This does sound awful. However, I understand trying to make the best out of a bad situation.
As you write, it is extremely hard to numerically quantify intellectual work. As such, I would strongly recommend going with an extremely simple weighting scheme, so as to minimize the acrimony of discussions that will certainly come. You don't want people to discuss why somebody got 15% of a paper, while somebody else got only 10%, because people are extremely fast in figuring out what this 5% difference means in $$$.
For each paper, get someone impartial to administer this. Then have all authors quantify everyone's contribution on a scale of 1-3. Don't go any finer, because anything finer is impossible. Let the impartial person pull all these together, average everyone's estimate of everyone's contribution and assign percentages based on the final number of points.
Advantages:
- This is simple and understandable.
- It requires no special software, apart from a few spreadsheets.
- And it gets the job done.
Disadvantages:
- It can easily be gamed. If someone consistently gives himself top marks, the impartial facilitator may want to have a discussion with this person.
- How can a junior author, perhaps an undergraduate student, assess the contribution of the PI and how much time he spent writing grants to get the money?
So it may well be that this is impractical, given the disadvantages. In which case you may need to fall back on someone senior unilaterally assigning contributions.
In such a case, I'd again work only with three-point scales. If your scale only includes three possible grades, you can meaningfully grade contributions into "minor", "medium" and "major". Anything more fine-grained, like a four-level scale, and people will start arguing why they only got a 2 when they obviously deserved a 3.
Everyone, please feel free to point out further shortcomings in the comments.
(And: try to get this policy revoked. It is horrible. Either the bonuses are too small to spend much time on such a scheme, and to fight over it - and someone will always pick a fight over this, no matter how trivial the sums are. Or the bonuses are high enough to matter, in which case the fighting will be worse. Better not to give bonuses based on paper contributions at all. Scientists should be motivated to write papers for other reasons, like tenure or recognition, which still seems to motivate enough people to write but should have drastically lower chances of poisoning your work environment.)
