 While it is possible to construct perfectly plausible examples of test spaces that are not algebraic, many test spaces that one encounters in nature do enjoy this property. In particular, the Borel and quantum test spaces described in the preceding section are algebraic. The more important point is that, as an axiom, algebraicity is relatively benign, in the sense that many test spaces can be “completed” to become algebraic. In particular, if every outcome has probability greater than 1/2 in at least one state, then \(\mathcal{A}\) is contained in an algebraic test space \(\mathcal{B}\) having the same outcomes and the same states as \(\mathcal{A}\) (see Gudder [1989] for details).