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Quorum and audits

tasqnetwork.io/benchmark/quorum

Mode R accepts a result when q of r independent seats agree. These simulations check the capture formula (Eq. 6), the distinct-machine rule, and the economics of an adversary that controls several seats. The attack simulation is what exposed a flaw in the first design: with public seat selection a coordinating adversary profits at any unit value. Hidden audits fixed it.

0.0012Largest gap, Eq. 6 versus simulation

400,000Draws per uniform point

Within 5%Simulated break-even versus Eq. 7

2.8%Wrong acceptance, no audits, ρ = 0.1

Capture probability: Eq. 6 against simulation

r = 3, q = 2r = 5, q = 3r = 7, q = 5Eq. 6 (dashed)

Dots are simulated with uniform seat selection, dashed lines are Eq. 6. Stake-weighted results are in the CSV.

Source: S1_quorum_capture.csv, sim_protocol.py

Distinct-machine rule

Identities per machine	Identity share ρ	Capture without rule	Capture with rule	Trials
1	0.1	0.0277	0.0277	30,000
1	0.2	0.1033	0.1033	30,000
1	0.3	0.2153	0.2153	30,000
2	0.1	0.0291	0.0288	30,000
2	0.2	0.1035	0.1029	30,000
2	0.3	0.2145	0.2142	30,000
4	0.1	0.0277	0.0271	30,000
4	0.2	0.1044	0.1033	30,000
4	0.3	0.2154	0.2144	30,000
8	0.1	0.0280	0.0258	30,000
8	0.2	0.1026	0.1001	30,000
8	0.3	0.2180	0.2150	30,000

The rule stops one machine from filling several seats of the same unit. Its effect grows with the number of identities per machine: at 8 per machine and ρ = 0.1 it lowers capture from 2.8% to 2.6%. It is a backstop, not the main defence. Hidden audits are.

Source: S2_distinct_machines.csv

Attack economics with hidden audits

audit rate π = 0audit rate π = 0.05audit rate π = 0.1audit rate π = 0.2

Coordinating adversary with ρ = 0.1, r = 3, q = 2. Profit above zero means the attack pays. Without audits it pays at every value.

Source: S3_attack_economics.csv

Break-even value versus the admission rule

Audit rate π	Simulated break-even V / σS	Eq. 7 rule	Difference
0.05	0.110	0.105	4.5%
0.1	0.226	0.222	1.5%
0.2	0.504	0.500	0.8%
0.3	0.862	0.857	0.6%

The rule V ≤ πqσS / (1 − π) sits slightly below the simulated break-even at every audit rate, so it errs on the safe side.

Source: S3b_breakeven.csv

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