I. ILLUSTRATING THE UNDERLYING LOGIC OF THE EPISTEMIC APPROACH

Ten students go into a room one by one and cut off a piece of red string and a piece of blue string from the respective balls of string. We want subsequently to form justified – not infallible, but justified – beliefs about which is longer overall, the red strings combined or the blue strings combined. We initially know nothing about the students and nothing about their strings. They each now individually compare which of their strings personally is longer, the red or blue. Seven have red strings longer than their blue ones; three have blue strings longer than their red ones. Which combined strings, red or blue, should we believe is overall longer? That is, how can we form a justified belief about overall string length from ordinal evidence – i.e. about which is greater, less or the same – about individual string lengths? One way we can do so is by adopting Unbiasedness and Coherence:

Given Unbiasedness and Coherence, if all – and this is a crucial clause – if all the evidence we have is that seven students have red strings longer than their blue, and three have blue strings longer than their red, then we would be justified in believing that the red strings (‘R’) collectively are longer than the blue ones (‘B’), or giving a greater credence to the theory ‘R > B’ than the theory ‘B > R’. (Hereafter a capital letter – such as R – refers to the overall amount of the quantity in the arrangement R, and r(i) that of individual i in the arrangement R). Unbiasedness ensures that we give each student's information equal weight, and this combined with Coherence ensures that learning that there are more red strings longer than the blue justifies, absent any other evidence, believing the red is overall longer.

Now, it is true that in adopting Unbiasedness, and implicitly not assuming that anyone's overall combined string is greater in length than anyone else’s, we have not guaranteed infallible beliefs: it might be that some student, Robert, took lots more string than all others combined, a veritable string monster. But with absolutely no evidence for this we would violate Unbiasedness in giving Robert's evidence more weight than that of others (it might incidentally be that he took much less). In the string case our intuitions may be nebulous and not always support this. But in the welfare/good case Unbiasedness is a much more compelling general condition as it may be sufficiently justified in either of two ways: methodologically or morally. Which ultimately is adopted will potentially impact the type of result: if Unbiasedness stems from a methodological commitment then the result will not be a direct argument for overall-good based moral theories (merely permissive of them), but if it stems from a moral understanding of Unbiasedness then this seems to lend some credence to the idea that treating people equally involves giving equal weight to their interests.

The first broad justification of Unbiasedness is to see it as a basic methodological principle, roughly as a generalization of something like Harsanyi's ‘principle of unwarranted differentiation’ whereby ‘If two objects of human beings show similar behaviour in all their relevant aspects open to observation, the assumption of some unobservable hidden difference between them must be regarded as a completely gratuitous hypothesis and one contrary to sound scientific method.’Footnote ⁶ This is a broadly evidentialist view of empirical method – that ‘the epistemic justification of a belief is determined by the quality of the believer's evidence for the belief’Footnote ⁷ – though it would also be straightforwardly entailed by Bayesianism with uniform priors.Footnote ⁸

Second, however, Unbiasedness may be sufficiently justified not only by a methodological principle but also by an ethical one, by the principle of equal moral concern: if we show bias towards the good of some individuals without any good-based reason for so doing, then this discrimination against others cannot be justified. All humans are worthy of equal moral concern, under this principle, and this means that the comparative weight we give them in evaluating what happens to them should be equal. A very, very broad range of approaches to morality seem capable of motivating this, such as that biased treatment could be reasonably rejected,Footnote ⁹ that it is not compatible with treating people as free and equal,Footnote ¹⁰ or that it violates the principle that each counts for one and only one.Footnote ¹¹ The sceptic, in arguing for biasedness, therefore minimally has to show the falsity of both the methodological and moral justifications of Unbiasedness.

Coherence is that beliefs about the overall amount of something should supervene upon beliefs about the individual amounts of that thing, that for instance your beliefs about whether there are more boys than girls in a particular class should supervene upon your beliefs about how many boys and girls there are in the class: if you think there are ten boys, six girls, and more girls than boys, then there is something wrong with your beliefs. In the string case Coherence entails that beliefs about the overall lengths of particular string colours should cohere with beliefs about the lengths of the particular bits of strings, such that if we find out that Jack has a red string longer than his blue string we should be more confident that the red is overall longer than if we had learned that Jack had identical-length strings, or his blue were longer than his red. (Absent other information. Obviously, if we have actual evidence that Bob likes to copy Jack, or that most of the class like to shun Jack's choices, then this needs including too.)

In the good or welfare case it means that beliefs about the overall amount of good or welfare are based upon beliefs about the amount of good or welfare of all the individuals. Coherence may, on some accounts, simply be a consequence of defining the overall amount of good/length of the red (or whatever) string as the sum of the particular amounts of good/bits of red (or whatever) string, and asserting that various constraints on justified beliefs necessarily follow from this. It is included as a separate principle for clarity. It is, however, Unbiasedness that really does the major work in the results that follow, and that as such raises the most interesting meta ethical issues, as discussed in section IV. Unbiasedness and Coherence permit us to form justified beliefs about the overall lengths of the strings based on any information about the students’ individual string lengths and, using the same logic, do so for the overall good.

One way in which the earlier example may mislead, however, is that when we are dealing with small numbers of individuals, or when we are dealing with large numbers but where the ratios of different options are fairly similar, we might as such just be not that confident in any conclusions. The thought would be: can we really be very sure?

This isn't a rejection of the overall epistemic approach however: it's an endorsement of it. It is only by having an account of how individual-level information impacts overall beliefs that we can have a second-order account of how confident we can be in the conclusions. Compare the following two scenarios where all you know is how each individual's author words relate to their birth-city words (and you know strictly nothing else, and only one scenario obtains – so it isn't indirect evidence for the other):

In both cases, if this is all the information you have, under Unbiasedness and Coherence you will be justified in believing the author-words-combined have more letters than the city-words-combined. However, intuitively, in the second case you can also be more confident of this. Similarly, imagine you have just three students and they are asked to write down their favourite author, birth city, species of first pet, favourite singer's first name, last-sport-played, mother's maiden name and last holiday destination. They are as follows:

Here it seems you can be more confident that the author words combined are longer than the city words than if you just knew the following:

Many will have intuitions that the more the categories are apart – both in terms of numbers of individuals and in terms of other categories – the more confident we can be that one is overall longer than the other. Unbiasedness provides a justification for these intuitions: each individual's information (and category) is in principle treated with equal epistemic weight (unless we have evidence to the contrary), thus the more individuals who have the ranking author > city, the more confident you can be that the author words combined are longer than the city words combined, and similarly the more words between someone's author and city, the more confident you can be that the difference between these words is larger. Unbiasedness and Coherence endorse and justify all of these judgements. (One further thought here is that there are only so many letters, so we can guestimate some discrete differences. This is a side issue: if distracted by it then re-run the example with string lengths.)

More generally, Unbiasedness and Coherence are useful because often we have some evidence of underlying phenomena but not full evidence of them. Even if, for example, we cannot know the actual numbers of letters in all the words, we can still use evidence of the rankings of the students to form justified beliefs about which contains more words overall: the cities, authors or pets. Presumably there will be some underlying probabilities depending on where one does this and if we could obtain evidence of these then that could bear on our credences too. But if all the information we have is the individual rankings – in this case it might not be, but in the welfare/good case for the sceptic it is – then we can still form justified beliefs overall.

The string/word to welfare/good analogy is thus inexact. It is stipulated in these examples that direct individual-level information is all the evidence we have, as that is true in the good/welfare cases. However, we probably have multiple rather diffuse intuitions about pets, authors and cities. These examples, of strings and words, are thus meant to be illustrative of the underlying logic, even if some additional implicit background evidence – about dog versus kangaroo prevalence perhaps – requires ignoring. For someone who struggles to avoid bringing in such ‘background evidence’, then, a better analogy might be if the example instead involved students in an unknown foreign language and place. All you know is the rankings (you don't even know the categories, nor how many letters there are in the alphabet or anything). This, after all, is the premise the sceptic asserts: you don't have direct evidence of the underlying values at all.

The overall epistemic approach simply says that we should use evidence about individual amounts (individual words/strings/good/welfare) to form coherent beliefs about overall amounts (overall words/strings/good/welfare), and do so in a manner that treats all unbiasedly (with equal moral concern). What you would do in the word and string cases you should simply do in the welfare case because you know the same sorts of things and are in the same epistemic situation (if you are an interpersonal comparison sceptic that is: if rough interpersonal comparisons are possible by empathy or such like then we don't need this, but then scepticism fails too).

II. FORMALIZING THE APPROACH

The substantive normative discussion continues in section III; this section simply sets out one (of the many) ways of formalizing the overall logic. It does not ‘prove’ the epistemic approach justified; the substantive arguments in favour of it are considerations to that effect. It merely (I hope) makes it somewhat easier to understand and to criticize for some readers at least.

To formalize the above discussion we can adopt a credence framework or use the concept of expected value. (The two yield functionally identical results, but one may be easier to use than the other in particular contexts. Cognitively, an expected value approach is easier to follow, thus that is used here.) To do so, we need to set just three values. First, we need to decide whether the identity of individuals should affect their relative weight in the calculation of expected values. Second, we need to decide in principle what relative expected value to give to B and R, before we have any evidence whatsoever. Third, if we learn of an individual that for them R has more of the quantity than B – that r(i) > b(i) – then we need to decide how this should affect our overall expected values compared to what they would be had we learned different information. Unbiasedness and Coherence allow us to do all three.

Here are three basic axioms in an expected value framework, where E[R] represents the expected value of any arrangement R before the evidence, E[R / e] represents the expected value of R after learning e, and e*i = r(i) > b(i), r(i) = b(i), or r(i) < b(i) for individual i and all r, b such that r ≠ b.

1. 1. Equal treatment ‘ET’: For all individuals i, j and arrangements R let E[R / e*(i)] = E[R / e*(j)].

2. 2. Pre-evidential indifference ‘PI’: Before any evidence E[R] = E[B] for all R, B.

3. 3. Equal positive supervenience ‘EPS’: For all R and all individuals i, j, where y>0 then E[R / r(i) > b(i)] = E[R] + y; E[R / r(i) = b(i)] = E[R]; and E[R / r(i) < b(i)] = E[R] − y

Equal treatment and pre-evidential indifference stem from Unbiasedness: to be biased towards one arrangement represents an implicit bias towards those favoured by that arrangement; to give the information of some individuals more weight than that of others is to be biased toward them. Equal positive supervenience is based on the fact that the overall amount of something is comprised of the amount in its constituent parts. Rejecting equal positive supervenience would mean, for example, that the more students you learned had red strings longer than their blue ones, the more confident you would become that the blue strings were overall longer (violating Coherence) or that your beliefs about string lengths would be affected by the identities of individuals rather than information about their strings (violating Unbiasedness).

Given Equal Treatment, Pre-Evidential Indifference and Equal Positive Supervenience it follows that, for body of evidence E, if n(r +) is the number of individual-level pieces of evidence that r > q, if n(r = ) is the number of individual-level pieces of evidence that r = q, and if n(r −) is the number of individual-level pieces of evidence that r < q, all where Q ≠ R, then for all R, Q, B:

To put this verbally:

It should be noted, however, that in the string or word cases this does not ensure we have infallible beliefs, merely that they are justified. It is possible, for instance, to think of possible distributions of string lengths that would permit us to form false beliefs, but we have no reason to think these distributions hold. This is the epistemic approach: we use evidence to form justified beliefs. Section IV discusses how in the welfare case true beliefs might in fact simply be justified beliefs given all possible evidence.

What is particularly striking about this overall result is how minimal are the conditions we require to produce it. If we seek beliefs that are unbiased and coherent then merely with ordinal information we can form justified beliefs about the overall good/welfare, and thus make justified interpersonal comparisons.

Since the aim of this article is to show how scepticism about interpersonal comparisons of the good/welfare may be overcome by adopting the epistemic approach, the focus here is thus on explicating and defending comparisons given only ordinal information, as this is the case most favourable to the sceptic (from any cardinal set of information one can infer ordinal information, thus if comparisons based on ordinal information are possible, determinate and meaningful, then so are ones given cardinal information). Discussion of comparisons using cardinal evidence is therefore put to one side, though it is implicitly covered for those who think that cardinal information is solely obtained via ordinal evidence (such as the lotteries over outcomes individuals would rationally chooseFootnote ¹³ ). The ordinal is, however, sufficient to illustrate the basic epistemic logic, and the ways in which the epistemic approach may be misinterpreted. It is to these that this article now turns.

III. THREE FALLACIES TO AVOID

You are a peasant. Consider the following options:

1. 1. The king takes all your property.

2. 2. The king takes three-quarters of your property, but has to work for a week digging turnips.

3. 3. The king takes half your property.

We could collect information on how these compare and then might find of them that the king has more welfare in 1 than 3, and more in 3 than 2 (he is very wealthy already, and really hates digging turnips). You have more welfare in 3 than 2, and more in 2 than 1. If this is all we know then it might seem we would be justified in believing that 1 represents more overall welfare than 2. But this seems absurd. Which it is: the belief that 1 represents more welfare than 2 is unjustified because it violates Unbiasedness, in that Unbiasedness covers both how we treat individual-level information, and how we select and structure it. More specifically, even if the above options were the three options we had to choose between, if we use them alone to structure the evidence in so doing we would be committing the first of three fallacies, namely:

The issue here relates to how we select the different options about which we seek and incorporate evidence. If we (wrongly) think of welfare by analogy with voting, then the domain appears naturally to be the candidates or choices, and overall beliefs justified by the individual information about these. In contrast, however, for the epistemic approach the options are selected and distinguished based on our theory of the good and the evidence. The key point is this: if we have to choose between a set of options it is the alternatives about which we can gain distinct evidence that represent the potential domain which we use to form justified overall beliefs, not merely the options at hand. Even if we are only choosing between red and green strings, the blue strings can be informative as to that choice, and all such string information could be potentially included. Hence for justified beliefs we need to seek out and include a set of evidence that can be justified by Unbiasedness and our theory of the good, not necessarily simply by the options under consideration.

The unjustified domain fallacy is very closely related to a second way we can go wrong in using the epistemic approach, namely:

For example, consider someone arguing that slaveholders prefer to keep a domestic slave, such a slave prefers to be free, and thus if this is all the information we have then we are justified in believing that either arrangement is of equal welfare, thus the epistemic approach must be wrong. This is fallacious as the correct judgement about the conclusion's implausibility stems from the vast, rich and detailed evidence and understanding we have about what it is like to be a slave, what slaveholding entailed, what the effects of it were as an institution, and how much of what is most valuable in human life was denied the slave. As social beings in a rich cultural environment we have an very detailed and complex understanding of a wide range of patterns of human valuation, of suffering, hope, pain, dignity, freedom from domination, the enjoyment of security, the determinants of social respect, the ability to develop one's potential and shape one's life, and so on. If we ignore vast swathes of evidence we will reach conclusions that, with this evidence in mind, seem unjustified. But it is the ignoring of the evidence that is at fault, not the attempt to use evidence to form justified beliefs.

It is also for a similar reason that this article explicitly separates out two questions: (1) What comprises evidence of the good of individuals? (2) How, in principle, given an account of the good of individuals, should we combine evidence thereof into beliefs about the overall good? If we fail to treat these as distinct then disagreement about 1 will risk fuelling disagreement about 2 as each theorist will, from the other theorist's perspective, have ignored evidence (the relevant evidence that arises from the different accounts). Finally there is:

That is, it might be that in a range of situations we think that people's welfare is of a similar absolute level, that for instance we think the welfare level of everyone sleeping (without dreaming) or being dead is identical. However, if we use the epistemic approach based on only ordinal or cardinal information then these values might come to differ: someone who would knowingly and consistently take a higher risk of death for a large range of goods assuming they live could be assigned a lower level of welfare to death than someone who was much more relatively death averse. (It is assumed in this case that people's welfare is partially based on what they value, and that what they would choose is evidence of what they value.) But if we think being dead must represent the same welfare for all people then the epistemic approach seems to have given us the wrong answer. Such an argument does not support scepticism about the good/welfare, however, as it presupposes the very falsity of such scepticism.

For example, consider the previous example where everyone writes down their birth city, favourite author and species of first pet. We learn how the numbers of letters in each of these compare for each individual, and form beliefs about the overall number of letters in the city, author and pet words combined. Now we learn that everyone was born in the same city and yet our previous comparisons had implicitly assigned a lower value to the cities of individuals who had more letters in their pet and author words than those who had the most letters in their city words. This is mis-premised as a criticism as what we had previously were justified beliefs given that we could not make absolute comparisons, i.e. directly compare people's city words. The epistemic approach is needed when we only have ordinal or cardinal information: we know how options compare, but not their absolute values. If we assert such absolute values for some options, however, then our previous comparisons will not reflect that information. But this is not a problem, it is an advantage: we can make direct interpersonal comparisons and scepticism fails.

As such we can see how the overall approach fits with other arguments in the literature about how we might come to know welfare information, such as via extended sympathy. These theories – if they succeed – are analogous to where we have evidence of absolute amounts, something with which the epistemic approach is perfectly compatible. Its real value, however, is if these arguments fail, for the sceptic still needs to provide an account of why we are not justified in using the epistemic approach.

The overall point of emphasizing all three fallacies is to try to pre-empt the conflation of localized disagreement over a particular conclusion based on the epistemic approach with generalized counter-arguments applying to the approach. If we choose biased domains, ignore evidence or assert absolute comparisons then, having done so, we will risk conflict with epistemically justified comparisons implicitly based on unbiased domains, included evidence or absent absolute comparisons. This, however, is an argument for evaluative consistency and the updating of one's beliefs, not scepticism.

IV. METAPHYSICAL IMPLICATIONS

The role of the analogies with both string and word lengths was to highlight how we can use well-established epistemic principles in order to combine individual-level information about various quantities into beliefs about the overall amount of various quantities. There is one way this may be potentially misleading, however: both the length of string and the overall number of letters in words are directly empirically verifiable properties in that they have values which we justifiably believe exist. There are eight letters in Melville, not nine or two. If we think that welfare is like that, in that there can be some empirical truth to Bob somehow having 57 (rather than any other number) units of welfare in situation A then we can still form justified beliefs and make, by implication, interpersonal comparisons. As such the determinacy and possibility critiques fail. But welfare need not be like this, and as a result there potentially could be nothing necessarily metaphysically mysterious about overall welfare or the overall good.

Consider the hypothetical case where we know all there is possible to know about the relative good or welfare of every possibility for each of the individuals affected: we have complete cardinal information about how much better or worse each possible scenario is for each individual. Now, if we assume that there is some ‘overall good/welfare’ that actually exists as the sum of individual-specific values that themselves empirically exist then it is possible that in using the individual-level information to gain justified beliefs about overall good/welfare we would still have false beliefs, notably that some individuals may just be more important for the overall good in ways that cannot be known based on any information about them. In this case in combining their individual-level information in a way that was unbiased we could form justified but false beliefs.

This we might label ‘physical realism’ about the good. This sort of position appears to be what the ‘metaphysical critique’ implicitly has in mind as both problematic and necessary. It seems to be a strong version of a cognitivist, truth-apt and non-error theory, one that conceives of the good very much in the same way as it conceives of empirical entities. Hopefully the label ‘physical realism’ manages to capture this.

The physical realist position is that the overall good exists in something like the same way in which the number of letters in the previous sentence exists as the sum of its nine constituent words. If we make certain assumptions about how this good relates to the good of individuals we can still use evidence about the good of individuals to form justified beliefs about the overall good (and this is what we did, for instance, with string). Such beliefs are, however, justified but not necessarily true. For the physical realist the same applies to the overall good: there are true facts about the absolute level of an individual's welfare (for instance) – such as that in situation X Meghna has a welfare of 21 – even though we cannot ever conceivably gain direct knowledge of this number, nor indeed can Meghna. But it exists. Overall welfare is the sum of these numbers.

There is an alternative, however: that the overall good is a construct that is created by combining information about the good of individuals in a justified manner. That is, once we have an account of justification then the true overall good is that which we would be justified in believing were we to know all possible information about the relative good of individuals. There is nothing more: the status of Jack having a welfare of ‘57’ in A is simply an epistemic construct, it is not that an omnicognizant being could look into Jack's head and count 57 welfare units or measure his welfare to be 57. The welfare/good as a construct position would perhaps be:

1. 1. There are true empirical facts about how different arrangements relate to individuals.

2. 2. A justified theory of the good/welfare would supervene on these facts to yield facts about how, for each individual, different arrangements relatively compare in terms of their good/welfare.

3. 3. Combining all possible such facts in a justified manner would yield true facts about the overall good/welfare.

4. 4. We can use individual-level evidence to choose between theories about the overall good/welfare and, in principle, were we to believe all such potential evidence and reason correctly, we would have true beliefs about the overall good/welfare.

The point of introducing the good-as-construct position here is not to demonstrate that it is the right meta ethical stance, and indeed the outline above is at best a suggestive sketch, not a proper defence. The point instead is to stress that there is nothing necessarily metaphysically mysterious about the overall good, it being a justified construct being one (potentially among many) meta ethical positions that is able to make sense of the overall good without requiring the existence of a social mind or of empirically real absolute individual welfare levels.

A different way of capturing the same conclusion is to consider what the underlying individual-level mental facts might be like. Assume – for argument's sake – that people's welfare is based somehow on their desires or what they value (the logic can be re-run using alternative conceptions). There seem to be two possibilities for the underlying mental facts. First, desires could have some objective mental strength or quantity, such that my desire for A will ultimately be derived from some quantity-like feature of part of my mental infrastructure (some feature of how strong the neurons link or how many link etc.). If so, the string and word length analogies are directly applicable, but as such there is the possibility of having justified but false beliefs (about overall welfare, overall string lengths, overall word lengths).

Alternatively, imagine that the only individual-level mental valuation facts are comparative, thus it is not that there are mental facts about the desire for A but rather only about the desire for A compared to B. Here, although the string and word analogies are less tight, if anything the epistemic approach can be more confidently used, for the more evidence we get the more confident we can be that epistemically justified beliefs are converging on true beliefs (if we treat people unbiasedly).

One notable implication is that if the mental evaluative facts are ultimately comparative then there cannot be a ‘utility monster’. If they are absolute then there could be such a monster, but without evidence about who this is we would be unjustified in attributing this to a particular set of individuals, thus this does not entail the impossibility of justified interpersonal comparisons.

Which set of mental evaluative facts apply to humans (and non-human animals) is open to dispute. The point here is that whichever does we don't have to assert the existence of a social mind, and even if there are no absolute welfare-level facts for individuals in a situation, only comparative ones between situations, then the overall welfare/good is a meaningful concept about which we can gain evidence and form justified beliefs.

V. REVISITING SCEPTICISM ABOUT THE GOOD

For the epistemic approach, the possibility critique is addressed simply by virtue of the possibility of having evidence about the good of individuals: if we don't need to get ‘into’ the minds of individuals to gain evidence of their good or welfare, then when using epistemic principles to combine this evidence we don't need to do so either. The possibility of individual-level evidence about the good entails the possibility of justified beliefs about the overall good. Just as we don't need to see all the students’ words to start to form justified beliefs about the overall length of the word-combinations, so we don't need to ‘see’ people's welfare in their heads to start to form justified beliefs about overall welfare as we gain evidence about their welfare.

The determinacy critique, that we cannot have determinate knowledge of overall welfare, is addressed in two ways. First, the epistemic approach denies that determinate knowledge is the necessary goal: what we seek are justified beliefs, for these allow us to evaluate actions, policies and institutions, the reason for seeking interpersonal comparisons in the first place. For the determinacy critique rests on the following mistaken reasoning:

Now, if we assume a physical realist account of the good, then the premise will be almost always true. But even if so the conclusion is unwarranted. Indeed, if the general reasoning were correct then it would potentially entail the impossibility of much empirical method in general, for it is rare for evidence to prove a general theory and on some accounts it is normally impossible.Footnote ¹⁴

The second way the determinacy critique may be addressed is that, if the welfare/good-as-a-construct approach is correct, then the overall good simply ‘is’ that represented by justified beliefs given all possible evidence, and the determinacy critique cannot even arise as the gap between justified beliefs and true beliefs is, in principle at least, bridge-able. If the overall-good-as-construct approach is correct, as we gain more evidence justified beliefs will be expected actually to converge on true beliefs and, were we to gain complete evidence, represent true beliefs with no possible indeterminacy.

The ultimate problem for the possibility and determinacy critiques is that the conditions that supposedly justify them – our lack of access to the actual values of the various individual quantities, or inability to experience values across individuals – are exactly the conditions that hold in the string and word examples (and many, many, many more). A sceptic is potentially forced either to accept that determinate justified beliefs about string, word-lengths, welfare and the good are all possible; or that they are all not. That is, the difficulty for the sceptic comes because they must specify which of the following holds:

1. 1. The sort of epistemic information we have in the string/word case on the one hand, and in the welfare case on the other hand, is not of the same type.

2. 2. The sort of epistemic information we have in the string/word/welfare cases are of the same type and we cannot form justified beliefs about the overall amounts of string/words in these sorts of situations.

3. 3. The sort of epistemic information we have in the string/word/welfare cases are of the same type; we can form justified beliefs about the overall amounts of string/words in these sorts of situations but we cannot form justified beliefs about the overall amounts of welfare in these sorts of situations.

4. 4. We can form justified beliefs about the overall amounts of welfare in these types of situations.

Now 1 is false: in both cases, by stipulation, we only have ordinal information. This, after all, is supposed to be the most sceptic-favourable case (if we have absolute information – such as via extended sympathy – then scepticism can be overcome straightforwardly).

To take 2 is to take a very odd general position in epistemology. Bayesians would certainly deny it. If this is necessary to sustain welfare-comparison scepticism then the position is a very strong one and has a large justificatory hurdle to clear.

Position 3, however, seems arbitrary. It is conceded that we know the same sorts of things – that is we know ordinal rankings for the relevant variables and they alone. And it is conceded that in every other case (apart from welfare) we can use such rankings to form justified beliefs about overall amounts. But it is still maintained that we cannot in the welfare case. At a minimum the sceptic here has to address both the apparent arbitrariness and to set out exactly why welfare is relevantly different (it is obviously different in a range of ways, just as strings are different from words, but our epistemic situation in the various cases does not appear relevantly different.)

Moreover, individual welfare is presumably based on some individual mental facts (see section IV), thus the sceptic needs to say what these are if they are not absolute or comparative in nature (and as such welfare-comparison scepticism becomes a very contingent empirical hypothesis in neurobiology, and a slightly mysterious one at that). If 1, 2 and 3 fail, however, then 4 follows as a matter of logical exhaustion. This is ‘The Sceptic's Challenge’, namely to do the following:

It is a challenge because SC1 is a very tractable task, and applying the results of SC1 to the welfare case is as such conceptually relatively trivial (just use the same principles). It is the sceptic here who owes us an explicit account: it is not enough simply to note that it is impossible to get into other minds or to note that in the welfare case we cannot directly observe the values and thus infallibly know a determinate ranking.

Finally, as noted previously, if the possibility and determinacy critiques can be addressed, the metaphysical critique loses much of its force and, if the good-as-construct is correct, it is removed. In a sense, the metaphysical critique rests on a misanalogy. The individual good is potentially based on the brain/mind of the individual involved. But we need no social mind or group brain to form justified beliefs about the overall good, and we need no such group brain or group mind to account for the potential meaningfulness of this good.

Viewed through an epistemic paradigm, scepticism therefore looks problematic. This potentially has very important implications indeed. For it is virtually impossible justifiably to say anything about overall welfare or the overall good without interpersonal comparisons, a fact that is brutally unavoidable as there quite plausibly has never been a pareto-improving economic or political policy or institutional change undertaken by any state, at any time, at any point, in all of recorded history, and probably never will be. Indeed, I have a long-standing bet to this effect. No suggested pareto-improving policy has yet withstood scrutiny. Moreover, as a colleague, Hakon Tretvoll, pointed out, even if such an unlikely policy did exist, one final impact would be to cause me to lose the bet, which would leave me worse off, and entail that it couldn't be a pareto improvement. (This delightfully ingenious result is not terribly important, but it does, however, highlight the sheer improbability of saying anything useful about social welfare without some sort of interpersonal comparisons).

There are always winners and losers in terms of their personal welfare. A welfarism based on pareto rankings must either idealize human agents or causal chains to the point where they are barely recognizable, or opt for productive efficiency as a duplicitous welfare proxy and by doing so abandon seeking an unbiased normative justification.Footnote ¹⁵

Fortunately such a negative conclusion is not necessarily warranted, for the problem of interpersonal comparisons is ultimately a problem of how we justifiably combine evidence of individual amounts into beliefs about overall amounts, something that is both a tractable epistemic problem (assuming a basic account of justification), and one with intriguing implications for how we might understand the ontological status of the overall good.