 Now consider the following: If all alternatives were commensurable, then whenever one faced two alternatives neither of which was better than the other, slightly improving one of the alternatives would, it seems, ‘break the tie’ and render one alternative, namely the improved alternative, superior. But there seem to be cases in which there are two alternatives such that (i) neither alternative is better than the other and (ii) this feature is not changed by slightly improving one of the alternatives. Consider, for example, the following case: For Kay, neither of the following alternatives is better than the other: