cross-posted to ethresear.ch and LessWrong

Motivation

Quadratic funding^[1] is a powerful mechanism for resolving some collective action problems. But it has a major limitation - it relies on some third party, that provides a matching pool of funds.

In the most dangerous collective action problems, we don't have such third party helping us from above. Those situations already involve the most powerful actors, so we can't expect someone more powerful to resolve the conflict, like a galactic mom.

Some examples:

global superpowers trying to coordinate to fight climate change
AI organisations coordinating to pay AI alignment tax (more info here)
- for example by funding safety research
- or creating some large dataset together, that's useful for alignment
- or funding methods which are thought to be safer, like STEM AI or tool AI
in general, escaping inadequate equilibria (see this post for many great examples)
and most importantly, conflict between transformative AI systems or their owners^[2]

Solution

One thing we can try in this situation, is to create a smart contract where each party says "I'll pay more if others pay more". This way, if you decide to increase your contribution by 1$, it causes the pot to grow by more than 1$, because your dollar caused other agents to contribute some more. This leverage, in some situations can be enough to make someone pay, because the value they get out of the bigger pot is higher than what they have to pay.

Some properties that it would be nice to have in such a system are:

continuity - every increase in your payment causes an increase in others' payments
known payment limit - you won't have to pay more than some limit you chose
everyone is incentivised to contribute something - just like in quadratic funding, small contributions get a high leverage (it can get arbitrarily high, as you'll see later) - so even if you're only willing to pay if you get >100x leverage, there is always some contribution size that gives you such a high leverage

A very simple system that has these properties is given by those equations:

$h = \sum i \sqrt{p a y m e n t_{i} (h)}$ $p a y m e n t_{i} (h) = \frac{l i m i t_{i}}{\frac{π}{2}} a r c t a n (h * s a t u r a t i o n_s p e e d_{i})$

$p a y m e n t_{i} (h)$ is the amount that i'th agent has to pay
$l i m i t_{i}$ is the i'th agent payment limit
$s a t u r a t i o n_s p e e d_{i}$ tells how quickly i'th agent's limit will be approached as new agents make contributions (the choice of this parameter is underspecified for

...

Quadratic voting

Further reading

Related entries