Discussing charity through marginal price discrimination

Author: Vitalik Buterin

Original Title: 《A Note On Charity Through Marginal Price Discrimination》

Published on: March 11, 2017

Here is an interesting idea I proposed two years ago, which I personally believe has promise and can be easily implemented in the context of the blockchain ecosystem, although it can certainly be implemented using more traditional technologies if needed (the blockchain would help achieve network effects by placing the core logic on a more neutral platform).

Suppose you are a restaurant selling sandwiches, and you typically sell them for $7.50. Why do you choose to sell them for $7.50 instead of $7.75 or $7.25? It is clear that the production cost cannot be $7.49999, because in that case, you would have no profit and could not cover fixed costs; therefore, in most normal cases, if you sell for $7.25 or $7.75, you can still make some profit, albeit less. Why not below $7.25? Because the price is lower. Why not below $7.75? Because you get fewer customers. Coincidentally, $7.50 is the optimal balance point between these two factors.

Note one consequence of doing this: if you make a slight distortion to the optimal price, then even compared to the magnitude of the distortion, the loss you face is minimal. If you raise the price by 1%, from $7.50 to $7.575, then your profit will drop from $6750 to $6733.12—only a 0.25% decrease. This is profit—if you donate 1% of the price of each sandwich, your profit will decrease by 5%. The smaller the distortion, the more favorable the ratio: raising the price by 0.2% will only reduce your profit by 0.01%.

Now, you might argue that stores are not completely rational and not fully informed, so considering all factors, they may not actually charge the optimal price. However, if you do not know the direction of any given store's bias, then even in expectation, the scheme still works in the same way—except for a loss of $17, it is more like a coin toss, gaining $50 half the time and losing $84 the other half. Moreover, in the more complex schemes we will describe later, we will adjust prices in both directions simultaneously, so there will be no additional risk—regardless of how correct or incorrect the original price is, the scheme will give you a predictable small net loss.

Furthermore, the above example is one where the marginal cost is very high and customers are very price-sensitive—in the above model, charging $9 would result in no customers at all. In cases where the marginal cost is much lower and customers are less sensitive to price, the losses from raising or lowering prices would be even lower.

So what is the point of all this? Well, suppose our sandwich shop changes its policy: it sells sandwiches to the public for $7.55 but lowers the price to $7.35 for those who voluntarily participate in maintaining some local parks for charity (let's say this is 25% of the population). The shop's new profit is $6682.5x0.25 + $6742.5x0.75 = $6727.5 (a loss of $22.5), but the result is that you now pay 20 cents to all 4500 customers, giving them 20 cents each to volunteer for that charity—a reward amount of $900 (if you only count the customers who actually volunteer, that would be $225). Thus, the shop loses a little but gains tremendous leverage, effectively contributing at least $225, depending on how you measure it, at a cost of only $22.5.

Now, what we can start to do is establish a "sticker" ecosystem, where these stickers are non-transferable digital "tokens" that organizations distribute to those they believe contribute to valuable causes. The tokens can be organized by category (e.g., poverty alleviation, scientific research, environment, local community projects, open-source software development, well-written blogs), and merchants can charge slightly lower prices to token holders representing any cause they personally support.

The next stage is to make the program recursive—becoming or working for merchants that offer lower prices to green sticker holders is enough to earn you a green sticker, although its effectiveness is lower and the discount you receive is smaller. In this way, if the entire community supports a particular cause, then starting to offer discounts for the relevant stickers may actually maximize profits, so economic and social pressures will maintain a stable balance of spending and participation in the cause.

In terms of implementation, this requires:

• Sticker standards, including wallets for people to hold stickers
• A payment system that supports charging lower prices to sticker holders
• At least some organizations that issue stickers (the minimum overhead might be issuing stickers for charitable donations and easily verifiable online content, such as open-source software and blogs)

So this can certainly be guided in a small community and user base, and then grow over time.

March 14, 2017 Update: This is an economic model/simulation showing the above implementation as a Python script.

July 28, 2018 Update: After discussions with others (Glen Weyl and several Reddit commenters), I realized some additional things about this mechanism, some encouraging and some concerning:

• The above mechanism can be used not only by charities but also by centralized corporate participants. For example, a large company could bribe a store to offer a 20-cent discount to any customer of its products for $40, thus generating far more than $40 in additional revenue. So it is empowering but has potential dangers in the hands of bad actors… (I haven't researched it, but I'm sure this technique has been used in various loyalty programs)
• The above mechanism has the property that merchants can "donate" $x at the cost of $x^2$ (note: $x^2 < x$ on the scale we are discussing here). This gives it an economically optimal structure in some ways (see quadratic voting), as merchants with a twice as strong feeling about certain public goods will tend to provide twice the subsidy, while most other social choice mechanisms tend to either underestimate (as in traditional voting) or overestimate (as through lobbying to purchase policies) stronger versus weaker preferences.