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.