3.2. New result. Our new result is that, for the compact and convex paradigm of exchange- able processes, there exists an infinite prequential test which is non-manipulable. Therefore, Proposition 2 about manipulability of infinite tests does not hold for convex and compact paradigms. In contrast, Proposition 1 about manipulability of finite tests holds for every compact and convex paradigm. For the rest of the paper we fix the set of outcome S = { 0 , 1 } . Theorem 1 below and its proof applies with minor changes to the case of arbitrary finite set of outcomes, however since we are mainly interested in a counter-example the restriction to a two-elements outcome set is worth the notational convenience it provides. We identify the set forecast p ∈ Δ( S ) with p [1] ∈ [0 , 1]. Before stating our result, we give two simple examples of paradigms for which Proposition 2 does not hold. In Example 1 the paradigm is compact but not convex and in Example 2 the paradigm is convex but not compact. Example 1. Let Γ be the paradigm of all i.i.d distributions. Let T be the test that passes the expert if and only if (3) p$_{n}$ = lim sup k →∞ ( s$_{0}$ + · · · + s$_{k}$$_{−}$$_{1}$ ) /k for every n ≥ 0 (so that the expert passes if he makes the same prediction in all days and this prediction matches the empirical frequency of outcomes). Then T accepts the data- generating process in Γ with probability 1 and is strongly non-manipulable w.r.t. Γ. Example 2. Let Γ be the convex hull of the paradigm of all i.i.d. distributions. Let T be the test that passes the expert if and only if (3) is satisfied for all but finitely many n -s. Then T accepts the data-generating process in Γ with probability 1 and is strongly non-manipulable w.r.t. Γ. A theory µ ∈ Δ( S $^{N}$) is exchangeable if µ ( N ( s$_{0}$, . . . , s$_{n}$$_{−}$$_{1}$ )) = µ ( N ( s$_{π}$$_{(0)}$, . . . , s$_{π}$$_{(}$$_{n}$$_{−}$$_{1)}$ )) for every partial realization ( s$_{0}$, s$_{1}$, . . . , s$_{n}$$_{−}$$_{1}$ ) ∈ S < N and every permutation π over { 0 , 1 , . . . , n − 7