of the sixth contribution.
  • It shouldn't be too complex to be computationally unfeasible (although, if you know of something complex but interesting, I'd like to know about it).

As a clarification, the situation is such that you want to give a single award (instead of a variety of them).

Maybe you know some established theory dealing with this kind of stuff. Let me know if that's the case.

By the way, I searched in Google Scholar but I didn't find anything relevant.

Thanks!

  • 0
    Anyway, I changed 'best' to 'good' to avoid any confusion :-)2012-06-10

1 Answers 1

1

Your reward function can follow the Erlang distribution for instance. If $c$ denotes the contribution, then the reward is $r(c)$ given as $r(c) = r_{\max} \int_{x=0}^c \dfrac{\lambda^k x^{k-1} \exp(-\lambda x)}{(k-1)!} dx$ where $r_{\max}$ is the maximum reward one can earn. This is the Erlang distribution. The parameters $\lambda$ and $k$ affect the rate of decay and the shape of the distribution respectively.

  • 0
    @Marvis Well, now I don't understand what you mean. Did you actually mean integrate over 'contributions'?. How do you do that? What is a mean contribution?. I thought this makes perfect sense in the following sense: "The Erlang random variable describes the time interval between any event and the kth following event". Fundamentals of Applied Probability And Random Processes by Oliver Chukwudi Ibe.2012-06-10