$$ \newcommand \PSfunction {\textbf{function }} \newcommand \PSreturn {\textbf{return }} \newcommand \PSendfunction {\textbf{end function}} \newcommand \PSswitch {\textbf{switch }} \newcommand \PScase {\textbf{case }} \newcommand \PSdefault {\textbf{default}} \newcommand \PSendswitch {\textbf{end switch}} \newcommand \PSfor {\textbf{for }} \newcommand \PSendfor {\textbf{end for}} \newcommand \PSwhile {\textbf{while }} \newcommand \PSendwhile {\textbf{end while}} \newcommand \PSdo {\textbf{ do}} \newcommand \PSif {\textbf{if }} \newcommand \PSelseif {\textbf{else if }} \newcommand \PSelse {\textbf{else}} \newcommand \PSthen {\textbf{ then}} \newcommand \PSendif {\textbf{end if}} \newcommand \PSnot {\textbf{not }} \newcommand \PScomment {\qquad \small \textsf} $$

$$ \newcommand \Priority {\mathrm{Priority}} \newcommand \VRF {\mathrm{VRF}} \newcommand \ProofToHash {\mathrm{ProofToHash}} \newcommand \SoftVote {\mathrm{SoftVote}} \newcommand \Hash {\mathrm{Hash}} \newcommand \Sortition {\mathrm{Sortition}} \newcommand \Broadcast {\mathrm{Broadcast}} \newcommand \RetrieveProposal {\mathrm{RetrieveProposal}} \newcommand \DynamicFilterTimeout {\mathrm{DynamicFilterTimeout}} \newcommand \Soft {\mathit{soft}} \newcommand \Prop {\mathit{propose}} \newcommand \Vote {\mathrm{Vote}} \newcommand \loh {\mathit{lowestObservedHash}} \newcommand \vt {\mathit{vote}} \newcommand \ph {\mathit{priorityHash}} \newcommand \c {\mathit{credentials}} $$

Soft Vote

The soft vote stage (also known as “filtering”) filters the proposal-value candidates available for the round, selecting the one with the highest priority to vote for.

Priority Function

Let \( \Priority \) be the function that determines which proposal-value to soft-vote for this round, as defined in the normative section:

$$ \Priority(v) = \min_{i \in [0, w_j)} \left\{ \Hash \left( \VRF.\ProofToHash(y) || I_j || i \right) \right\} $$

Where:

• \( v \) is a proposal value for this round,
• \( I_j \) is the proposer address identified by the subscript \( j \),
• \( w_j \) is the weight of the credentials for \( v \) by proposer \( I_j \),
• \( y \) is the \( \VRF \) proof as computed by proposer \( I_j \) using their \( \VRF \) secret key.

The function selects the minimum among a set of \( w_j \) hash values calculated as \(\Hash \left(\VRF.\ProofToHash(y) || I_j || i \right)\), with \(i \in [0, w_j)\).

The higher the credentials’ weight \( w_j \), the larger the set, the higher the chances for the proposer \( I_j \) to get the lowest value among all the players for this round.

Algorithm

\( \textbf{Algorithm 4} \text{: Soft Vote} \)

$$ \begin{aligned} &\text{1: } \PSfunction \SoftVote() \\ &\text{2: } \quad \loh \gets \infty \\ &\text{3: } \quad v \gets \bot \\ &\text{4: } \quad \PSfor \vt_p \in V^\ast \PSdo \PScomment{The subset of votes corresponding to proposals} \\ &\text{5: } \quad \quad \ph \gets \Priority(\vt_p) \\ &\text{6: } \quad \quad \PSif \ph < \loh \PSthen \\ &\text{7: } \quad \quad \quad \loh \gets \ph \\ &\text{8: } \quad \quad \quad v \gets \vt_p \\ &\text{9: } \quad \quad \PSendif \\ &\text{10:} \quad \PSendfor \\ &\text{11:} \quad \PSif \loh < \infty \PSthen \\ &\text{12:} \quad \quad \PSfor a \in A \PSdo \\ &\text{13:} \quad \quad \quad \c \gets \Sortition(a_I, r, p, \Soft) \\ &\text{14:} \quad \quad \quad \PSif \c_j > 0 \PSthen \\ &\text{15:} \quad \quad \quad \quad \Broadcast(\Vote(a_I, r, p, \Soft, v, \c)) \\ &\text{16:} \quad \quad \quad \quad \PSif \RetrieveProposal(v) \PSthen \\ &\text{17:} \quad \quad \quad \quad \quad \Broadcast(\RetrieveProposal(v)) \\ &\text{18:} \quad \quad \quad \quad \PSendif \\ &\text{19:} \quad \quad \quad \PSendif \\ &\text{20:} \quad \quad \PSendfor \\ &\text{21:} \quad \PSendif \\ &\text{22: } \PSendfunction \end{aligned} $$

⚙️ IMPLEMENTATION

Soft vote filtering reference implementation.

Soft vote issuance reference implementation.

The soft vote stage is run after a timeout of \( \DynamicFilterTimeout(p) \) (where \( p \) is the executing period of the node) is observed by the node (see the dynamic filter timeout section for more details).

Let \( V \) be the set of all observed votes in the currently executing round. For convenience, we define a subset, \( V^\ast \) to be all proposals received; that is \( V^\ast = \{\vt \in V : \vt_s = \Prop\} \).

With the aid of a priority function, this stage performs a filtering action, selecting the highest priority observed proposal to vote for, defined as the one with the lowest hashed value.

The priority function (Algorithm 4 - Lines 4 to 9) should be interpreted as follows.

Consider every proposal value \( \vt_p \) in the subset \( V^\ast \) and the hash of the \( \VRF \) proof \( \ProofToHash(y) \) obtained by its proposer in the sortition.

For each index \( i \) in the interval from \( 0 \) (inclusive) up to the proposer credentials’ weight¹ \( w_j \) (exclusive), the node hashes the concatenation of \( \ProofToHash(y) \), the proposer address \( I_j \) and the index \( i \), as \( \Hash(\VRF.\ProofToHash(y) || I_j || i) \) (where \( \Hash \) is the node’s general cryptographic hashing function.

See the cryptography normative section for details on the \( \Hash \) function.

Then, the node keeps track of the proposal-value \( v \) that minimizes the concatenation hashing (Algorithm 4 - Lines 6 to 8).

After running the filtering algorithm for all proposal votes observed, and assuming there was at least one proposal in \( V^\ast \), the broadcasting section of the algorithm is executed (Algorithm 4 - Lines 11 to 15).

For every online account (registered on the node), selected to be part of the \( \Soft \) voting committee, a \( \Soft \) vote is broadcast for the previously filtered value \( v \).

If the corresponding full proposal has already been observed and is available in \( P \), it is also broadcast (Algorithm 4 - Lines 16 to 17).

If the previous assumption of non-empty \( V^\ast \) does not hold, no broadcasting is performed, and the node produces no output in its filtering step.

1. Corresponds to the \( j \) output of \( \Sortition \), stored inside the \( \c \) structure. ↩