Patron based proposal for mechanism 1.1 (instead of $-based goals)

You are right. I didn’t calculate that correctly.

tl;dr @mray is actually right :grinning:

We discussed 3 hours in mumble and found out where we talk past each other and where able to agree on things.

He is right that i can’t compare a 10 patron goal to a 100$ goal. I have just invented those numbers for my example.

To compare that, we would need real world numbers. In one case with a crowd-size goal and in another parallel reality the same patrons and a money goal. That is not possible. And projects are different. Popular projects have many patrons and niche projects could have enthusiastic patrons that pledge a lot of money. We could do A/B testing to get real world data.

So i simplified my example more to argue for my point. We have a money goal. Say there is someone that want to join the crowd and think how much they should contribute. They are on the project page on our platform and put in 5$ in the text field. They get direct feedback how that affect the rate (%). Now they put 10$ into the field and the bar moves more. They understand that 10$ has a higher impact than 5$.

Robert agreed that this effect exists. But in a realistic case, we have more patrons and a higher goal than in my simplified example and the difference is so small, that you don’t even see it. Less than 1%!


rate = total pledges / money goal x 100
rate = 25,000$ / 50,000$ x 100
rate = 50%
project get 12,500.00$

5$ pledge
rate = 25,005$ / 50,000$ x 100
rate = 50.01%
project get 12,505.0005
you pay 2.5005
your matching is 2.5$

10$ pledge
rate = 25,010$ / 50,000$ x 100
rate = 50.02%
project get 12510.002
you pay 5.002
your matching is 5$

100$ pledge
rate = 25,100$ / 50,000$ x 100
rate = 50.2%
project get 12600.20
you pay 50.2
your matching is 50$

500$ pledge
rate = 25,500$ / 50,000$ x 100
rate = 51%
project get 13005
you pay 255
your matching is 250$

it’s interesting that you pay always slightly more than your matching

Robert argues that you could show a similar number with a crowd-size goal, like: “your 1$ donation will result in X$ matching from the crowd”.


the project also want to get 50,000$ and know the average pledge is 5$

rate = number of patrons / crowd-size goal x 100
rate = 5,000 / 10,000 x 100
rate = 50%
project get 12,500

1$ pledge
rate = 5,001 / 10,000 x 100
rate = 50.01%
project get 12,503.0001 ((5000 x 5 + 1) x 0.5001)
you pay 0.5001
your matching is 2.5$

5$ pledge
rate = 5,001 / 10,000 x 100
rate = 50.01%
project get 12,505.0005 (5,001 x 5$ x 0.5001)
you pay 2.5005
your matching is 2.5$

500$ pledge
rate = 5,001 / 10,000 x 100
rate = 50.01%
project get 12,752.55 ((5000 x 5 + 500) x 0.5001)
you pay 250.05
your matching is 2.5$

it’s interesting that the matching is always 2.5$. your pledge has no effect

5$ pledge / 2000 patrons
rate = 2,001 / 10,000 x 100
rate = 20.01%
project get 2,002.0005 (2,001 x 5$ x 0.2001)
you pay 1.0005
your matching is 1$

5$ pledge / 4000 patrons
rate = 4,001 / 10,000 x 100
rate = 40.01%
project get 8,004.0005 (4,001 x 5$ x 0.4001)
you pay 2.0005
your matching is 2$

5$ pledge / 8000 patrons
rate = 8,001 / 10,000 x 100
rate = 80.01%
project get 32,008.0005 (8,001 x 5$ x 0.8001)
you pay 4.0005
your matching is 4$

5$ pledge / 9999 patrons
rate = 10,000 / 10,000 x 100
rate = 100%
project get 50000 (10000 x 5$ x 1)
you pay 5
your matching is 5$

Robert also said, that i get less matching when i pledge more with a money goal. I guess that’s correct, but i haven’t calculated it.

At the end, i said that i’m happy that we can still talk friendly with each other, even tho we disagree a lot in the forum. At times it can feel like we fight each other, but in the end we work on the same goal and know we have the same values. I’m happy with this result. Thanks for your time!

Before thinking further about this approach, i will check out the new proposals.

3 Appreciations

I think this is back to being incomparable and/or needing real-world data.

In a dollar-based goal, if you pledge a ton, you can get the crowd closer to the goal point, and doing that could result in lowering the number of patrons involved in hitting the goal. Proof: goal is $1,000 and I pledge $1,000 (given I’m allowed to), then I get no matching at all. If I’d pledged smaller, a crowd could grow.

In a crowd-based goal, if I pledge a ton, it won’t affect the number of patrons needed to hit the goal, so I will still be matched by the same number of others.

But in a situation with a dollar-goal that never is reached, then you could argue that higher-pledges get more matching.

In the end, more or less matching is possible in either scenario, and it all depends on how real people actually behave or respond to the different mechanisms.

Meta: thank you both for your persistence! I still strongly believe we come out of this stronger by working to find alignment, much better than if we don’t really work through things and just force a decision or something. But I do hope along the way we also learn how to continually improve our communication and efficiency! Cheers!

2 Appreciations

Today we talked 4 hours and 30 minutes. We agree on most parts!

Robert says, in both mechanisms, every patrons gives in relation to the success of the project, the match rate (%). It makes no difference if we measure it in crowd-size or total pledges. I agree, you can say it that way.

Based on that, Robert says “matching” don’t exist. It is no real money, only virtual. It exist only in the perspective of a single patron (A). The matching that A “receives” is the money that others give. So when looking from outside, the money the project get payed out is the money each patron give and the matching each patron receives for contributing at the same time. I use the same money 2 times and label it differently. Robert considers that dishonest and manipulation of patrons. But i think it is OK to explain the impact a new patron has with their action of joining from their perspective, that’s what they understand best.

I disagree that the matching is virtual, since it is real money the project get payed out from the other patrons, because i joined! Without my contribution, the project would not get it. It is no money that magically appear, but money our mechanism holds back.

Robert understand why i say the mechanisms are different, but because this difference is based on the matching he considers only virtual, he think this difference is also not important.

This difference is distribution of matching.

With a money goal, a patron receives more matching when they pledge more money (about 1:1). You see that in my examples in my previous post. You could frame matching as a reward for contributing. New patrons have an incentive to pledge more, because the project get also more money from the existing crowd. It is important for Robert, that i point out that this is not only the impact of the new patron, but also from the crowd, that provides the matching.

I think that is a good explanation we should use, because it can effect the decision of new patrons to pledge more. (based on the success of matched funding)

With a crowd-size goal, the total matching is distributed equally between all patrons. So every patron receive the same amount of matching, independent from their pledge. Someone who pledges more can provide matching for other patrons and create an incentive for them to join. That might be an incentive to contribute more. But they have to think around multiple corners.

So in the first case, a new patron consume matching the existing crowd offers (until it is exhausted = goal reached) and in the other case, a new patron can provide matching.

What i like about the money goal is that a new patron get a direct reaction from the crowd (matching) based on their action (pledge amount). In reality, that does only matter when the money is payed out and until then things can change, but i think that is obvious to new patrons. They might actually pay more % from their pledge and receive also more matching. But that is in their interest.

What do you think about this difference?

3 Appreciations
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 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. 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.

2 Appreciations

Nobody claims money getting payed isn’t real. It is the fact that you count it twice when using it as a selling point for how great crowdmatching is. When you count money twice – despite it only being present only once, what would you call that “extra” amount of money? I think it can becalled virtual, fake, make-up, theoretical, fantasy-money but most importantly it is not one thing: actual money.

I just propose we don’t advertise our mechanism with a by-product of theorisizing about matching mechanisms. Let’s keep it as a tool to quantify strength of connections, not equivocate it with actual money, especially with people that don’t wrap their head around that as much as we do.

1 Appreciation

If you agree that you have to leave economics and math we are on the same page. Things happening in your brain (e.g positive thinking) may have an impact on how you interact with the world, but it does not have a direct impact on your purse. So when observing “matching” happening more or less in different scenarios you may very well see an impact on peoples emotions, but that does not mean that dollar values have REAL value, they only suggest the idea of a value (that factually is made up).

When convincing people how crowdmatching is great – I don’t want to have to paint a mirage of amounts of money to make things appear awesome. No matter how well the effect may be proven to exist.

Matching is the potential of money being paid, that gets released – in tandem, by you AND THE OTHER patron, so we need to always be clear to not make it appear that it just your input that “creates” that extra money.

This is exactly what is going wrong when we only look at one patron and how actions of that one patron affect others. A surplus of matching from one person necessarily comes at the expense of the matching from the other side.

Attention: most of the time you can be on either side of that – the “winning” or the “losing”, even AFTER!!! you pledge.

1 Appreciation

Since we can abstract both concepts in ANY context to a mere “quantifying the success” of a project I don’t see how actuall values we assign can change anything.

A good analogy that exposes the error of thinking here would be the idea that expressing the worth of an amount of money depends of the currency you use to describe it. Yes, there are differences between currencies, and yes you can spot different numbers being used. But the very thing you set out to describe remains the same: The initial worth of money.

All I say is that among the ACTUAL differences we can ACTUALLY observe this is one of them - in some cases. I don’t say that is the only difference. I do in fact not see benefit in caring about rounding errors when comparing two mental models. I’m happy to change my mind as soon as I see relevant errors. So far I just mention them for completeness and for accuracy’s sake.

I think the whole misunderstanding/disagreement is that @mray only looks at plain math (what project get, same in both mechanisms) and i try do understand und explain the dynamic of matching.

He does agree that my equations and calculations are correct.

He also agrees that the money a project get payed out is real money.

And he is right that we now enter FRAMING territory.

Because i say, from the perspective of a new patron, the money the project get more after they joined consists his part and the matching the crowd pays.

And Robert does agree with what i say. He only disagrees because he don’t like the words i use or that i miss a detail. Of course the matching is payed by the existing crowd and does not just appear!!! We hold it back to reward new patrons. Please let us not waste time with such things and help me phrase it better!

That is what i said, only in slightly different words.

A (potential) new patron has questions and we can answer them on the website, so he can get a feel for how this “crowdmatching” works. That i’m able to answer them now is a big achievement for me!

  • What happens when i join the crowdmatching?

You pay a fraction of your pledge amount based on the % the goal is reached. The (existing) crowd will match that (about 1:1). When you pledge more, everyone gives more to the project. (this is the important part, the matched funding that is known to work!)

  • What happen when more patrons join?

When more patrons join or patrons pledge more, the goal is more reached and everyone donates more to the project.

  • What happen when patrons leave the crowd or lower their pledge?

The goal is less reached and everyone donates less to the project.

  • What is my role in the crowd?

You donate to the project with the existing crowd. The fraction you don’t pay yet is used to match patrons that join after you.

  • What happens when the goal is reached?

Since the goal is 100% reached, every patron pays 100% of their pledge. No further matching can happen. The project should set a higher goal to enable more matching.

(i’m talking only about money goal)

2 Appreciations

This is the touchy bit. And it highlights my point about goal-will-happen vs goal-won’t-happen, which are really two very different games.

If the goal will happen, then it’s not really true to say “when you pledge more, everyone gives more to the project.” If the goal will happen no matter whether or what you pledge, then you are either just enabling someone else to freeride (aka you are claiming a spot in the crowd instead of someone else) or adding non-matching funds on top of the goal or spreading the burden etc.

It could be rephrased like this:

When you pledge more, everyone gives more to the project, as long as this month is still below the goal.

The rest of your statements really only apply to the B scenario I described, the won’t-hit-the-goal-yet assumption.

I think that the matching idea is more effective with ambitious goals that won’t be hit, we should describe the goals as a budget-cap, and that we could then, in practice, function just as you describe. The framing and the matching won’t work if the goal is too low.

And both the project and the patrons should want a high goal in order to enable the matching motivations to continue.

Concrete example: Task Coach has 10,000 users that want it to be better. If they aim for 5,000-patron crowd as a goal, that allows all the matching motivations for a long time up to getting half the users to be patrons. That could result in a lot more funding, even if they never hit the goal. If they think even just 50 patrons would be nice and set it to that, maybe they could get the 50, but that number might just donate even with a simple “please donate” email. The matching motivation is basically not going to happen.

1 Appreciation

I added a Q+A about when the goal is reached.

Let’s discuss reaching goals/updating goals in another thread.

A more visual angle to wrap your head around:
If we can agree that the result is the same – we also have to agree that the freedom (or its absence) of having different properties prior to the result are irrelevant. Despite being factually different, and despite the properties on their own may be relevant in other contexts.

In our particular context the question of dollar vs. goal is purely cosmetic. Even if looks matter, I do not want to see us selling crowdmatching along its irrelevant properties of a “matching rate”. We have actual meaningful arguments like the idea of matching itself.

Yes the balls hit the wall at the same time, no matter where you put them. Check the link.

The result is only the same precisely at the goal point. But as I said this above, there’s two games I labeled A and B for will-hit-goal and won’t-hit-goal. They are not the same, and in the B scenario where you don’t hit the goal, the differences in the models remain different. Your visual is only valid for the A game, and “payout” is the wrong label, it’s “goal”. This reinforces my guess that you’ve been only focused on the A game all this time, whereas I think B is specifically the game we want to be playing more and will be mostly playing.[1]

For the B game, the payout points are along the curve and will not hit the end point at payout time, so how far along we are at the monthly payout is variable.

To make the match-rates comparable at all, we need at least the average sized pledge to get the same increase with either dollar-based goals or patron-based goals. Here’s the simplest example:

  • 10 patrons, each has pledged $100 toward $10,000 goal
    • match-rate is $1 per $100 pledged, so each gives $10, crowd total is $100
  • 10 patrons, each has pledged $100 toward 100-patron crowd goal
    • match rate is $1 per patron, so each gives $10, crowd total is $100

Consider a new patron deciding whether to join and what level. Assume they are confident that this month’s payout point will happen with no other changes and the goal will not be reached.

If they pledge:

  • Same $100 as everyone else
    • both scenarios grow to $121 total
      • That’s extra $10 from the existing crowd and $11 from the new patron (difference is because patron matches himself essentially)
  • Lower than the existing average, say only $10
    • Dollar-goal version grows to $102.01 total
      • That’s $1 extra from the existing crowd, $1.01 from new patron
    • Crowd-goal version grows to $111.10 total
      • That’s $10 extra from existing crowd, $1.10 from new patron
  • Higher than average, say $1,000
    • Dollar-goal version grows to $400 total
      • That’s $100 extra from the existing crowd, $200 from new patron
    • Crowd-goal version grows to $220 total
      • That’s $10 extra from existing crowd, $110 from new patron

Thus, the crowd-based goal gets proportionally more matching of a pledge when patrons make below-average pledges, and the dollar-based goal gets proportionally more matching of a pledge when patrons make above-average pledges. The differences do not collapse, and they are not virtual or illusory. This difference could happen and then immediately after that, a payout point occurs.

Within the assumption that the month’s payout will not hit the goal point, we can fairly conclude that there exists motivation toward lower pledges in the crowd-based game and toward higher pledges in the patron-based game. That conclusion is based on the math alone and does not account for whether patrons want to be extra generous (i.e. to offer extra matching to others) or other questions about real people’s motivations and behavior.

  1. Also, as long as players behave differently, then even the A game goal-point will be different. It might lead to different amount of patrons or different amount of funding. That's harder to compare, but because of the different way of getting to the goal point, the actual goal even in the A game can be different between the two models. ↩︎

2 Appreciations

Yes, that was always the feeling i had and now we see it very clear and can explain it. :tada:

As said earlier, you can see the matching as a reward for contributing, since it means the project gets more money and that is what the patron wants. When they get a higher reward when they pledge more, they will at least consider it, given that they understand this relation.

Maybe the text on the image was misleading? That’s not the goal. The end of the track is the end of the month: You pay what you pay, others pay what they pay, everybody pays for the reason they pay – it is payday! And it is the same in a patron based or dollar based matching scenario.

Matching rate is just where you put the ball on the track. You may feel “positive” to place it at the tippity top – but if you think that’s going to have an impact in the end – you’re about to be surprised.

This thread is about what we want to express with any “%” - value. Please show me how your two new games are relevant to that question.

Robert, you can’t say the math is wrong.

My post above has exactly the same set of patrons. Two identical scenarios as much as comparing is possible at all. The patrons make the same pledge sizes. The output, i.e. the actual amount of money that the project gets at payday is different between the two mechanisms.

1 Appreciation

Yes I can! But I didn’t – what is going on here?

  • identical scenarios
  • same set of patrons
  • patrons pledge the same
  • different payout?!?!!?!?

So … where did the money go that did not get spent in the one scenario? (or were the scenarios really identical :thinking:)

The scenarios start out as close to identical as you can get with a crowd-goal vs a dollar-goal. The same patrons are indeed making the same size pledges. The payout is indeed different.

The two mechanisms respond differently to the different input. It’s that simple.

Here’s how it works:

  • in crowd-based goals, each pledge has a fixed effect on the % of the goal that has been reached
  • in dollar-based goals, each pledge can have a variable effect on the % of the goal that has been reached

And this is also factually true, not an interpretation. This is a fact about the incentives the mechanism sets up (but I’m not saying these are the only incentives or that how much this particular patron description matches the motivations of real-world patrons):

Given a patron with the goal of maximizing the amount of money that others give to the project but to do so at the least possible cost to themselves, then:

  • in crowd-based goals, their winning strategy is to make the minimum allowed pledge
  • in dollar-based goals, their winning strategy is to make the maximum allowed pledge[1]

These are the necessary outcomes of simply programming a computer to find the winning strategy given setting the program to have these goals.

  1. for this case, assume they are not allowed to just make the crowd hit the goal and that the goal in fact won't be reached ↩︎

1 Appreciation