Scenario-II (p%-rule) risk measure

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 : 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.

See also

dominoise-package paper's proposition 5

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