Resolving Disputes with a Statistical Court
Dispute resolution for uninsured transactions
The statistical court mechanism builds on the idea that we may not be able to resolve every individual dispute. Instead, we can aim to reward providers and buyers that consistently behave properly, and have negative consequences for providers and buyers that consistently misbehave.
If Quorum for a court resolution was not reached, the provider's collateral $l$ is simply burnt. However, the statistical court mechanism will ensure that if the transaction was originally between an unreputable buyer and a reputable provider, the collateral $l$ was a small amount in the first place.
The key insight we build on, is that the graph value $G_u$ and $G_v$ we have designed, gives us a notion of how real and valuable a given provider and buyer are.
A provider's (buyer's) reputation is based on the satisfaction scores they have received from real and valuable buyers (providers). Having a low reputation will, in turn, diminish your graph value, which entitles you to fewer rewards, and reduces your leverage for demanding collateral $l$.
We summarize the mechanism in the following steps:

When a transaction takes place between a provider, $u$ and a buyer $v$, the provider locks $l$ as collateral. When the transaction is finished, $u$ gives $v$ a review $r_{vu}$, and $v$ gives $u$ a review $r_{uv}$. These reviews are a numerical score from 0 to $r_{\rm max}$ (for example a 5star system). If no review is given, it is assumed $r_{\rm max}$ was given.

The provider builds a reputation score over time given by a weighted average over all the reviews from all transactions, weighted by the graph value of the reviewer.
$r_u=\frac{1}{N_{\rm reviews}}\sum_{\rm reviews} r_{uv}G_v$Similarly, there is a buyer reputation,$r_v=\frac{1}{N_{\rm reviews}}\sum_{\rm reviews} r_{vu}G_u$ 
Note that if all the reviewers have low graph values, even if they all give $r_{\rm max}$ scores, the total reputation will be low. To gain a high reputation, a good number of reviews by valuable users is needed.

The reputation is incorporated into the provider and buyer's graph value, $G_u\to G_u\cdot r_u$, $G_v\to G_v\cdot r_v$.
Suppose a buyer consistently makes false claims that the service was not completed. If a large enough number of real and valuable providers give bad reviews to this buyer, they will lower the buyer's graph value. This, in turn, means that the buyer can only demand a small amount of collateral $l$ for transactions, which means they cannot harm more providers by continuing to claim services were not delivered.
In summary, the graph value function for producers can look like,
For buyers, the collateral for each transaction $l$ is determined as a function of the total transaction fee, $f$, and the graph values of producer and buyer, $l(f,G_u,G_v)$, is a function that,
 $l(f,G_u,G_v)$ is proportional to $f$.
 $l(f,G_u,G_v)$ monotonically decreases with increasing $G_u$.
 $l(f,G_u,G_v)$ monotonically increases with increasing $G_v$.