Strong non-manipulability. The definition of strong non-manipulability appeals to a topo- logical notion of ‘large’ set of distribution as a co-meager set. The goal of the definition is to capture the idea that, regardless of the strategy he uses to creates forecasts, the unin- formed expert will fail on a large set of stochastic processes. This definition has been used in the expert testing literature, but we recognize that such topological notion has well-known drawbacks. In particular, it does not indicate odds of discrediting the uninformed expert. We view the main contribution of our theorem to be the very fact that there exists a test which is not manipulable. The strong non-manipulability property is a bonus. De-Finetti’s Theorem. For every λ ∈ Δ([0 , 1]) let ε$_{λ}$ ∈ Δ( { 0 , 1 } $^{N}$) be the distribution of infinite sequence of i.i.d coins with probability q of success, where q is drawn from λ : Clearly the distribution ε$_{λ}$ is exchangeable. De-Finetti’s Theorem states that the map λ ∈ Δ([0 , 1]) ↦→ ε$_{λ}$ is one-to-one and onto the set Γ of exchangeable distributions over { 0 , 1 } $^{N}$, and its inverse is given by µ ∈ Γ ↦→ ¯ µ ∈ Δ([0 , 1]) where ¯ µ ∈ Δ([0 , 1]) is the push-forward of µ under L (i.e., ¯ µ ( B ) = µ ( L − $^{1}$( B )) for every Borel subset B of [0 , 1]) and L : { 0 , 1 } N → [0 , 1] is the limit average Since the map λ ↦→ ε$_{λ}$ is continuous and its domain Δ([0 , 1]) is compact it follows that the maps λ ↦→ ε$_{λ}$ and µ ↦→ ¯ µ are homeomorphisms. A non-manipulable test. Our proof uses the following proposition. Proposition 3. Let Q be a compact metric space and let Δ( Q ) be equipped with the weak- ∗ topology. There exists a Borel function t : Δ( Q ) × Q → { FAIL , PASS } such that 9 (5) L ( s$_{0}$, s$_{1}$, . . . ) = lim sup n →∞ ( s$_{0}$ + · · · + s$_{n}$$_{−}$$_{1}$ ) /n. (4) ε$_{λ}$ ( N ( s$_{0}$, . . . , s$_{n}$$_{−}$$_{1}$ )) = ∫ n − 1 ∏ i =0 q s i (1 − q ) 1 − s i λ (d q ) . 4. Proof of Theorem 1 4.1. Preliminaries.