Probability that an insider contributing X2 to the aggregate infers the
dominant contribution X1 to within +/- beta, by subtracting their own
contribution from the disseminated total (Proposition 5 of the paper):
mu_II(rho, rho2) = F_Z((1+beta)rho + rho2 - 1) - F_Z((1-beta)rho + rho2 - 1),
with Z the relative loss at dominance rho.
Usage
assess_risk_II(rho, rho2, sigma_nu, sigma_eps, n, beta)
Arguments
- rho
Share of the largest contribution, X1/Y, in (0,1]. Recycled.
- rho2
Share of the second contribution, X2/Y. Recycled.
- sigma_nu, sigma_eps, n
Mechanism parameters. Recycled.
- beta
Accuracy threshold of the inference.
Value
mu_II(rho, rho2), vectorised.
Details
The worst case (IIa) has the two largest contributors sharing the whole cell
(rho + rho2 = 1); the relaxed case (IIb) leaves a residual share to the
other contributors, typically rho + rho2 = 0.95.
Examples
# worst case IIa at rho = 0.5
assess_risk_II(0.5, 0.5, sigma_nu = 0.4, sigma_eps = 0.031, n = 4, beta = 0.1)
#> [1] 0.7907045