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The test is finite if, for some n ∈ N , T depends only on the forecasts and outcomes of the first n periods. 

Definition 2. Fix a prequential test T and let µ be a theory. 

(1) µ passes the test over a realization x = ( s$_{0}$, s$_{1}$, . . . ) ∈ S N if µ ( N ( s$_{0}$, . . . , s$_{n}$$_{−}$$_{1}$ )) > 0 for every n and T ( p$_{0}$, s$_{0}$, p$_{1}$, s$_{1}$, . . . ) = PASS, where p$_{k}$ is the forecast of µ over x at period k . 

(2) The acceptance set of µ under T , denoted A ( T ) µ is the set of all realizations x ∈ S N such that µ passes the test over x . 

Definition 3. The prequential test T accepts the data generating process in a paradigm Γ with probability 1 − ϵ if µ ( A ( T ) µ ) ≥ 1 − ϵ for every µ ∈ Γ. 

If the test accepts the data generating process with high probability and Bob’s theory µ is the data generating process then Bob is assured that he will pass the test with high probability. 

Definition 4. Let Γ be a paradigm. A test T is ϵ -manipulable w.r.t Γ if there exists some distribution ζ over Γ such that 

for every theory µ ∈ Γ. 

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If a test is ϵ -manipulable then Bob can randomize a theory according to ζ and be sure that, with high probability, he passes the test regardless of the data generating process µ . 

If a test is not manipulable then every strategy to fake theories fails on at least one data-generating process. Following Dekel and Feinberg (2006) and Olszewski and Sandroni (2009b), we use in this paper a stronger condition, which entails that every strategy employed by an ignorant expert will fail on a topologically large set of data generating processes. Recall that a set M of a separable metric space Z is co-meager if it contains a countable intersection 

