BFT Quorum Thresholds

BFT Quorum Thresholds

Supermajority threshold: 6667 basis points (66.67%) via has_supermajority().

All quorum checks use lib_types::consensus::threshold::has_supermajority(votes, total).
No raw >= / > / < comparisons. One function, one threshold, one source of truth.

Quorum Table

Validators	Needed	Percentage	Byzantine faults tolerated
3	3/3	100%	0
4	3/4	75%	1
5	4/5	80%	1
7	5/7	~71%	2
10	7/10	70%	3
14	10/14	~71%	4
21	15/21	~71%	6
50	34/50	68%	16
100	67/100	67%	33

Formula

threshold_bps = 6667  (66.67%)
has_supermajority(votes, total) = votes * 10_000 >= total * 6667

This is mathematically equivalent to votes >= floor(total * 2 / 3) + 1 for all positive integers, proven by exhaustive test for n=1..200.

Why 66.67%

BFT tolerates f < n/3 Byzantine validators. Safety requires n - f honest validators to agree, which is n - floor((n-1)/3) = ceil(2n/3). The 6667 bps threshold encodes this bound exactly.

• Below 6667 bps: breaks the mathematical proof that BFT tolerates f < n/3.
• Above 6667 bps: stricter, safe, but reduces liveness (more validators needed to commit).

Governance Tiers (future)

The same meets_threshold(numerator, denominator, threshold_bps) function supports governance voting tiers:

Proposal Type	Quorum	Approval
Operational	1000 bps (10%)	5001 bps (>50%)
Sector Policy	1500 bps (15%)	6000 bps (60%)
Network Parameter	2500 bps (25%)	6667 bps (66.67%)
Constitutional	4000 bps (40%)	8000 bps (80%)