The published Chapter 13 of On What Matters addresses moral dilemmas as a way of responding to the universalisation tests that Kant uses when motivating consideration of the Law of Nature formula. In relating the universalisation tests to moral dilemmas Parfit is following the precedent set by him in previous drafts of this material.
The basic question that is asked in the universalisation test concerns whether a maxim can be one that can include its own willing in the universalisation of it. Parfit asks, concerning this test, not whether it works, as has been common in the secondary literature on Kant and universalisation, but rather what the alternative to such willing would be. In raising this point Parfit moves the considerations involved in a definite direction since the adoption of a maxim as a universal law is taken to be something we can endorse if the outcome of adopting a different one would be worse than the adoption of this one. So the standard set immediately is an axiological one. Parfit's discussion thus begins with putting the good prior to the right.
Parfit assumes that the Law of Nature formula works best when it is applied to maxims of which 3 things are true: a) that it would be possible for many people to act on the maxim in question; b) when the effects of such acts will be similar regardless of the number so acting; c) when the effects would be distributed equally between different people. Having made this point Parfit next introduces classic dilemmas from games theory, dilemmas generically described by him as "each-we" coordination problems and which include the group known as prisoners dilemmas. The general structure of these dilemmas is that if each of us does what is best for themselves this will be worse for all of us collectively. There are various ways such dilemmas arise as policy questions, including with regards to public goods that benefit all, including those who do nothing to produce them and with regard to "fisherman's dilemmas" where if we all pursue activities of certain kinds we will collectively deplete the resource we are interested in though for each one of us it appears plausible to act in the specified way.
These general dilemmas tend to be structured on a peculiar model of rational agents where such agents are generically assumed to be personal utility maximisers, an implicit assumption that is not interrogated by Parfit. Parfit does, however, expand the arena of the utility maximisation by discussing how, according to common sense morality, we have special obligations to others and we tend to incorporate these special obligations into our calculations thus meaning that we need not be seen, even on this model, purely as egoistic utility maximisers. In political terms the consideration of treatment of these dilemmas tends to be undertaken through coercive measures that impose heavy costs on non-compliance with activities taken to have wider value than even that of our enlarged sense of self-interest allows. Morally consequentialists take themselves to have ways of addressing the problems of such dilemmas including associated difficulties with free riders.
There is a further class of dilemmas, called by Parfit, "unsolved" dilemmas in which no one is performing in the right way. With regard to such "dilemmas" Kant's universalisation procedure is regarded by Parfit as particularly useful since it prompts attitude adjustment in just the right way. One of the results of this is to lead to all of us seeing that acts that, taken individually, might not be "wrong" may be so in an accumulative sense and this will challenge us and lead to a different valuation being placed on these acts.
However, whilst Parfit introduces the relationship between dilemmas and the universalisation test by showing one way in which the latter can respond to a form of the former, his general attitude in this chapter is not favourable to the practice of universalisation tests as a response to the problems posed by the dilemmas. The reason why Parfit's reaction to universalisation tests takes this negative turn is due to his invocation of what he terms the "threshold objection". This objection basically states that there are thresholds that relate to the effects of actions and this is a salient criteria that should be invoked in terms of actions that we should perform. Given this salient criteria we should not simply invoke universalisation as a blunt tool to tell us what to do since the threshold determines the way our actions will impact on others and it is this that balances simple universalisation.
Having invoked this objection Parfit considers some possible responses Kant might make to it. The first response is to put universalisation tests in hypothetically conditional form. The second is to follow a suggestion of Thomas Pogge and to see the question as requiring us to invoke criteria of moral belief. However what becomes clear in the course of Parfit's discussion is that the threshold objection is really another form of the "mixed maxims" objection that was raised in the previous chapter of On What Matters. And when this becomes clear it also becomes evident that the threshold objection turns on how maxims are understood as did the "mixed maxims" objection. Essentially maxims can either be said to state aims or policies. Policies are adopted in order to realise aims whilst aims are the general thing that policies are guided by. Kant is after a formulation of aims with his universalisation test that will give us a formal way of relating to policies rather than viewing policies as ends we have selected due to some prior commitment to the good. Thus Kant's methodological approach is not akin to that which Parfit follows.
This division can be seen as Parfit moves to reformulate the Law of Nature formula so that it refers to what can be "rationally" willed in "similar circumstances" where the nature of the circumstances appears not just to require a sense of adjustment of policies as Parfit gives us the impression is the case but to affect the way we are to understand appropriate aims.
One of the ways this becomes apparent is when Parfit motivates the second major objection of this chapter, the so-called "Ideal World Objection". This differs from the "threshold objection" as it concerns not simply the effects produced after tipping points have been reached but also the plausibility of standards derived from ideal theory in a non-ideal world. Here Parfit argues that viewing universalisable maxims as stating ideal willing can produce counterproductive effects as attention to the actions of others doesn't lead me to adjust my own actions. The "coordination" required here is one in which my own willing is governed by what is achievable given the way others are behaving. Again Parfit considers conditional forms of maxims which, however, lead to the production of too permissive results. In response to this point Parfit arrives at the result that we should be aiming not to answer the question expressed as "what if everyone did that" but instead the answer to the question, "what if everyone thought this way". The revision in thought is meant to be governed by the attempt to coordinate action with others rather than to be concerned with universalisation as such.
The general shift away from universalisation tests as a generic procedure of action towards one that concerns how to inculcate the right kinds of moral beliefs is governed by a process of considering right results as "good" ones, i.e., ones in which the best consequences are produced by the following of the right rules. The result is that a kind of rule consequentialism is favoured rather than a Kantian morality. In reply it is worth pointing out that the Kantian question is not asked or considered in its own terms but always evaluated in terms that are alien to its account of the right structure of moral theory.