Editing Validation Pool

The Validation Pool is the mechanism for holding REP-weighted votes on every assertion made in the DAO. It's function is roughly similar to a betting pool, in that members may register their votes with REP tokens, then, in a binding vote, those voting for the losing side have their tokens redistributed to the winners proportionally. 

== Specification ==
Suppose a DAO with a total of <math display="inline">R_T</math> reputation tokens has <math>n</math> members <math>m_k</math> for <math>0\leq k\leq n-1</math> where member <math>m_k</math> has <math>R_k</math> tokens. So <math display="inline">R_T=\sum_{k=1}^{n-1}R_k. </math> An instantiation of the Validation Pool Smart Contract (VPSC) takes as input a new post's address in the Forum and a cash fee. Each post in the Forum includes a set (possibly empty) of weighted references to older posts. VPSC then allows each member <math>m_k</math> to encumber each of their REP tokens with an input <math>v_k</math> of upvote (<math>v_k=+1</math>) or downvote (<math>v_k=-1</math>) or default abstention (<math>v_k=0</math>). Once the timeout is reached, VPSC counts the votes by calculating <math display="inline">V_T:=\sum_{k=1}^{n-1}v_k R_k. </math> If <math>V_T\geq 0</math> that means the total REP used to upvote <math display="inline">R_U:=\sum_{ \{ i|v_i>0\}}R_{i} </math> outweighs the total REP used to downvote <math display="inline">R_U\geq R_D:=\sum_{ \{ i|v_i< 0\}}R_{i} </math>. Therefore if <math display="inline">V_T\geq 0</math> the assertion is validated. If <math>V_T< 0</math> then the downvote wins and the assertion is invalidated.

=== Binding vs. non-binding ===
A VPSC can be binding or non-binding. If an instantiation of the VPSC is binding, that means the REP tokens of all those who voted against winning side lose the tokens they encumbered to those who won, proportionally. E.g., if the assertion is validated, then all the REP used to downvote <math display="inline">R_D </math> is redistributed to those who upvoted, meaning each voter <math>m_j</math> with <math>v_j>0</math> receives <math display="inline">\frac{R_j}{R_U} R_D</math> new tokens.

Finally, a VPSC can be <math>p</math>-binding for any <math>0 \leq p \leq 1</math>. A <math>p</math>-binding VPSC redistributes the fraction <math>p</math> of the losers' tokens to the winners.

== Consequences ==
The Validation Pool can be set to binding or non-binding votes to serve executive or legislative governance. A binding vote means the REP tokens were [https://vitalik.ca/general/2017/12/17/voting.html tightly-coupled] with the voters' assertions--if the assertion fails, the voter loses their tokens. This is a destabilizing situation in any