Editing Forum reference mechanisms


The reference mechanisms which support the [[judicial governance]] process of reweighting the [[Forum]] WDAG under [[DAO Governance Framework|DGF]] are leaching and donating. Combined with an incinerator function, these primitives are [[Forum reference mechanisms#Completeness|complete]], in the sense that using only those functions, any possible [[Forum]] WDAG can be re-weighted in any way desired.

Complex combinations of these primitives give sophisticated governance mechanisms for reviewing past actions recorded in the Forum.

== Primitives ==
Forum references allow review. The Forum is a collection of posts (comments, proposals, work evidence, etc.), each one potentially having a set of references to older posts. As such the Forum is a DAG (directed acyclic graph), since the posts are nodes in the graph, and references are directed edges between posts. The Forum graph is acyclic, since older posts cannot reference newer posts. The Forum is weighted by the REP that each post earns during the [[Reputation#REP Token Minting Mechanism|REP Token Minting Mechanism]] stage and the strength of each edge reference. The Forum is reweighted every time a new post is added, allowing a decentralized means of review. 

Donating, leaching, and incinerating are primitives of all possible reference mechanisms. They are complete in the sense that any complicated type of revaluation mechanism can be achieved by combining these three primitives in series.
=== Donating ===
??A donation is also called a positive citation or a positive reference.

==== Donating reference code ====
''Main page: [[Donating reference code]]''

=== Leaching ===
??Leaching is also called negatively citing or negatively referencing.

==== Leaching reference code ====
''Main page: [[Leaching reference code]]''

=== Incinerator ===
The incinerator is an account which permanently destroys any [[Reputation#REP token design|REP]] value sent to it. The REP sent to an incinerator does not collect fees from the REP salary.

==== Incinerator code ====
''Main page: [[Incinerator code]]''

== Complex operations ==
Combining primitives gives more complicated operations.

==== Leach-donate ====
A post may simultaneously leach and donate to another post. It is important to note that the order in which the references are executed matters. By default, a post with both leaching and donating references executes leaching first and donating second, though this can be reversed by fiat.

If there are several leaching references, it is also important to note that the order in which the leaching references are executed matters – switching the order of execution may change the outcome. This non-commutativity arises because the order of references in time is different. For example, suppose <code>post3</code> leaches from an older <code>post1</code> first, then leaches from a newer <code>post2</code> which has already leached from <code>post1</code>, then you get a lesser result for <code>post3</code> than when the order is reversed.  

=== Swap value from one post to another ===
[[File:WDAG Reweighting Primitive.png|center|519x519px|Reweighting the Forum|alt=Reweighting the Forum|thumb]]


The figure displayed illustrates a scheme for redistributing power from Post1 to Post2.

In this case we can imagine governance concluding that Post1 was bad and Post2 was good. Then governance makes Post3 with power 10 REP and validates it. Then in the displayed example the Forum WDAG has been revaluated, i.e., re-weighted. This is the primitive that allows governance to review previous judgements and correct mistakes made in the past. The incinerator is a complication that allows this re-weighting action to keep the total graph weight constant.

This isn't the only way to achieve re-weighting. Every approach has its own advantages and disadvantages. This approach encourages stability because it is particularly inefficient. E.g., it costs 10 to move 10, and 10 REP is destroyed. So conscious effort is required to reweight the Forum to correct past mistakes. This effort requires the sacrifice of 10 REP on the part of those who make the change (the 10 REP from Post3 was governance value). 

However note that in this case, the 10 REP "sacrifice" will not burden any particular member to achieve the revaluation, if it is done in concert with the governance tax. In this case the governance tax is free since the total amount of REP in the DAO before and after the revaluation is unchanged, because the excess governance tax is incinerated.

=== Chains of references ===
Donation and leaching are not perfectly symmetric. By default, a chain of posts which all donate will recalculate the values of the posts down the chain when a new donating post is added to the chain. However, a leaching post only affects the value of the post it references – value changes from leaching do not propagate down the chain. 

For example, suppose <code>postK</code> at time <math>j</math> has value <math display="inline">R_{K,j}</math>. If <code>post1</code> with initial value <math display="inline">R_{2,0}</math> donates 0.5 to <code>post0</code>, and <code>post2</code> donates 0.7 to <code>post1</code>, then at time 2 we have <math>R_{1,2}=R_{1,1}+0.7R_{2,2}</math> and <math display="inline">R_{0,2}=R_{0,0}+0.5R_{1,1}+(0.7)(0.5)R_{2,2}</math>. So at time 2 the value from <code>post2</code> flows down through <code>post1</code> to <code>post0</code>. 

However, a post which leaches does not propagate down the chain. It only leaches value from the post it references, which does not affect any ancestors of the object post. For instance, continue the example in the previous paragraph, adding <code>post3</code> which leaches with strength -0.4. Then we get <math display="inline">R_{2,3}=(1-0.7)R_{2,2}-0.4R_{3,3} </math> and <math>R_{3,3}=R_{3,3}+0.4R_{2,2}</math> assuming the initial value of <code>post3</code> is smaller than  <math>0.4R_{2,2}</math>. The other <code>post0</code> and <code>post1</code> do not change value with the addition of <code>post3</code>. 

If the DAO wishes to leach value from several posts, it must make separate leaching references to each one.

=== Leaching from a leaching post ===
??   Add the following examples from Ladd's work at https://dgov.io/

=== Leaching from a weaker leaching post ===

=== Redistribute power ===

=== Redistribute power through subsequent support ===

=== Destroy a post after it has received positive citations ===

=== Initially zero-valued posts later receive citations ===

=== Negatively cite a zero-valued post ===

=== Correct a previous post which was leached ===

== Judicial governance proposals ==
''Main page: [[Judicial governance proposal]]''

Combining several of the above examples gives governance proposals that can express more complicated intentions of the will of the [[DAO]] to revaluate its past REP distribution. 

== Forking and merging DAOs ==
The way to create hard forks and mergers (i.e., divergence and convergence, i.e., [https://www.frontiersin.org/articles/10.3389/fhumd.2021.641731/full dissensus] and consensus) in DGF would be through Forum post reference mechanisms and the Validation Pool. 

Say person1 creates a new type of REP, call it nREP, by sending a fee to the Validation pool associated with his nPost without referencing any existing post with REP. Now person1 could have been a member of an old 1REP DAO supposing they owned some 1REP. That means person1 made a hard fork from 1DAO to nDAO. That's divergence. That's dissensus.

Then when another person with old REP1 cites nPost with 1REP, that means she gives some 1REP to nPost. That means nPost is re-admitted to 1DAO. That's consensus. That's convergence.


Alternatively, there is another type of divergence that happens naturally in the function of DGF, which is simply referencing different posts. When you reference one chain, but not another, then you are strengthening a subset of the DAO and not the complement of that subset. So you are creating divergences just by moving forward in time.

== Completeness ==
A set of reference primitives is complete if any finite WDAG can be changed into any other finite WDAG through a finite series of new posts. (Equality of WDAGs here is measured by weights. A WDAG which includes a post with 0 REP value is equal to a WDAG that deletes that post.)

The single mechanism of simultaneous donation and leaching is complete when combined with the incinerator mechanism, as we now demonstrate.

'''Proof of completeness:'''

Given <code>post1</code> with weight <code>W<sub>1</sub></code> we can reweight it to any other weight <code>W</code> by creating <code>post2</code> which donates to <code>post1</code>  if <code>W<sub>1</sub></code> < <code>W</code> or leaches from <code>post1</code> if <code>W<sub>1</sub></code> > <code>W</code>. If leaching is required, <code>post2</code> simultaneously donates to the incinerator with strength 1. Thus <code>post2</code> ends with 0 REP value.

This is not the end of the proof, since other posts in the sub-DAG of referenced ancestors are now changed, as well as the set of descendants affected by leaching from <code>post1</code>. We need to balance all the changes so that the leaching and donating processes affect the entire DAG correctly. We will need to solve a system of linear equations in order to find the right reweighting.  

To organize the process, first note that any DAG can be given a total order. Since our Forum is a finite WDAG, we can define a Layer 0 consisting of all the roots of the DAG, i.e., those posts with no ancestors, i.e., those posts which have no references going out, but only references possibly coming in. Layer 1 is the set of all posts which reference out only to Layer 0 posts. Layer 2 posts are those which have references out to Layer 1 and possibly Layer 0. Inductively, Layer <math display="inline">i+1</math> posts are those which reference posts in Layer <math display="inline">i</math> and possibly Layer <math display="inline">k</math> for any <math display="inline">k<i</math>.  

We now work inductively on layers. The posts in Layer 0 may be reweighted without difficulty by leaching or donating. The posts in Layer 1 can be reweighted, but any change in such a post must also reweight any post from Layer 0 that is referenced. To do this we solve the following linear equation:  

??mathy matheta MATH-a math-math?? 

'''End proof.'''

== Alternate primitives ==

=== Absolute redistribution bounded by the value of a post ===
Another complete set of primitives exist which are more restrictive. For example, an even more restrictive governance protocol would only allow the sum of absolute values of redistribution to be less than the value of a post. In this case, for instance, a DAO would use Post3 to only leach 10 and incinerate it. Then a Post4 is required to donate 10 to Post2. With this restriction it would take 20 REP and two posts to achieve the same redistribution that 10 REP completes with one post as demonstrated in the previously displayed figure.

This same limitation could be enforced under the previous hard protocol primitives by instituting a soft protocol requiring it in all posts. Therefore we consider the previous primitives as a better default for DAO governance.

=== Governmental fiat ===
Consider another system that a DAO may choose is much less inefficient, but also less stable. We can alternatively program primitives that give governance complete control by fiat. Specifically, a DAO may choose to make a primitive which allows any redistribution desired without any cost in REP. In this case, as long as an arbitrary redistribution was validated it could be achieved if the DAO allowed that primitive. 

In general, this is much more dangerous than the previous examples of primitives, because one validated post could put all the value of the entire WDAG into any new account the poster wishes. However, it would be extremely efficient if the DAO wishes to move quickly and trusts its governance.
==Applications==
==See Also==
==Notes & References==