Snowveil Protocol: Consensus & Discovery

• Snowveil is a dual-purpose protocol that enables decentralized preference aggregation and leaderless metastable consensus for censorship-resistant decision-making.
• It employs random peer-sampling, gossip-based aggregation, and iterative locking mechanisms to achieve rapid convergence and scalability in large networks.
• Empirical analyses demonstrate linear convergence, robust performance, and a theoretical foundation bridging social choice theory with distributed consensus.

Snowveil refers to two independent protocols in distributed computation: (1) a decentralised preference discovery protocol for robust social choice under censorship resistance and partial information, and (2) a family of metastable, probabilistic BFT consensus protocols for leaderless distributed ledgers. Both share key algorithmic motifs—random peer-sampling, gossip-based aggregation, and rapid metastable convergence—but address distinct problem domains. The following exposition synthesizes both frameworks as introduced in their respective papers (Kotsialou, 20 Dec 2025, Rocket et al., 2019).

1. Decentralised Preference Discovery: Protocol Structure and Algorithmic Flow

Snowveil, in the sense of decentralised preference discovery, is a protocol that aggregates subjective preferences of a large electorate without reliance on any central authority, while ensuring resistance to censorship, privacy loss, and network asynchrony. The protocol divides the construction of a full preference ranking into $m$ iterative rounds, electing one candidate per round via decentralized, iterative peer-sampling.

Each voter $v_i$ maintains a lock-state $s_i \in \{\perp\} \cup P$, where $\perp$ denotes "unlocked" and $P$ is the current candidate set. The system state at time $t$ is $S_t = (s_1(t),\dots,s_n(t))$. For each candidate $p_j$, the locked set $L_j(t) = \{v_i | s_i(t) = p_j\}$ and its cardinality $N_j(t) = |L_j(t)|$ track support. Unlocked voters $U(t) = \{v | s(v) = \perp\}$ are sampled uniformly at random.

Protocol Pseudocode (summary):

Algorithm Snowveil(V, P, Preferences, k, γ, τ_max, τ_min, Q, α, β, λ) FinalRanking ← [ ]; Available ← P for rank = 1 to m-1: for all v in V: s(v) ← ⊥ repeat: pick an unlocked voter v ∈ U(t) uniformly at random result ← UpdateVoter(v, Available, V, k, γ, τ_max, τ_min, α, β, λ) if result = LOCK(p*): s(v) ← p* until ∃ p* with N_p* ≥ ⌈Q·n⌉ FinalRanking.append(p*) Available ← Available \ {p*} FinalRanking.append(the last remaining project) return FinalRanking

The UpdateVoter subroutine performs $\gamma$ robustness rounds: each time, a sample of $k$ peers is drawn, the CHB rule (see Section 2) is applied, and local counters $C[p]$ are tallied. If any $C[p]$ reaches threshold $\tau_{\max}$, the voter immediately locks on $p$; else, a candidate with $C[p]$ maximal and meeting $\tau_{\min}$ can be locked, using a recency tie-break.

Key parameters:

• $n$ = total voters; $m$ = candidates;
• $k$ = sample size (constant, $k \ll n$);
• $\gamma$ = robustness rounds per update;
• $\tau_{\max}, \tau_{\min}$ = local lock thresholds;
• $Q \in (\frac{1}{2}, 1]$ = global quorum.

2. Preference Aggregation Rule: Constrained Hybrid Borda (CHB)

The protocol's preference aggregation engine is based on the CHB rule, a hybridization of positional scoring (Borda) and plurality.

Given a $k$-voter sample, for every candidate $p_j$, the Borda score is $$B(p_j) = \sum_{v \in \text{sample}} (m - \text{pos}_v(p_j))$$ and the first-place count is $t_j = |\{ v: p_j \text{ is top in } v\}|$.

The CHB rule proceeds by filters:

• Step 1: Find $p_B = \arg\max_p B(p)$. If $t_{p_B} \geq \lceil \alpha k \rceil$, return $p_B$.
• Step 2: Define $$\text{Eligible} = \{ p | t_p \geq \lceil \alpha k \rceil \wedge B(p) \geq \beta \max_q B(q) \}$$. If nonempty, compute for $p \in \text{Eligible}$,

$$H(p) = (1-\lambda)\frac{B(p)}{k(m-1)} + \lambda \frac{t_p}{k}$$

and return the argmax $H(p)$ (lexicographic tie-break).

• Step 3: Otherwise, return $p_B$.

CHB parameters:

• $\alpha$ (popularity filter), $\beta$ (consensus filter), $\lambda$ (Borda/plurality interpolation), all in $[0,1]$.

CHB preserves determinism, positive responsiveness, and computability—axioms necessary for protocol convergence.

3. Convergence Analysis: Potential Function and Submartingale Framework

Let $\Phi(S_t) = \sum_{j=1}^m (N_j(t))^2$ denote the protocol's potential function. The evolution of $\Phi$ forms a submartingale:

• Each time a voter locks on $p_k$, $\Phi$ increases by $2N_k(t) + 1$.
• In any non-terminal, non-quorum state, an unlocked voter has nonzero probability of locking on their sampled outcome (Positive Decision Probability).
• If $N_a(t) > N_b(t)$, the probability an unlocked voter locks on $p_a$ exceeds that for $p_b$ (Amplification of Plurality), as implied by CHB's Positive Responsiveness.

By Doob’s submartingale convergence theorem and the transience of fragmented states, the protocol almost surely absorbs into a single-winner state for each round (i.e., some $N_j \geq \lceil Q n \rceil$), after which the winner is removed and the procedure repeats for lower ranks.

4. Scalability Bound and Empirical Performance

Each unlocked voter has a constant, $n$-independent probability $c_2 > 0$ of successful locking in a single UpdateVoter due to sharp concentration bounds (Chernoff-Hoeffding over $k$-samples). Accordingly:

• Expected steps per lock $\leq 1/c_2 = O(1)$
• Total expected protocol steps to absorption $\leq n / c_2 = O(n)$

Empirical simulations (n up to 10,000; m=5; k=10; $\gamma=10$) confirm $O(n)$ scaling for convergence time. The accuracy (probability that the decentralized selection matches the canonical CHB winner) is robust under both impartial culture and polarized two-faction models. The "cautious voter paradox"—slower local decision ($\gamma$ up) can accelerate global consensus—is observed. Policy parameters $(\alpha,\beta,\lambda)$ smoothly interpolate the global winner, with negligible effect of $\lambda$ on speed. Sensitivity analyses show that increasing the sample size $k$ quickly suppresses error and plateaus speedup.

Baseline: $n=100$, $m=5$, $k=10$, $\gamma=10$, $\tau_{\max}=6$, $\tau_{\min}=3$, $\alpha=0.1$, $\beta=0.8$, $\lambda=0.5$, $Q=0.67$ (Kotsialou, 20 Dec 2025).

5. Axiomatic Generality and Rule Substitution

The convergence theory applies to any aggregation rule $F$ which is:

• Deterministic and unique: each $k$-sample profile yields exactly one winner.
• Positively responsive: if a candidate's support increases (e.g., via Borda points), it cannot lose and can be made to win by a single marginal improvement.
• Computable in finite time.

CHB fulfills these requirements, as do other scoring or majority-based rules with sufficient responsiveness. The convergence proof is agnostic to the details of $F$ provided these axioms hold, yielding a modular framework for constructing new DPD protocols.

6. Snowveil and Leaderless Metastable BFT Protocols

Independent of its social choice applications, "Snowveil" is also used as an umbrella term for the Snow protocol family (Slush, Snowflake, Snowball, and Avalanche) in the context of leaderless, probabilistic BFT consensus (Rocket et al., 2019). Each protocol employs $k$-sized random peer sampling and metastable amplification to drive the global system into one of two states, achieving network-wide probabilistic consensus with logarithmic convergence in $N$ nodes under strong safety and liveness trade-offs. Consensus protocols derived from Snowveil (in the BFT context) are characterized by:

• Leaderless, quiescent operation (no leader, no work if idle)
• O(k) communication per round, total O(kN) per decision with $k\ll N$
• Probabilistic $\varepsilon$-safety, tunable by parameters
• Strong scaling: log-factor convergence, 200 ms–1.5 s latencies for 2000 nodes and 3,400 TPS on EC2 deployments
• Green operation: no proof-of-work

Snowveil (in both senses) exemplifies how metastable sampling protocols yield highly scalable, robust consensus or aggregation without requiring global knowledge, global synchrony, or O($N^2$) messaging (Rocket et al., 2019).

7. Comparative Context and Significance

In decentralised preference discovery, Snowveil provides a rigorous bridge between scalable, asynchronous consensus algorithms and axiomatic social choice frameworks. Its separation of aggregation rule from convergence engine, strong theoretical guarantees (linear time convergence, correctness under broad axiomatic classes), and empirical robustness render it suitable for large-scale, censorship-resistant decision platforms (Kotsialou, 20 Dec 2025).

In distributed systems, the Snowveil protocols (Slush/Snowflake/Snowball/Avalanche) represent a shift from classical leader-based consensus (e.g., PBFT’s O($N^2$) cost), enabling robust, efficient, and adaptive state machine replication in adversarial and large-scale settings (Rocket et al., 2019).

Both uses of Snowveil highlight the power of randomized, sampling-driven, metastable dynamics for rapid, scalable convergence in multi-agent systems, and furnish formal frameworks applicable across decentralized governance, blockchain consensus, and distributed computation.