2. RABINOWICZ'S FITTING-ATTITUDE ANALYSIS OF VALUE RELATIONS

Rabinowicz's account is an attempt to characterize value relations within the framework of the Fitting-Attitude (FA henceforth)-analysis of value (Brentano Reference Brentano, Chisholm and Schneewind1889; Ewing Reference Ewing1947; Gibbard Reference Gibbard1990; Scanlon Reference Scanlon1998; Rabinowicz and Rønnow-Rasmussen Reference Rabinowicz and Rønnow-Rasmussen2004). In the non-comparative case, the FA-analysis holds that an item is valuable if and only if that item is a fitting object of a favouring attitude. The concept of value is thus analysed in terms of a normative component, captured by the notion of ‘fittingness’, and a psychological component, captured by the notion of ‘favouring’.Footnote ²

Rabinowicz's initial account of comparative value is laid down in ‘Value Relations’ (Reference Rabinowicz2008). It is based on four claims. The first states the generic FA-thesis about comparative value. It says that comparative value judgements are equivalent to normative assessments of preferences. The second concerns the normative component of the analysis. According to it, fittingness has two levels, i.e. the level of ‘permissibility’ and the level of ‘requiredness’. The third and the fourth concern the psychological component of the analysis. Rabinowicz maintains, on the one hand, that preferences are dyadic attitudes, i.e. attitudes in favour of one item over another; and, on the other hand, that they are choice dispositions, i.e. dispositions to choose one item over another.

Rabinowicz begins by offering an informal FA-analysis of value relations. He characterizes the standard trichotomy of value relations in the following way. For any options x and y:

Next, Rabinowicz offers a characterization of parity. As mentioned above, parity is supposed to hold between two items when neither is better than the other, nor equally good, and yet the two items are comparable in terms of value. Within Rabinowicz's FA-analysis, parity is defined as follows.

Finally, Rabinowicz offers an FA-analysis of value incomparability.

One question immediately arises. According to (I), two items are incomparable if and only if one is required to have no preferential attitudes towards them. Since preferences are conceived of as choice dispositions, it follows that one is required to have no choice dispositions towards these items. This seems to imply that one cannot be disposed to make any choice among incomparable items. However, choice involving incomparable items does seem to be possible. Moreover, choice is always the result of some dispositions. The question is: How can we make sense of the behaviour of a subject who judges two items to be incomparable – and, thus, judges that lacking a choice disposition towards these items is required – and, yet, makes a choice between them on the basis of some choice dispositions? One possibility is that the subject is irrational, i.e. she has choice dispositions that she judges impermissible to have. However, this explanation does not seem to correctly describe all cases of choice between incomparable items. Indeed, such choices do not seem to necessarily manifest any form of irrationality. An alternative possibility consists in distinguishing between different sorts of choice dispositions. This is the strategy pursued by Rabinowicz.

Rabinowicz distinguishes between choice dispositions in a narrow sense, i.e. roughly, choice dispositions that are based on the balance of reasons, and choice dispositions in a broad sense, i.e. roughly, all choice dispositions that are involved in choice-making, whether or not they are based on the balance of reasons. According to Rabinowicz, what matters for an FA-analysis of value relations are choice dispositions of the former type. The analysis of value incomparability should thus be interpreted accordingly: judging that two items are incomparable is equivalent to judging that the balancing of reasons does not succeed, so that one is required not to adopt any preferential attitude towards these items (see Rabinowicz Reference Rabinowicz2012: 140). This analysis is still compatible with the possibility that the subject makes a choice between the items on the basis of some choice disposition. However, her choice stems from a choice disposition that is not based on the balance of reasons, but is the result of some other physical or psychological features of the individual (see Raz Reference Raz1986 on the same point).Footnote ³

Rabinowicz provides also a more formal interpretation of his FA-analysis. The starting point is the observation that, when we compare different items in terms of value, we typically make reference to several dimensions with respect to which such items can be evaluated. In some cases, these dimensions can be weighed against each other in a number of different, yet equally legitimate, ways. Formally, this means that, in such cases, there exist several vectors of weights, which can be applied to the dimensions relevant for comparison in an equally justified way. If we think of each of these dimensions as a different ‘reason’ for preferring one item to another, it follows that there exist different ways in which reasons can be balanced. This generates a whole set of permissible preference orderings, i.e. a set of different ways in which different items can be legitimately ordered on the basis of the balance of reasons. The set of permissible preference orderings constitutes the basis for Rabinowicz's formal FA-analysis of value relations.

According to Rabinowicz, each value relation can be defined in terms of the intersection of all the permissible preference orderings. More formally, suppose that K is the (non-empty) class of all the permissible preference orderings. Rabinowicz assumes that, within K, weak preference (that is, the union of strict preference and indifference) is reflexive and transitive, but not necessarily a complete relation. This allows for the existence of preferential gaps between items. According to Rabinowicz, there are 15 logically possible ways in which two items can be related within K. That is, there are 15 logically possible value relations. Rabinowicz summarizes them by means of the table in Figure 1 (Rabinowicz Reference Rabinowicz2012: 147).

As Rabinowicz explains,

Figure 1.

Summary of the 15 logically possible value relations (Rabinowicz Reference Rabinowicz2012: 147).

Rabinowicz is thus able to offer a complete taxonomy of value relations. The standard trichotomy of value relations is characterized as follows. For any two items x and y:

The notion of incomparability is characterized as follows:

Parity is defined as follows:

It is worth noticing that parity so defined is not only represented by column 6 in the table. Indeed, there are other cases where the conditions listed by (P) are satisfied. For instance, these are cases where x is strictly preferred to y in some ordering in K, y is strictly preferred to x in some other ordering in K, and x is permissibly related to y by some other preferential attitudes in other orderings in K. Columns 7, 8 and 9 in the table represent such cases. Clearly, these combinations, as well as the others in the table, may have no actual instantiations, but be only conceptual possibilities. An analysis should nonetheless make room for them – a constraint that Rabinowicz's account fully respects.

3. THE PREFERENCES VS. VALUE JUDGEMENTS OBJECTION

As Rabinowicz himself recognizes, his initial FA-analysis of value relations is subject to various objections.Footnote ⁴ In this paper I focus on one of them in particular, namely, the Preferences vs. Value Judgements objection. The objection is the following.

According to Rabinowicz's informal account, two items are on a par if and only if it is both permissible to strictly prefer one to the other and permissible to have the opposite strict preference. The problem is that, if preferences are conceived of as mental states that necessarily involve a comparative value judgement,Footnote ⁵ then Rabinowicz's account entails that two items are on a par if and only if it is both permissible to judge that one is better than the other and permissible to have the opposite judgement. However, this is in contrast with the intuitive understanding of parity, according to which, when two items are on a par, neither is better than (nor equally good to) the other.

Rabinowicz notices that the Preferences vs. Value Judgements objection does not arise only with respect to a conception of preferences in terms of comparative value judgements. In fact, the objection remains even if preferences are conceived of as mental states involving comparative reason judgements.Footnote ⁶ Indeed, Rabinowicz's account implies that, if two items are on a par, it is both permissible to judge that one is supported by stronger reasons than the other and permissible to have the opposite judgement. Once again, however, this claim contrasts with the intuitive understanding of parity, according to which, when two items are on a par, neither is supported by stronger reasons. The scope of the objection is thus broader than one might have initially thought.

In fact, Rabinowicz interprets the Preferences vs. Value Judgements objection in two slightly different ways. On the one hand, he sees the objection as raising a ‘consistency problem’.Footnote ⁷ Suppose that an agent judges that two items x and y are on a par. Suppose also that the agent forms a strict preference for x over y, as it is permissible for her to do in light of Rabinowicz's analysis of parity. If preferences involve a comparative value judgement, then, by forming a strict preference for x over y, the agent forms the judgement that x is better than y. However, this judgement is inconsistent with the judgement entailed by the intuitive understanding of parity, according to which, when one judges that two items are on a par, one recognizes that neither item is better than (nor equally good to) the other. The question is the following: For any two items x and y that are on a par, how can an agent consistently prefer x to y, and, thus, judge that x is better than y, while, at the same time, denying that x is better than y?

On the other hand, Rabinowicz sees the Preferences vs. Value Judgements objection as raising a more ‘substantive problem’.Footnote ⁸ As we have seen, if preferences involve a comparative value judgement, his analysis entails that, when two items x and y are on a par, it is permissible to judge, e.g. that x is better than y. According to the intuitive understanding of parity, however, this is an incorrect judgement, since neither item is better than (nor equally good to) the other. The question arises: How can it be permissible for an agent to prefer x to y, and, thus, to judge that x is better than y, if the latter judgement is incorrect, given that, as a matter of fact, when x is on a par with y, x is not better than y?

Rabinowicz has explored three different solutions to the Preferences vs. Value Judgements objection, in a series of recent papers (Reference Rabinowicz2009, Reference Rabinowicz and Reboul2011, Reference Rabinowicz2012). In the rest of this section, I shall present, and raise some doubts about, each of these solutions. While assessing them, it is important to keep in mind the difference between the two versions of the Preferences vs. Value Judgements objection, since some of the solutions offered by Rabinowicz work with respect to one version, but not with respect to the other.

Rabinowicz's first solution consists in allowing only for non-judgementalist conceptions of preferences.Footnote ⁹ For instance, one possibility is to conceive of preferences as mental states involving value perceptions, rather than value judgements. Accordingly, preferring x to y involves perceiving x as better than y, rather than judging x to be better than y. Perceptions are understood here as fallible, possibly non-veridical, experiences. Thus, perceiving one item as better than another does not imply knowing that the former is better than the latter. The analogy is with the perception of a stick immersed in the water. Clearly, one can perceive a stick in the water to be broken and, yet, know that the stick is not actually broken.

This seems to offer a straightforward solution to the first version of the Preferences vs. Value Judgements objection. Indeed, if preferences involve value perceptions, then Rabinowicz's account entails that two items are on a par if and only if it is both permissible to perceive one as better than the other and permissible to have the opposite value perception. Since value perceptions do not imply value judgements, it is perfectly possible for one to have either one of these perceptual experiences, while recognizing that neither is veridical and, thereby, while judging that neither item is better than the other. There seems to be no inconsistency here.

However, Rabinowicz's first solution presents two problems. The first is that, insofar as it excludes from the start some independently plausible conceptions of preferences, such as the one in terms of value judgements,Footnote ¹⁰ it loses generality. The second, and most important, is that it is vulnerable to a variant of the second version of the Preferences vs. Value Judgements objection. Let me explain. As we have seen, the ‘substantive problem’ with Rabinowicz's analysis arises as soon as one notices that there is something puzzling in the claim that it is permissible to have an incorrect value judgement. By contrast, Rabinowicz's first solution assumes that there is nothing puzzling in the claim that it is permissible to have an incorrect value perception. The question is why. The answer seems to come from the analogy with sensory perceptions. The idea is that, in some circumstances, it is perfectly normal to have non-veridical sensory perceptions, even if one knows that they are incorrect. In turn, this seems to imply that, in those circumstances, it is permissible to have non-veridical sensory perceptions. If the analogy between sensory and value perceptions holds, it follows that, in some circumstances, it may also be permissible to have non-veridical value perceptions.

The problem with this line of thought has to do with the inference from ‘normality’ to ‘permissibility’. More precisely, the problem is that the claim that, in some circumstances, it is ‘normal’ to have non-veridical sensory perceptions does not imply that, in those circumstances, it is ‘permissible’ to have such perceptions. In fact, sensory perceptions are not mental states that it is permissible or impermissible to have at all. In other words, sensory perceptions are not mental states for which a justification or a reason can be given. Rather, they are mental states which admit only of causal explanations. For instance, in our previous example, it does not make sense to ask for a justification as to why an individual mistakenly perceives a stick in the water as broken. The only thing that we can ask for is a causal explanation as to why she has such a perception – an explanation which, in this case, is readily available: given her visual apparatus, she just could not have perceived the stick differently. This shows that the sense in which it is ‘normal’, in some circumstances, to have a non-veridical sensory perception is purely descriptive: this is how our perceptual system works in those circumstances.

These considerations provide the basis for the following argument against Rabinowicz's solution to the ‘substantive problem’. Either value perceptions are akin to sensory perceptions or they are not. If they are, then value perceptions cannot be based on reasons. As such, it can neither be permissible nor impermissible for one to have value perceptions. A fortiori, it cannot be permissible for one to have non-veridical value perceptions – contrary to what Rabinowicz's solution presupposes. On the other hand, if value perceptions are not like sensory perceptions, in that they can be based on reasons and be assessed as permissible or impermissible, then it is unclear how Rabinowicz's solution addresses the ‘substantive problem’. Indeed, the problem seems to reappear in just a slightly different form. Recall that the original question was: ‘How can it be permissible to have preferences that involve incorrect value judgements?’ The question now becomes: ‘How can it be permissible to have preferences that involve incorrect value perceptions?’ One can no longer appeal to the analogy with sensory perceptions, since the analogy has broken down. More specifically, one can no longer say that, in the same way as it is normal, in some circumstances, to have non-veridical sensory perceptions, so is it normal, in some circumstances, to have non-veridical value perceptions. The reason is that ‘normal’ has two different meanings in the two cases, i.e. respectively, a descriptive and a normative meaning. One may of course make reference to the existence of a vector of admissible weights that, when combined with the dimensions relevant for comparison, determines a balance of reasons that makes it permissible to have a non-veridical value perception. However, this only pushes the problem one step back. For the question now becomes: How can an admissible vector of weights make it permissible to have an incorrect value perception?Footnote ¹¹ Or, in other words, how can a value perception generated by an admissible vector of weights be itself permissible, if it is non-veridical? We still lack an explanation to this puzzle.

Rabinowicz has offered a second solution to the Preferences vs. Value Judgements objection, which he presents as follows:Footnote ¹²

As is clear from this quote, here Rabinowicz focuses on the formulation of the Preferences vs. Value Judgements objection in terms of reasons. That is, he works with a conception of preferences according to which these involve reason judgements, rather than value judgements. Rabinowicz's idea is the following. Whenever an agent adopts an admissible vector of weights and applies it to the dimensions relevant for comparison, she arrives at a particular balance of reasons. For instance, when comparing two items x and y with respect to a specific vector of weights, she may arrive at the conclusion that x is supported by stronger reasons than y. This seems to force her to judge that x is better than y. However, to the extent that she realizes that the vector of weights that led her to that balance of reasons is optional, she may also realize that this way of balancing reasons is optional as well and that there may be other optional, but conflicting, ways of balancing reasons. Because of this, she may consistently deny that x is better than y.

Here is a slightly different way of illustrating Rabinowicz's second solution. According to Rabinowicz's FA-analysis, saying that x is better than y is equivalent to saying that one is required to prefer x to y. In turn, if preferences involve comparative reason judgements, saying that one is required to prefer x to y involves saying that one is required to judge that x is supported by stronger reasons than y. But if one is required to judge that x is supported by stronger reasons than y, then it seems that one is also required to judge that x is better than y. Taking this into account, suppose that an agent adopts a specific vector of weights, which leads her to prefer x to y. The worry underlying the Preferences vs. Value Judgements objection is that, because of this, the agent is required to judge that x is supported by stronger reasons than y. If this is true, then, in light of the previous conditions, it follows that the agent cannot permissibly deny that x is better than y. Against this conclusion, Rabinowicz's solution suggests that if the agent realizes that the vector of weights that determines her preferences is optional, then she can also realize that she is actually not required to judge that x is supported by stronger reasons than y, but merely permitted to do so. But if it is simply permissible for the agent to judge that x is supported by stronger reasons than y, then she can permissibly deny that x is better than y.

The problem with Rabinowicz's second solution is that, once again, it provides at most a solution to the first version of the Preferences vs. Value Judgements objection, but not to the second version. Indeed, even if we grant that his account of parity allows an agent to both prefer x to y and deny that x is better than y, it is still the case that his account makes it permissible for an agent to prefer x to y and, thereby, to judge that x is supported by stronger reasons than y. If so, however, the question underlying the ‘substantive problem’ arises again: How can it be permissible for an agent to prefer x to y, and, thus, to judge that x is supported by stronger reasons than y, if the latter judgement is incorrect, given that, as a matter of fact, x is not supported by stronger reasons than y?Footnote ¹³

Rabinowicz's third solution involves a modification of his initial FA-account.Footnote ¹⁴ In particular, Rabinowicz suggests replacing the conception of preferences as dyadic, choice dispositional attitudes, with a conception of preferences as relations between monadic attitudes, each admitting of degrees.Footnote ¹⁵ This conception holds that, for any two items x and y, x is preferred to y if and only if x is favoured to a higher degree than y; x is equi-preferred to y if and only if x is favoured to the same degree as y; and x is in a preferential gap relation with y if and only if the degrees to which x and y are favoured are incommensurable.Footnote ¹⁶

Rabinowicz shows that, if we make this modification, we can address the Preferences vs. Value Judgements objection (as well as the other objections raised against his initial FA-analysis), while preserving the same taxonomy of value relations (Rabinowicz Reference Rabinowicz2012: 154). Consider the formulation of the objection in terms of value judgements. Rabinowicz's reasoning is the following. If preferences are conceived of as relations between monadic attitudes, then the agent does not engage in a direct value comparison. Indeed, preferences are no longer conceived of as dyadic, hence directly comparative, attitudes. Consequently, preferring an item to another does not involve judging that the former is better than the latter. This provides a clear solution to the ‘consistency problem’, for it implies that an agent can consistently prefer an item to another and judge that the former is not better than the latter. In addition, Rabinowicz's new account seems to provide a solution also to the ‘substantive problem’. Indeed, if preferences do not involve value comparisons, saying that it is permissible to prefer one item to another does not imply saying that it is permissible to judge that the former is better than the latter. In other words, Rabinowicz's new account of parity does not sanction as permissible an incorrect value judgement.Footnote ¹⁷

Nevertheless, Rabinowicz's solution is vulnerable to at least two objections. Suppose that the attitude of favouring an item x to degree n involves the judgement that x is good to degree n. Likewise, suppose that the attitude of favouring another item y to degree m involves the judgement that y is good to degree m. For reasons of psychological realism, degrees must here be interpreted non-numerically.Footnote ¹⁸ Having said that, let us assume that there is an appropriate, non-numerical sense in which n > m. We can thereby say that x is favoured to a higher degree than y. By definition of preference, this is equivalent to saying that x is preferred to y. But the judgement that x is favoured to a higher degree than y implies the judgement that x is good to a higher degree than y, or, more simply, that x is better than y. By transitivity, it follows that the preference for x over y implies the judgement that x is better than y. The ‘consistency problem’ reappears: the agent cannot consistently prefer x to y and judge that x is not better than y. The only difference with respect to the initial objection is that, since preferences are not dyadic mental states, they are not constituted by a betterness judgement. Rather, they imply it. For similar reasons, Rabinowicz's third solution fails to address the ‘substantive problem’. Indeed, if the preference for x over y implies the judgement that x is better than y, then saying that it is permissible to prefer x to y implies saying that it is permissible to judge x to be better than y. Rabinowicz's modified analysis implies once again that it is permissible to have an incorrect value judgement.

The argument against Rabinowicz's third solution to the Preferences vs. Value Judgements objection may take an even more direct form.Footnote ¹⁹ A key element of Rabinowicz's modified account is the claim that each favouring attitude admits of degrees. However, the notion of degree seems to be inherently comparative. Indeed, we know from measurement theory that degrees are always relative to two points, which fix the origin and the unit of the scale of measurement. Thus, saying that an item is favoured to an intermediate degree n is equivalent to saying that such an item is favoured more than one item (i.e. the item fixing the origin of the scale of measurement), but less than another (i.e. the item fixing the unit of the scale of measurement), in a way that preserves certain relational properties between these items. These features seem to remain in place, mutatis mutandis, also when degrees are understood non-numerically. The implication is the following: If we assume that the attitude of favouring involves a value judgement, then we should admit that the attitude of favouring an item x to degree n involves a comparative value judgement, namely, the judgement that x stands in a specific betterness relation with some other items, i.e. it occupies a specific position in the (non-numerical) betterness scale, relative to the most and the least favoured items. From this, it follows that the judgement that x is favoured to a higher degree than y involves the judgement that x occupies a higher relative position than y in the (non-numerical) betterness scale and, as such, that x is better than y. If this is the case, however, the connection between favourings and comparative value judgements appears to be as direct as the connection between preferences and comparative value judgements in Rabinowicz's initial account.

4. SOLVING THE PREFERENCES VS. VALUE JUDGEMENTS OBJECTION

In this section, I shall propose an alternative solution to the Preferences vs. Value Judgements objection. The starting point is the observation that both the ‘consistency problem’ and the ‘substantive problem’ could be solved if it were somehow possible to ‘relativize’ Rabinowicz's definition of parity. Suppose, for instance, that instead of saying that two items x and y are on a par if and only if it is permissible simpliciter to strictly prefer one item to another and permissible simpliciter to have the opposite strict preference between them, we could say that two items x and y are on a par if and only if it is permissible to strictly prefer x to y, relative to an admissible vector of weights, and permissible to strictly prefer y and x, relative to a different admissible vector of weights. This account would not generate either the ‘consistency problem’ or the ‘substantive problem’ associated with the Preferences vs. Value Judgements objection. Indeed, if preferences involve value judgements, this account would imply that, when two items x and y are on a par, it is permissible to judge x to be better than y, relative to an admissible vector of weights, and permissible to judge y to be better than x, relative to another admissible vector of weights. There is no inconsistency here. In fact, it is perfectly possible for one to make relativized judgements of betterness of this kind, while denying that one of the two items is better than the other simpliciter. Likewise, saying that it is relatively permissible, i.e. relative to an admissible vector of weights, to judge one item to be better than the other does not imply saying that such a judgement is permissible simpliciter.

The problem with this solution, however, is that, at first sight, such a ‘relativized’ account of parity seems to collapse back into Rabinowicz's account. The reason is that the claim that a preference relation is permissible relative to an admissible vector of weights appears to entail the claim that such a preference relation is permissible simpliciter. After all, if a vector of weights is ‘admissible’ sans qualification, then it seems to generate preference relations that are also ‘admissible’ sans qualification, that is, permissible simpliciter. This seems actually the reason why Rabinowicz describes the set K of preference orderings generated by the admissible vectors of weights as the set of preference orderings that are permissible simpliciter. If this is the case, then the ‘relativizing’ strategy cannot solve either the consistency or the substantive problems associated with the Preferences vs. Value Judgements objection.

However, in what follows I will show that one version of this ‘relativizing’ strategy can be successfully defended. More specifically, I will show that, contrary to the initial appearances, each admissible vector of weights does not determine a preference ordering that is permissible simpliciter, but only a preference ordering that is relatively permissible, that is, permissible only relative to one of the admissible vectors of weights. In order to do that, I will introduce some distinctions that will lead us to further expand the taxonomy of value relations proposed by Rabinowicz. In particular, I will argue that, for any value relation V, there exists an important distinction between a strict V, a quasi-strict V, a rough V and a weak V, which must be taken into account in developing an account of value relations. I shall then explain how these features of the account allow us to address the Preferences vs. Value Judgements objection, in both of the versions distinguished above.

Let us begin by letting W be the set of admissible vectors of weights. As we have seen, each vector in W determines, in combination with the dimensions that are relevant for comparison, a preference ordering. More precisely, if we take the dimensions relevant for comparison as ‘reasons’ in favour of the compared items, then we can say that each vector in W generates a specific balance of reasons, which, in turn, determines a preference ordering. The interesting question is: In what sense exactly does the balance of reasons ‘determine’ each preference ordering? One intuitive possibility consists in saying that all the preference relations that form a given preference ordering are required by the balance of reasons. However, it seems plausible to think that not all preference relations might be recommended by the balance of reasons in this way. In fact, in some cases, the balance of reasons may be such as to make some preference relations merely permissible. This raises a further question: How can we characterize the notions of ‘requiredness’ and ‘mere permissibility’ so as to allow for this possibility?

One suggestion is the following. Suppose that a given vector in W generates a balance of reasons such that the reasons in favour of one item x are stronger than the reasons in favour of another item y and such that the difference in the overall strength of reasons supporting the two items lies above a specified threshold t. In this case, it seems that one is required to strictly prefer x to y, since the balance of reasons decisively favours x over y. On the other hand, suppose that a given vector in W generates a balance of reasons such that the reasons in favour of one item x are as strong as the reasons in favour of another item y, so that the difference in the overall strength of reasons supporting the two items is equal to zero. In this case, it seems that one is required to be indifferent between x and y, since the balance of reasons is equally favourable to each of them and, thus, decisively recommends indifference.

The interesting situation is the one in which the balance of reasons does not decisively favour either a strict preference relation or an indifference relation. Suppose, for instance, that a given vector in W generates a balance of reasons such that the reasons in favour of one item x are stronger than the reasons in favour of another item y, but also such that the difference in the overall strength of reasons supporting the two items lies below the specified threshold t. In other words, suppose that the difference in the overall strength of reasons supporting the two items varies in the open interval (0, t). What should we say of such a situation?

Since the difference in the overall strength of reasons supporting the two items is inferior to the required threshold, the balance of reasons does not decisively favour x over y. Nevertheless, since the reasons in favour of x are stronger than the reasons in favour of y, there is still sufficient reason to strictly prefer x to y. However, this does not mean that there is not also sufficient reason to have a different preferential attitude. In fact, since the difference in the overall strength of reasons supporting the two items is quite small, it seems that there is also sufficient reason to be indifferent between x and y, for the two are roughly equal. In other words, when the difference in the overall strength of reasons supporting two items x and y varies in the open interval (0, t), there is sufficient reason both to strictly prefer x to y and to be indifferent between them.Footnote ^{20 ,} Footnote ²¹

I believe that a similar distinction between decisive and sufficient reason can be drawn with respect to the preferential gap relation. Suppose, for instance, that the conflict of reasons in favour of two different items x and y cannot be resolved because two (or more) dimensions relevant for comparisons cannot be balanced against each other. Suppose that, were it not for those dimensions, the conflict of reasons could be resolved in one way or another (i.e. either by favouring one item over the other or by favouring them equally). Finally, suppose that, relative to a given admissible vector of weights, the above-mentioned dimensions are not especially important, i.e. the weights assigned to them are particularly small. In this case, it seems that one is not required to have a preferential gap between x and y. Rather, it is merely permissible for one to have a preferential gap between them, relative to that vector of weights. This means, however, that it is also merely permissible for one to adopt a different preference relation. In particular, it is merely permissible for one to adopt the preference relation favoured by the balance of reasons generated by the vector of weights under consideration and by the other relevant dimensions. Stretching the language a bit, we can say that, if some unimportant dimensions relevant for comparing x and y cannot be balanced against each other, then there is sufficient, but not decisive, reason to have a preferential gap between x and y, relative to a given vector of weights. Let us contrast this case with the following. Suppose that the conflict of reasons supporting two items x and y cannot be resolved because either all or the most important dimensions relevant for comparison cannot be balanced against each other. In this case (and only in this case), one is indeed required to have a preferential gap between x and y. In other words, if all or the most important dimensions relevant for comparing x and y cannot be balanced against each other, then there is decisive reason to have a preferential gap between x and y, relative to a given vector of weights.

In light of these considerations, we can characterize the notions of ‘requiredness’ and ‘mere permissibility’ more precisely. We can say that, for any two items x and y, a preference relation (i.e. strict preference or indifference or preferential gap) between x and y in a given preference ordering is required if and only if there is decisive reason in favour of that relation, relative to an admissible vector of weights. Moreover, we can say that a preference relation (i.e. strict preference or indifference or preferential gap) between x and y in a given preference ordering is merely permissible if and only if there is sufficient reason in favour of that relation, but also sufficient reason in favour of an alternative preference relation, relative to an admissible vector of weights.

This is, of course, only a characterization of ‘requiredness’ and ‘mere permissibility’ relative to a given vector of weights. Clearly, however, some preference relations may be required or merely permissible relative to all the admissible vectors of weights. How can we characterize the notion of requiredness and mere permissibility in such cases? Things seem straightforward for the former notion. If we focus, for simplicity, just on the strict preference relation, we can say that a strict preference relation between x and y is required, relative to all the admissible vectors of weights, if and only if there is decisive reason to strictly prefer x to y in every ordering generated by the vectors in W. By extension, we can offer a similar characterization of mere permissibility. We can say that a strict preference relation between x and y is merely permissible, relative to all the admissible vectors of weights, if and only if there is sufficient reason to strictly prefer x to y, but also sufficient reason in favour of an alternative preference relation (i.e. either indifference or preferential gap), in every ordering generated by the vectors in W.Footnote ²²

The next step consists in noticing that if (and only if) a preference relation is required relative to all the admissible vectors of weights, then it is required simpliciter. Likewise, if (and only if) a preference relation is merely permissible relative to all the admissible vectors of weights, then it is merely permissible simpliciter. Moreover, if we distinguish between ‘mere permissibility’ and ‘permissibility’ (sans qualification) – where the latter is conceived of as the disjunction of ‘requiredness’ and ‘mere permissibility’ – then we can say that a preference relation is ‘permissible simpliciter’ if and only if it is either required or merely permissible, relative to all the admissible vectors of weights, that is, if it is either required or merely permissible in each of the preference orderings generated by the vectors in W.

These results have some important implications for the present discussion. First, they lead us to a different interpretation of Rabinowicz's framework. Indeed, according to Rabinowicz, a strict preference for x over y is permissible simpliciter if and only if it is permissible (i.e. it is either required or merely permissible) to strictly prefer x to y in some preference ordering generated by the vectors in W. By contrast, according to the current proposal, a strict preference for x over y is permissible simpliciter if and only if it is permissible (i.e. it is either required or merely permissible) to strictly prefer x to y in every preference ordering generated by the vectors in W.

This is the source of another important difference. According to the current proposal, the set of preference orderings that are permissible simpliciter is the set of preference orderings formed by preference relations that are permissible relative to all the vectors in W. Let us call this the set P. Crucially, P may not coincide with the set of preference orderings K, which includes all the preference orderings formed by preference relations that are permissible relative to at least one vector in W, but (typically) not relative to all vectors in W. In other words, contrary to what Rabinowicz maintains, the set K will (typically) not be the set of preference orderings that are permissible simpliciter, but only the set of preference orderings that are relatively permissible.Footnote ²³

Importantly, the previous considerations can also be used to draw more subtle distinctions between value relations. For instance, we can now distinguish between strict betterness (or, simply, betterness) (B), rough betterness (RB) and weak betterness (WB). These can be defined as follows:

It is worth noticing that weak betterness is equivalent to the disjunction of strict betterness, rough betterness, and another value relation, which can be labelled quasi-strict betterness (QB) and which can be defined as follows:

We can draw similar distinctions in the case of worseness, equality, and incomparability.Footnote ²⁵ Furthermore, in light of the previous considerations we can refine, and partly revise, our understanding of parity. Recall that according to Rabinowicz's informal account of parity, two items are on a par if and only if it is both permissible to strictly prefer one to the other and permissible to have the opposite strict preference. According to the current understanding, however, this account must be modified in two important ways. First, it must be kept in mind that ‘permissibility’ should be conceived of as the disjunction of ‘requiredness’ and ‘mere permissibility’. Second, it must also be kept in mind that cases of parity are not cases where it is permissible simpliciter to have opposite strict preferences between two items. Rather, they are cases where it is only relatively permissible to have opposite strict preferences between these items, i.e. permissible relative to different admissible vectors of weights. In light of this, we can distinguish between strict parity (or, simply, parity) (P), quasi-strict parity (QP), rough parity (RP) and weak parity (WP).

One important implication of this analysis is that there are even more possible configurations of parity than implied by Rabinowicz's analysis – especially considering that, relative to some admissible vectors of weights, it may also be permissible (i.e. either required or merely permissible) to adopt preferential attitudes other than strict preferences towards items that are on a par in the sense of (P), (QP), (RP) and (WP).

Another important implication concerns the issue of what value judgements preferences exactly involve. It is uncontroversial that, if preferences involve value judgements, then strict preferences involve betterness judgements. In this section, however, we have seen that there exist three main ways in which an item can be better than another: one item can be either strictly better, or quasi-strictly better, or roughly better than another. Thus, it seems that if strict preferences involve betterness judgements, they must involve judgements that are compatible with all these types of betterness. But the only such judgements are judgements of weak betterness. Indeed, weak betterness is conceived of as the disjunction of strict-betterness, quasi-strict betterness and rough betterness. Given this, we should conclude that strict preferences involve weak betterness judgements. Accordingly, strictly preferring one item to another involves judging that the former is either strictly better, or quasi-strictly better, or roughly better than the other.Footnote ²⁶

We now have all the elements in place to explain how the current proposal can address the Preferences vs. Value Judgements objection. For simplicity, in what follows I will only work with the formulation of the objection in terms of value judgements. Recall the two problems generated by Rabinowicz's analysis of parity. The first is a ‘consistency problem’: How can an individual consistently judge that one item is better than the other (as it is permissible for her to do), while at the same time denying that this is the case (since she judges that the two items are on a par and, hence, that neither is better than the other)? The second is a more ‘substantive problem’: How can it be permissible for an individual to judge that one item is better than the other, if this is an incorrect judgement (given that, when two items are on a par, neither is better than the other)?

As we have seen, the analysis of parity suggested in this paper presents two main differences with respect to Rabinowicz's. First, parity is defined in terms of relatively permissible opposite strict preferences. Second, strict preferences are now conceived of as involving weak betterness judgements. Together, these features imply that, contrary to Rabinowicz's analysis, cases of parity are not cases where it is permissible simpliciter to have opposite strict betterness judgements between two items. Rather, they are cases where it is either required or merely permissible for an agent to have opposite weak betterness judgements between two items, relative to different admissible vectors of weights. The proposed account is thus a refined version of the ‘relativized’ analysis of parity sketched at the beginning of this section. Because of this, it does not generate any of the problems that affect Rabinowicz's analysis. On the one hand, it may be perfectly consistent for an agent to strictly prefer x to y and, thus, to judge that x is weakly better than y, relative to one admissible vector of weights, while, at the same time, denying that x is weakly better than y simpliciter. On the other hand, saying that it is permissible (i.e. either required or merely permissible) to strictly prefer x to y and, thus, to judge that x is weakly better than y, relative to one admissible vector of weights, does not imply saying that it is permissible simpliciter to judge that x is weakly better than y. If this is the case, then the current proposal does not generate either the consistency or the substantive problems associated with the Preferences vs. Value Judgements objection.Footnote ²⁷

In fact, the current proposal seems always to deliver the correct judgements. Suppose, for instance, that one is required to strictly prefer x to y, relative to all the admissible vectors of weights. If strict preferences involve weak betterness judgements, the current account implies that one is required simpliciter to judge x to be weakly better than y. This judgement is actually correct. Indeed, if one is required simpliciter to strictly prefer x to y, then x is strictly better than y. If so, it is correct to judge that x is weakly better than y, since weak betterness is a disjunction of value relations including strict betterness. Likewise, suppose that it is merely permissible to strictly prefer x to y, relative to all the admissible vectors of weights. If strict preferences involve weak betterness judgements, the current account implies that it is merely permissible simpliciter to judge x to be weakly better than y. Once again, this is a correct judgement. Indeed, if it is merely permissible simpliciter to strictly prefer x to y, then x is roughly better than y. If so, it is correct to judge that x is weakly better than y, since weak betterness is a disjunction of value relations including rough betterness.

Before concluding, it is worth pointing out that the current proposal forces us to partially modify also the formal analysis of value relations. Indeed, since preferences can be either required or merely permissible, within each preference ordering in K, then, in order to determine which value relation holds, it is not sufficient to see whether a preference relation occurs in every preference ordering in K. In fact, one has to look at the underlying reasons supporting the different items. Taking only betterness as an example, we can say that:

The formal analysis of the other value relations can be similarly derived from the previous considerations.