Annual 'splitting' of funding gaps can be partial funging when gaps carry over across years

In a 2015 blog post, the Open Philanthropy Project contrasted several strategies for coordinating Good Ventures' donations with those of smaller donors. One was 'splitting,' in which a large donor commits to funding only a fixed percentage of a funding gap (between two thresholds of efficacy) in a given year. The advantage of this is said to be that a $1 marginal donation by a small donor will increase funding to the recipient charity by $1, in contrast to 'funging' where the large donor reduces its donation in response to the small donor, so that funding to the recipient charity increases by substantially less than $1. However, this distinction does not hold when funding gaps can substantially carry over from year to year. In the limit of perfect carryover, funging of small donors could approach 100%. With substantial stochastic carryover funging could be likewise substantial, while 'one-time' opportunities may suffer minimal funging. I suggest that some accounting for carryover across periods must accompany 'splitting' to avoid donor illusion.

In the 2015 giving season Holden Karnofsky, writing on behalf of the Open Philanthropy Project, discussed three categories of proposals for how its donation recommendations to Good Ventures should respond to the gifts of small donors: 'funging', 'matching', and 'splitting.'

1. “Funging” approaches. Individuals do most of their giving in December. We could wait until we’ve seen how much support comes in for each of our top charities, and then – in, say, February of 2016 – recommend Good Ventures grants to fill whatever funding gaps remain.
This would have the advantage of fully funding top charities, while not spending more (in the short run) than necessary to do so. However, it would have the disadvantage of creating a long-term incentive for individuals to stop supporting our top charities, since the only effect of their giving (in this scenario) would be to reduce the amount we recommend to Good Ventures. Most individuals would probably not notice this issue unprompted, but it’s very important to us to be open with our audience about the pros and cons of taking our recommendations, and we don’t want our offering to be valuable/attractive only to people who misunderstand it. 

There are a variety of “funging” approaches that are less precise and less obvious than the one outlined above, but that we feel ultimately have the same basic pros and cons. Any approach that is designed to ensure that the entire funding gap is always filled will be creating the kind of problematic incentives outlined here. 

2. “Matching” approaches. Rather than recommending that Good Ventures fill theremaining funding gaps after accounting for individuals, we could recommend that they give $1 for each $1 we track from individual donations. This would create the opposite incentives to those created by “funging”: it would mean that individuals had a magnified, rather than reduced, incentive to support top charities.
The disadvantage of this approach is that it would tie the recommended level (and allocation) of Good Ventures’s funding to decisions made by individuals. This could result in recommendations to give much less than is optimal, or much more, or much differently (e.g. with a much different allocation across charities). There are also logistical challenges involved with matching programs. 

3. “Splitting” approaches. When trying to coordinate with another funder who can’t be directly negotiated with, one approach is to come up with what seems like a “fair share” of the funding gap each would provide, and simply recommend that Good Ventures commit to providing its “fair share” – no more and no less, regardless of the other funder’s behavior. 

This approach has pros and cons somewhere in between those of the other two.

• Incentives: The incentives it provides other donors aren’t actively positive (as with matching). But they are neutral, provided that the “fair share” is chosen in a principled way rather than as a response to the projected behavior of the other funder.

• Amount and allocation: The amount recommended at a given time will not be optimal (as it is with “funging” approaches). But unlike with “matching,” we recommend closing a substantial proportion of each important funding gap, and prioritizing the higher-value funding gaps, regardless of how other donors behave.

Our preference at the moment. All three of these approaches have issues. Even in theory, it’s hard to reconcile the basic goals of (a) closing important funding gaps and (b) creating good incentives for other donors. When dealing with another major donor whom we can have a direct discussion with, it is often possible to be mutually honest about our thinking and agree to a fair-seeming split; but when thinking about how to coordinate with a large number of individual donors whose time and attention is scarce, any approach we take will be suboptimal in some major ways. 

For this year, we have chosen the “split” approach. It is relatively simple to execute (unlike “matching” approaches) and keeps incentives relatively simple for donors (unlike with “funging” approaches). It avoids the worst problems with each of the other approaches, while not being perfect by any criterion...

That discussion seemed to assume that splitting would result in a $1 donation from a small donor increasing funding to GiveWell top charities by approximately $1. Indeed, the post said that the rule would "avoid any reality or appearance of 'funging' that might create problematic incentives for individuals":

We are currently reasonably happy with the output of this approach. It reliably leads to recommending that Good Ventures fill a significant part of top charities’ funding gaps, while also being principled enough to avoid any reality or appearance of “funging” that might create problematic incentives for individuals. We felt this was the best approach we could come up with given time constraints, since we wanted to announce our recommendations to Good Ventures along with our recommendations to individuals, so that individual donors would have the knowledge of our recommendations to Good Ventures before making their own giving decisions.

The problem of funding gap carryover
The above analysis works best when considering a single giving season, where a funding gap is calculated once, the large donor commits to a split, and then small donors respond. But when the process is repeated, we get geometric series which can involve important funging. Consider the case of Daily Splitting:

As of December 1st, a funding gap of $1,000,000,000 exists for some charity, e.g. a scaled-up cash transfer charity such as GiveDirectly. Each day from December 1st-31st, a large donor calculates the remaining funding gap and donates half of that amount, after which small donors may donate to further reduce the gap.

In Daily Splitting, if no small donors ever make a donation then the large donor will fill $999,999,999.53 out of the $1,000,000,000 gap, leaving a 2^(-31) share of the original gap unfilled. A small donor who donates with n days left in the month will have the counterfactual impact of her donation on the end-of-year funding reduced by a factor of 2^(-n), relative to its face value.

When recalculation and re-splitting take place annually the numbers will not be so astronomical, but over a few years could still be substantial. E.g. suppose that funding gaps carry over perfectly for 3 years with annual recalculation and re-splitting. Then the donor is funged 50% after 1 year, 75%, after 2 years, and 87.5% after 3 years leaving a counterfactual impact 1/8th of the face value.

So if funding gaps carry over heavily then splitting, rather than avoiding any reality or appearance of funging, might involve drastic funging.

Carryover with predictable expiration dates
Suppose that funding gaps have a knowable lifetime of only a year or so and then expire, so new funding gap must be filled when it appears or in the next giving season. Will a small donor donating now reap higher marginal impacts by averting the expiration of opportunities? If charities follow a first-in, first-out (FIFO) system to minimize expiration, then almost all opportunities can be met before they expire.

Suppose each year $100 MM of new funding gap is added, and the large donor fills 50% of the total gap (including carryover), with no small donors involved. In year 1 the large donor gives $50 million, leaving a carryover of $50 million. In year 2 there is a total gap of $150 million, $50 million about to expire, and the donor gives $75 million, clearing the old gap and leaving $75 million of carryover. In the limit, each year carryover of $100 million is fully paid off.

If funding gaps are growing at an accelerating rate, there is even less danger of predictable expiration, but decelerating funding gaps could partially expire.

If expiration dates are much less than a year then a commitment could simply be effective.

Continual or stochastic decay of funding gap carryover
In the more realistic case where funding needs do not come with clear expiration dates, but decay each period, then any carryover bears a risk of permanently unmet funding needs. Suppose that carryovers decay at a constant rate of x% per annum, and addition of new funding gap is steady.

In the first year a donation of $100 averts $x of decay. In the second year it averts $x*(1-x%)(50%), continuing in a geometric series.

Decay rate	10%	25%	50%
Impact per small donor $100	$18.18	$40	$66.67

Splitting should be accompanied by an analysis of carryover funging effects
It appears to me as an observer at the sidelines that there is carryover for some of GiveWell's recommended charities, at least in probabilistic terms (fractional distributions, etc). This is not simply a universal feature of charitable donation, since many charities are primarily funded by donors who are not aggressively adjusting their donations to current needs and impacts but instead giving small amounts in social contexts, in response to direct mail, etc.

Should carryover funging be made explicit or eliminated?
Crude methods to reduce carryover funging might involve the large donor filling 50% of 'new funding gap,' or reducing calculated gaps by past unmet gaps. More complex methods might try to make unbiased estimates of funging effects and directly counter them (e.g. with matching).

As with more explicit funging, avoiding this means reduced control over total funding levels in the short run, and correspondingly increased risk of suboptimal funding allocations in hopes of preserving more funding for later expenditures.

Alternatively, Good Ventures might fill funding gaps like AMF, leaving GiveWell to recommend GiveDirectly or other future charities capable of extreme scaling. This would be especially appealing if money saved by Good Ventures would ultimately be used for opportunities substantially less attractive than AMF (e.g. marginal cash transfers added to an immense pool).

My own sense is that Good Ventures' opportunity cost (which might be the ten billionth or hundred billionth dollar donated) has a good chance of being a better bet (e.g. in QALYs, DALYs, and other metrics) than the direct effect of AMF. Some candidates that loom large in my mind include interventions that combine the leverage of science (including scientific reform) or politics with focus on the global poor, nonhuman animals, or future generations.

Many other considerations bear on this question, but regardless of the answer I would like to see accounting for cross-period funging. Even if splitting is replaced with filling or funging going forward, assurances about its non-funging were given in past years, and these should be addressed.

[Disclosure: I do some consulting work for GiveWell regarding the Open Philanthropy Project.]