 One of the questions raised by this radical proposal is whether arguments like the mere addition paradox themselves justify the rejection of transitivity or whether further arguments are needed since transitivity seems to be part of the meaning and logic of the relation “better than” (Broome 2004). However, it has been suggested that there are two “better than”-concepts, one based on intrinsic value and one based on the stance that one ought to take towards the evaluated objects (Arrhenius 2004; Rabinowicz 2012). The former is transitive in virtue of its meaning whereas the latter is non-transitive over different alternative sets, just like “ought to be chosen”. Moreover, Temkin (2012) argues that it is the latter “better than”-concept which is the important one for practical reasoning. This raises the question of the more general implications of this proposal for morality and practical reasoning and some worry that giving up the transitivity of “better than” would demand a major revision of our notion of practical reasoning (Temkin 1987, 2012). A transitive preference ordering has usually been assumed as part of the definition of a rational agent in economic and rational choice theory. For example, it seems that an agent with a non-transitive preference ordering can be exploited by a so-called ‘money-pump’ (see Section 5.1 of the entry on the  philosophy of economics).  The main problem with non-transitive value orderings in moral theory, however, is that such an ordering cannot form the basis of a satisfactory answer to the question of what one ought to choose. Coupled with the standard formulation of consequentialism (an action is right if and only if its outcome is at least as good as the outcomes of all the alternative actions, see the entry on  consequentialism),  for example, we get the counterintuitive result that no action is right in the mere addition paradox. Moreover, it has been shown that the mere addition argument and the like can be reconstructed on the normative level, in terms of what one ought to choose, without an appeal to transitivity (Arrhenius 2004). Instead of an non-transitive ordering of populations, one gets a situation in which all of the available actions are forbidden, i.e., a moral dilemma. Hence, it doesn’t look like we can exorcise the paradoxes of population ethics by giving up some formal condition like the transitivity of “better than”.