$$ \newcommand {\abs}[1] {\lvert #1 \rvert} \newcommand \A {\mathcal{A}} \newcommand \N {\mathbb{N}} \newcommand \Comm {\mathsf{Comm}} \newcommand \Addr {\mathrm{Addr}} \newcommand \Members {\mathrm{Members}} \newcommand \Votes {\mathrm{Votes}} $$

xGov Committee

xGov Committees are responsible for voting on Proposals.

The formalization of xGov Committees and their voting power, as defined by ARC-0086, is provided below.

Preliminaries

Let

• \( \A \) be the (finite) set of Algorand addresses;
• \( \N \) be the set of non–negative integers;
• \( g \) be the network Genesis Hash;
• \( R \in \N \) be the Application ID of the xGov Registry;
• \( B_c \in \N \) be the block at which the xGov Registry was created.

Governance Period

A governance period is a pair \( (B_i, B_f) \in \N^2 \) such that

$$ \begin{align} B_i &\equiv 0 \pmod{10^6}, \\ B_f &\equiv 0 \pmod{10^6}, \\ B_f &> B_c, \\ B_f &> B_i. \end{align} $$

And is intended as a range of blocks \( [B_i; B_f) \) (\( B_i \) included, \( B_f \) excluded).

\( B_i < B_c \) is valid and denotes a period across the xGov Registry creation.

xGovs and Voting Power

An xGov is an address \( a \in \A \) that has acknowledged the xGov Registry on block \( h \) and is therefore eligible to acquire voting power.

The xGov acknowledgement is defined by the pair \( (a, h) \) (represented on the xGov Registry as an xGov Box).

If xGovs unsubscribe, the xGov acknowledgement of their address \( a \) is lost and the pair \( (a, h) \) is removed from the xGov Registry state.

For a governance period \( (B_i, B_f) \), an address \( a \) is an eligible xGov in \( [B_c; B_f) \) if and only if there exists a block height \( k \) with \( B_c ≤ k < B_f \) such that the xGov Registry state at height \( k \) contains \( (a, h) \) for some \( h ≤ k \).

Once the xGov Registry has recorded an acknowledgement \( (a, h) \) with \( h ≥ B_c \), the address \( a \) is considered an eligible xGov for every governance period \( (B_i, B_f) \) such that \( h \in [B_c; B_f) \); in particular, it is not necessary to re-acknowledge the xGov Registry for subsequent governance periods.

For a fixed governance period \( (B_i, B_f) \), the voting power of an eligible xGov \( (a, h) \) in that governance period is the integer

$$ w((a, h); B_i, B_f) \in \N, $$

defined as the number of blocks proposed by an eligible address \( a \) in the governance period \( [B_i; B_f) \)¹.

If an xGov a has acknowledged the xGov Registry at some \( h \in [B_c; B_f) \) and has proposed one or more blocks in \( [B_i; B_f) \), then all such proposals in \( [B_i; B_f) \) contributes to its voting power, including those that occurred before \( h \).

Definition of xGov Committee

Fix an xGov Registry \( (g, R, B_c) \) and a governance period \( (B_i, B_f) \) as above.

An xGov Committee for \( (g, R, B_c, B_i, B_f) \) is a finite set

$$ C \subseteq \A \times \N_{>0}, $$

of address–weight pairs \( (a, v) \) such that:

$$ \begin{align} &\textbf{eligibility} && \forall (a, v) \in C, a \text{ is an eligible xGov in } [B_c; B_f), \\ &\textbf{voting power} && \forall (a, v) \in C, v = w(a; B_i, B_f), \\ &\textbf{uniqueness} && (a_1, v_1), (a_2, v_2) \in C \text{ and } a_1 = a_2 \Rightarrow v_1 = v_2. \end{align} $$

The corresponding xGov Committee object is the tuple

$$ \Comm := (g, R, B_c, B_i, B_f, C). $$

For convenience, we write

$$ \Addr(C) := \{ a \in \A \mid \exists v>0, (a, v) \in C \} $$

for the set of xGov Committee members (addresses) induced by \( C \).

xGov Committee Members

The number of xGov Committee members (or cardinality of the xGov Committee) is defined as

$$ \Members(\Comm) := \abs{\Addr(C)} = \abs{C}. $$

This value corresponds to the totalMembers field in the ARC-86 canonical JSON representation of the xGov Committee.

xGov Committee Voting Power

The voting power function of the xGov Committee is the map

$$ v_C : \Addr(C) \to \N_{>0}, \qquad v_C(a) := v \text{ such that } (a, v) \in C. $$

The total committee voting power is

$$ \Votes(\Comm) := \sum_{(a, v) \in C} v = \sum_{a \in \Addr(C)} v_C(a). $$

This value corresponds to the totalVotes field in the ARC-86 canonical JSON representation of the xGov Committee.

Optionally, the relative vote of a member \( a \in \Addr(C) \) is

$$ \mathrm{share}_C(a) := \frac{v_C(a)}{\Votes(\Comm)}, $$

whenever \( \Votes(\Comm) > 0 \).

xGov Committee ID

An xGov Committee is identified by the Committee ID, as defined in ARC-86 canonical JSON representation.

Selection

The xGov Committee selection and the assignment of their voting power is performed by the Algorand Foundation.

Declaration

The xGov Committee Manager SHALL declare on the xGov Registry:

• The current Committee ID;

• The current xGov Committee Members;

• The current xGov Committee Voting Power.

Assignment to Proposal

The xGov Daemon SHALL assign the current xGov Committee to Proposals upon creation (see Proposal Creation section).

1. If \( a \) is not eligible as an xGov in \( [B_c; B_f) \), its voting power is implicitly taken to be zero, and it is not included in the xGov Committee. ↩