on how "virtual" or real the matching is
The “virtual” matching as @mray puts it is the difference between two realities, one with the pledge (or with the higher or lower pledge) and the one without it. While only one scenario is “real” in any given actual specific project and point in time, it’s valid to make this comparison.
Saying that it’s all “virtual” is the same logic as saying that all decisions (in everything in life) only have virtual impacts, given that we only get to see one version of reality and the alternate reality is just an idea. As long as we accept the idea that any decision or action ever has a “real” impact, then the matching effect is “real” in that same sense. In all cases, we can only describe such impacts by imagining the alternate reality.
We can probably best get useful evidence about real-world differences through controlled observations like A/B tests or playing out the models in prototype games etc.
The idea that the difference is unimportant is a strong assertion that is not justified by labeling the matching “virtual”. For it to be unimportant, it has to actually not matter in terms of fundraising. But we can only strongly say that it affects fundraising by going all the way to the psychology, framing effects, etc.
Assuming reaching the goal or not?
I suspect there’s a key question that pumps different intuitions and may be a source for our misunderstandings and disagreements: Do we expect that the goal will get reached or not?
Two scenarios:
- A) everyone can realistically expect the project to reach its goal point
- B) everyone can realistically expect the project to not reach its goal point
The math, motivations, intuitions, psychology, the effects of pledges… these vary greatly between the A and B. They are different games almost.
Like iterative vs one-off game theory situations
Consider the difference between one-off vs iterative prisoner’s dilemma (PD) (see Snowdrift Wiki - The Snowdrift Dilemma for more among other links).
- One-off games always motivate betrayal
- Even an iterative game with a defined end-point degrades to the logic of betrayal.
- Only an iterative game without a clear end can logically motivate trust-building and cooperation
It’s important to note that the assumptions about the one-off or clear-end games do not hold when it’s iterative indefinitely!
Scenario A and freeriding
In A, more people may choose to freeride because they see that the project will succeed anyway! That’s true regardless of dollar-goal vs crowd-goal.
There might be differences in the motivations to pledge more or less (as opposed to whether to pledge at all or not), I’m not sure.
With a dollar-goal in the A scenario, higher pledges enable others to have lower goals or to freeride more. But in crowd-goal, higher pledges do get actually more funds to the project.
Of course, we might have to get into discussing what happens at the goal point (if new patrons still pledge or pledges are raised, what happens etc).
Perhaps @mray tends to think of the A game. That scenario collapses any difference between the amount of matching in the two types of goals.
But in the B scenario where the goal will not be reached (perhaps it is ambitious or just a long way off, e.g. Snowdrift.coop aiming for $36,000/month which nobody expects to happen any time soon, even though it’s feasible in principle), there’s effectively NO GOAL really. In the B scenario, the goal is only a framing of the match-rates and a failsafe to ensure pledges won’t run away into infinity.
I think the B scenario brings out the intuitive differences between dollar-goal and crowd-goal, but still these differences aren’t enough to conclude that one or the other is better. That’s almost certainly going to be based on values and other not-just-math-or-logic aspects of how real people and projects react to the two options.
Given the B scenario, I think the mathematically clearest distinction is:
- Crowd-based goal: a raised pledge raises the crowd’s mean donation but not the median
- Dollar-based goal: a raised pledge raises both the crowd’s mean and median donations
The difference could be more than a rounding error
@mray has described the difference here as a “rounding error”, and that might be fair, or it might not be. It’s not so clearly irrelevant that we can just dismiss it as such.
One could argue that a single patron’s modestly larger pledge gets lost in the crowd and that a penny more from the other patrons is near-zero. This would not hold true in the case of a huge pledge, one we might disallow to avoid excessive influence of one patron. It would also not be true if a large portion of the crowd makes higher pledges.
Whether the difference is enough to make noticeably greater motivation toward higher-pledges in the dollar-goal scenario (and whether that’s even something we want), I’m not sure. It probably depends on how we set up the points in a game-theory model or for real people, whether the principle of it motivates them or not.
I’m quite sure that this is a real not-just-rounding-error and not-just-virtual-matching distinction. But even acknowledging this, I don’t think this is the distinction that will make the difference in our decisions.