# Why does it seem like the average cost threshold protocol has a possible gain but no chance of loss?

So, the average cost threshold protocol is a theoretical protocol for crowd funding club goods (it can also be used to crowd fund public goods, but I'll only focus on club goods in this post). It is explained here, but I'll give a brief summary.

Let's say someone created a club good. As an example, I'll say the good is a ebook titled "Introduction to the Bean trade". The author decides to sell it using protocol.

To do this, he comes up with some price $$R$$. This is how much total revenue he wants to accrue by selling the book. He then announces to the public that he is selling his book using the average cost threshold protocol, and what value he assigned $$R$$.

Now, potential buyers announce how valuable they think the book is to them (they could lie, but as it turns out there is no incentive to do so). Let $$V_i$$ be the value consumer $$i$$ announced.

Now, most likely using a computer, a price $$P$$ is calculated. This price $$P$$ must the minimum price such that $$|B_p|P = R$$, where $$B_p$$ is the set of consumers such that $$P \le V_i$$. If such a price does not exist, the protocol failed, and no products or money change hands. It can however be attempted again if wanted, and may succeed if there are more buyers or the buyers announce a higher value. (In an actual implementation, if no $$P$$ is found, you can just wait until more buyers show up, instead of requiring them all to announce it at the same time.)

Finally, all customers in $$B_p$$ pay the author $$P$$ and the author gives each of them a copy of the ebook. The author has made his revenue $$R$$, as intended, and the customers got a copy of the ebook in exchange for a price no greater than how much they valued it.

The protocol is usually defined in such a way that more potential customers may announce prices, and previous potential customers who were not in $$B_P$$ may change their prices. If this causes the value of $$P$$ to change to $$P'$$, new customers pay $$P'$$ to the author and previous customers are refunded $$P - P'$$. However, for simplicity, I will say that protocol ends immediately after failing or a transaction being made.

Anyways, now for the paradox. If a custom believes that the book has value $$V_i$$, and they announce this price, then three things can happen:

• The protocol fails or $$V_i < P$$. They do not pay, nor do they get the book. Their net gain is $$0$$.
• The protocol succeeds with $$P = V_i$$. They pay $$P$$ and get the book of value $$V_i$$. Their net gain is $$0$$.
• The protocol succeeds with $$P > V_i$$. They pay $$P$$ and get the book of value $$V_i$$. Their net gain is $$V_i - P$$, which is positive.

The problem is that the net gain is always positive. I was under the impression that there are no guaranteed gains in economics. If there was, everyone would be using this all the time until people ran out of ideas for club goods.

Here are some potential explanations I thought of, but I have an issue with each one:

• If the protocol fails, the author eats the price of the book. A small modification can be made to fix this, however. Have the customers announce their prices before he writes, so he can determine if $$P$$ will exist. The only risk to him then is if he fails to complete the book. This risk can probably be factored into $$R$$. So the author would have a risk, but he would still probably take it (since he has to take it to write the book anyways, regardless of how he sells it), and the customers still have no risk.
• The author created value when he wrote the book, so of course the average gain will be positive. However, even when creating value guaranteed gains should not exist, since otherwise everyone would create value that way.
• The customers announce a price higher than their true $$V_i$$ for some reason, which makes incurring a loss a possibility. However, the possibility still remains that they could have gotten a guaranteed gain, so the paradox remains.
• The value of the book turns out to be less than the customer anticipated. For example, maybe the bean trade goes into decline. However, it should be possible to hedge something like this out. The customer can also require the author to publish a set of standards the book will meet before they announce a price, and make the payment contingent on the book meeting those standards. The customer can also announce a value that is a conservative estimate of the book's value.
• The customer incurs an opportunity cost by locking up their funds. This will not be recouped if they are not in $$B_P$$. This can be resolved by making sure it is quickly determined what $$P$$ is after the values are announced, if it exists. This way the customer only needs to lock up their funds if they are in $$B_P$$. When they announce their value, they can deduct the expected opportunity cost from it.

So, what is going on? What does it seem like this protocol results in a possibility of a gain without a possibility of a loss?

• If the protocol fails, repeatedly, the author lost a lot of time. Even if it succeeds for a lower R, what if R is less than the amount of rent the author had to pay during that time? Oct 25, 2021 at 8:59

Example. I buy an apple from Walmart for $$\1$$. I gain, because I value the apple at more than $$\1$$. Walmart also gains, because the cost of selling the apple is less than $$\1$$ for Walmart.