Editing Forum reference mechanisms (section)

== 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 ===