Here is how I think scientific funding should work.
Funding should be allocated by experts and stakeholders, using a voting mechanism, to problems (e.g. an unproven conjecture, a rare disease, an inconsistency in physical law) and not methods (a particular class of drugs, artificial neural networks, string theory, etc.). The non-expert stakeholders, especially, should not influence the way the problem is approached.
The voting mechanism should allocate money to problems proportionally to the votes received; it should not completely deny funding to unpopular problems.
Proposals to work on a particular problem should not pre-select a method of solution, but rather describe hypotheses about the problem.
Voting should again be used to match one or more proposals to problems. These votes represent a consensus of experts on both which hypotheses are most valuable to test and which investigators are most capable, not which solutions are most likely to work (which is generally impossible to predict, as demonstrated by the long history of upsets in science).
In this scheme, it is important to have a rotating subset of experts for each problem remain neutral/non-voting, as will be explained later.
This voting would ideally be conducted anonymously, to deter bribery, manipulation, and nepotism.
If proposals for a problem fall into categories by field, there should be a cap on the proportion of funding received by a single category; it makes sense, in the face of the unknown, to hedge our bets.
Funding should cover at least two years of work. It is hard to do good science in a hurry.
Upon completion, each project (the result of one proposal) should be evaluated by the neutral (non-voting) experts for that problem, and given a scalar success rating (say, from 0 to 10). Each voting expert should have the weight of their vote rebalanced based on the cumulative average success rating of projects they voted for.
Success need not mean “the hypothesis in the proposal was correct.” Showing that the hypothesis is false is still good science. Furthermore, coming to an entirely different conclusion (that the hypothesis was not meaningful) should be acceptable, to the extent that the experts find the conclusions useful.
The vote rebalancing scheme means that more established experts, with a track record of success, can confidently use their votes on risky proposals, since the risk to their average success will be minimal.
One would expect the established experts to have a better view of the field, and that their bets would pan out more frequently.
This most important part of this scheme is that it partially decouples the work one does from standing as an expert—someone who consistently predicts successful projects, but chooses to spend their time doing risky or niche work, is still considered valuable. Furthermore, one need not wait to become established to do risky work; all that’s necessary are votes from people willing to bet on it.