Would you need to choose the leverage schedule so that you’re unlikely to fully fund the project? Otherwise, the leverage guarantee could be misleading: once it is (nearly?) fully funded, leverage must decrease with the number of donors, since some could have dropped out without reducing overall funding to the project.
(i) the project has a strict upper limit on funding required. In this case, if you must (a) limit the pool of participants, and/or (b) their allowed contribution scales, and/or (c) maybe indeed the leverage progression, meaning you might incentivize people less strongly.
(ii) the project has strongly decreasing ‘utility’-returns for additional money (at some point). In this case, (a), (b), (c) from above may be used, or in theory you as organizer could simply not care: your funding collection leverage still applies, but you let donors judge whether they find they discount the leverage for large contributions, as they judge the value of the money being less valuable on the upper tail; they may then accordingly decide to not contribute, or to contribute with less.
Finally, there is simply the possibility to use a cutoff point, above which the scheme simply must be cancelled, to address the issue that you raise, or the one I discuss in the text: to prevent individual donors to have to contribute excessive amounts, when more than expected commitments are received. If that cutoff point is high enough so that it is unlikely enough to be reached, you as organizer may be happy to accept it. Of course one could then think about dynamics, e.g. cooling-off period before you can re-run the cancelled collection, without indirectly (too strongly) undermining the true marginal effect in a far-sighted assessment of the entire situation.
In reality: I fear even with this scheme, if in some cases it hopefully turns to be practical, many public goods problems remain underfunded (hopefully simply a bit less strongly) rather than overfunded, so, I’m so far not too worried about that one.
Would you need to choose the leverage schedule so that you’re unlikely to fully fund the project? Otherwise, the leverage guarantee could be misleading: once it is (nearly?) fully funded, leverage must decrease with the number of donors, since some could have dropped out without reducing overall funding to the project.
You’re right. I see two situations here:
(i) the project has a strict upper limit on funding required. In this case, if you must (a) limit the pool of participants, and/or (b) their allowed contribution scales, and/or (c) maybe indeed the leverage progression, meaning you might incentivize people less strongly.
(ii) the project has strongly decreasing ‘utility’-returns for additional money (at some point). In this case, (a), (b), (c) from above may be used, or in theory you as organizer could simply not care: your funding collection leverage still applies, but you let donors judge whether they find they discount the leverage for large contributions, as they judge the value of the money being less valuable on the upper tail; they may then accordingly decide to not contribute, or to contribute with less.
Finally, there is simply the possibility to use a cutoff point, above which the scheme simply must be cancelled, to address the issue that you raise, or the one I discuss in the text: to prevent individual donors to have to contribute excessive amounts, when more than expected commitments are received. If that cutoff point is high enough so that it is unlikely enough to be reached, you as organizer may be happy to accept it. Of course one could then think about dynamics, e.g. cooling-off period before you can re-run the cancelled collection, without indirectly (too strongly) undermining the true marginal effect in a far-sighted assessment of the entire situation.
In reality: I fear even with this scheme, if in some cases it hopefully turns to be practical, many public goods problems remain underfunded (hopefully simply a bit less strongly) rather than overfunded, so, I’m so far not too worried about that one.