Symmetry, regularity and qualitative probability

Let ⪅ be a qualitative probability comparison for some collection F of subsets of a space Ω. Say that A ≈ B iff A ⪅ B and B ⪅ A, and that A < B provided that A ⪅ B but not B ⪅ A. Minimally suppose that ⪅ is a partial preorder (i.e., transitive and reflexive). Say it’s total provided that for all A and B either A ⪅ B or B ⪅ A. Suppose that G is a group of symmetries acting on Ω, and that F is G-invariant in the sense that gA ∈ F for all g ∈ G. Then we can define:

1. ⪅ is strongly G-invariant provided that for all A in G and all g in G we have A ≈ gA, and

2. ⪅ is weakly G-invariant provided that for all A and B in G and all g in G we have A ⪅ B iff gA ⪅ gB.

There is some reason to be suspicious of strong G-invariance. For in some interesting cases, say where Ω is a circle that G is the set of all rotations, there will be cases where gA is a proper subset of A, and by regularity we would expect to have gA < A rather than gA ≈ A. But weak G-invariance seems harder to question.

Say that g ∈ G is of order n provided that gⁿ = e, where e is identity. However, we also have:

Lemma 1. If ⪅ is total, g is of order 2, and A ⪅ B implies gA ⪅ gB for all A and B, then A ≈ gA for all A.

Proof: Since ⪅ is a total order, either A ⪅ gA or gA ⪅ A. Suppose A ⪅ gA. Then gA ⪅ g²A. But g²A = A. Hence gA ≈ A. Similarly, if gA ⪅ A, then g²A ≈ gA. But g²A = A, so gA ≈ A.

So, we have:

Proposition 1. If ⪅ is total and G is a group generated by elements of order 2, then weak G-invariance entails strong G-invariance.

Say that ⪅ is strongly regular provided that if A is a proper subset of B, then A < B. Weak regularity would say that if B is non-empty then ∅ < B. Weak regularity together with an appropriate additivity condition will imply strong regularity (details left to the reader).

Proposition 2. If G is generated by elements of order 2, and ⪅ is total and weakly G-invariant, then if there exists a g ∈ G and A ∈ F such that gA is a proper subset of A, then G is not strongly regular.

Proof: Strong regularity would require that gA < A, but that would contradict strong G-invariance which we have by Proposition 1.

Corollary 1. If F is a collection of subsets of the unit circle containing all countable sets and invariant under all reflections, and ⪅ is a total qualitative probability comparison weakly invariant under all reflections, then ⪅ is not strongly regular.

Proof: The group generated by all reflections includes all rotations. But there is a subset A of the circle and a rotation g such that gA is a proper subset of A. For instance, let A be the set of points at angles r, 2r, 3r, ... in degrees, where r is irrational, and let g be rotation by r. Then rA is the set of points at angles 2r, 3r, 4r, ... in degrees.

Now, imagine an infinite line on which there are infinitely many evenly spaced people, stretching out in both directions, each of whom flips a fair coin. Let Ω be the probability space describing these flips. Let H_n be the event that all the flips starting with person number n (i.e., n, n + 1, n + 2, ...) land heads. Suppose that F contains all the H_n and is invariant under all reflections of the situation (where we reflect the setup either about the point at which some person stands or at a point half-way between two neighboring people).

Corollary 2. If ⪅ is a total qualitative probability comparison weakly invariant under all reflections, then ⪅ is not strongly regular.

Proof: Let G be the group generated by the reflections. This group contains all translations. A non-trivial translation of H_n will either be a proper subset or a proper superset of H_n, depending on the direction of H_n. So by Proposition 2 we cannot have regularity.

Bibliographic note: Lemma 1 and Corollary 2 are analogous to Lemma 2 and Theorem 4 of this paper.

The choice between qualitative probabilities and generalized quantitative probabilities is illusory

There are two approaches to generalizing probabilities beyond the classical real-valued numerical approach.

1. Switch the values of the probability function from real numbers to values in some other ordered algebraic entity (e.g., the hyperreals, the surreals, an arbitrary totally ordered monoid).

2. Switch to qualitative probabilities, where instead of assigning values to events, one just compares the events probabilistically (this one is at least as likely than that one).

In the literature (including stuff I wrote myself!), the qualitative probability approach is treated as more general. But in fact, it’s not, at least not if we assume that the “at least as likely as” relation is transitive and reflexive, i.e., is a partial preorder. For suppose that we have a collection F of events and a partial preorder ⪅ on them. Say that A ≈ B iff A ⪅ B and B ⪅ A. Let V be the set of equivalence classes of events under the relation ≈, and define the partial order ≤ on V by [A]≤[B] iff A ⪅ B, where [A] is the equivalence class of A. (All this makes sense if ⪅ is a partial preorder.) Define P(A)=[A].

And that’s it! You now have a probability function P on F whose values are a partially ordered set V. So, what you do with qualitative comparisons you can do with values. Now that I’ve said it, it’s obvious to me and I’m kicking myself for not noticing it earlier. Perhaps some people in the field have noticed it and found it so obvious that it’s not worth saying.

And rather than thinking of there being a debate between probability functions with values and qualitative probabilities, we can now just stick to the probability function approach, and say that there is a serious debate as to what kind of a structure the values have: are they a real closed field, a totally ordered field, a totally ordered monoid (and if so, does its operation correspond to addition or to multiplication in the classical case), a mere partially ordered set, etc.?

The point here applies in other contexts, such as qualitative utilities, moral value comparisons, etc. Using the apparatus of set theory, we can replace a comparison relation by a value-assignment, which makes it more convenient to apply all the apparatus of ordered algebraic entities of different sorts.

As an application, in a recent post I said that given two very plausible axioms on probability functions, one cannot have a regular rotationally-invariant probability function on the measurable subsets of the circle. Using the above remarks, that point immediately extends to qualitative probabilities that satisfy the following two axioms:

1. If A and B are disjoint, A and C are disjoint, and B and C are equally likely, then A ∪ B and A ∪ C are equally likely, and

2. Ω − A and Ω − B are equally likely iff A and B are equally likely,

with rotational invariance being understood as saying that A is at least as likely as B if and only if ρA is at least as likely as B if and only if A is at least as likely as ρB for every rotation ρ, and with regularity understood as saying that every non-empty event is more likely than the empty event.

Gamifying planking

There is research that some video games can relieve pain. And boredom saps endurance. So the Stealth board product which lets you play games on your smartphone while doing core exercise on a specially shaped balance board seems to be a rather fine idea. But it's too expensive for me. So instead I cut a foam overlay with a phone slot and put it on my home-made balance board (with grippy skateboard tape). And the two free games for the Stealth board work great with this (I haven't bought their premium games).

Trivial Instructable here.

Result: I can plank more time on this than I can endure ordinary planking. Admittedly, the fact that the games involve some motion make the exercise less static. But it's still probably good core exercise.

Things God can't cause

It is widely held by Thomists that anything that a creature can cause can be caused directly by God without any creaturely involvement. Now suppose Sam thinks the following thought:

1. All my thoughts are caused in part by me.

But if God directly causes thought (1) in Sam, then God will directly be causing Sam to think a falsehood (since it will be false that all of Sam’s thoughts are caused in part by Sam). This seems contrary to divine truthfulness.

In an earlier post, I suggest that the Thomist retreat to the principle that for anything a creature can cause, God can directly cause something qualitatively identical to it. But that won't help with this problem, since anything qualitatively identical to (1) but caused directly by God will be false.

I suppose the Thomist can make a similar move here to the one Thomas makes when he says that God can do evil in the sense that he has the power to do it, but not the will. So we would deny that it is possible for God to directly cause anything that a creature can (since God’s goodness rules out God’s causation of some such things), but affirm that he has the power to do so.

Catastrophic decisions

Kirk has come to a planet with two intelligent species in the universe, the Oligons and the Pollakons. There are a million Oligons and a trillion (i.e., million million) Pollakons. They are technologically unsophisticated, live equally happy lives on the same planet, but have no interaction with each other, and the universal translator is currently broken so Kirk can’t communicate with them either. A giant planetoid is about to graze the planet in a way that is certain to wipe out the Pollakons but leave the Oligons, given their different ecological niche, largely unaffected. Kirk can try to redirect the planetoid with his tractor beam. Spock’s accurate calculations give the following probabilities:

• 1 in 1000 chance that the planetoid will now miss the planet and the Oligons and Pollakons will continue to live their happy lives;

• 999 in 1000 chance that the planetoid will wipe out both the Oligons and the Pollakons.

If Kirk doesn’t redirect, expected utility is 10⁶ happy lives (the Oligons). If Kirk does redirect, expected utility is (1/1000)(10¹² + 10⁶)=10⁹ + 10³ happy lives. So, expected utility clearly favors redirecting.

But redirecting just seems wrong. Kirk is nearly certain—99.9%—that redirecting will not help the Pollakons but will wipe out the Oligons.

Perhaps the reason intuition seems to favor not redirecting is that we have a moral bias in favor of non-interference. So let’s turn the story around. Kirk sees the planetoid coming towards the planet. Spock tells him that it has a 1/1000 chance that nothing bad will happen, and a 999/1000 chance that it will wipe out all life on the planet. But Spock also tells him that he can beam the Oligons—but not the Pollakons, who are made of a type of matter incapable of beaming—to the Enterprise. Spock, however, also tells Kirk that beaming the Oligons on board will require the Enterprise to come closer to the planet, which will gravitationally affect the planetoid’s path in such a way that the 1/1000 chance of nothing bad happening will disappear, and the Pollakons will now be certain, and not merely 999/1000 likely, to die.

Things are indeed a bit less clear to me now. I am inclined to think Kirk should rescue the Oligons (this may require Double Effect), but I am worried that I am irrationally neglecting small probabilities. Still, I am inclined to think Kirk should rescue. If that intuition is correct, then even in other-concerning decisions, and even when we have no relevant deontological worries, we should not go with expected utilities.

But now suppose that Kirk over his career will visit a million such planets. Then a policy of non-redirection in the original scenario or of rescue in the modified scenario would be disastrous by the Law of Large Numbers: those 1/1000 events would happen a number of times, and many, many lives will be lost. If we’re talking about long-term policies, then, it seems that Kirk should have a policy of going with expected utilities (barring deontological concerns). But for single-shot decisions, I think it’s different.

This line of thought suggests two things to me:

• maximization of expected utilities in ordinary circumstances has something to do with limit laws like the Law of Large Numbers, and

• we need a moral theory on which we can morally bind ourselves to a policy, in a way that lets the policy override genuine moral concerns that would be decisive absent the policy (cf. this post on promises).

Regularity and rotational invariance

Suppose that we have some sort of (not merely real-valued) probability assignment P to the Lebesgue measurable subsets of the unit circle Ω.

Theorem: Suppose that the probability values are rotationally invariant (P(A)=P(ρA) for any rotation ρ) and satisfy the two axioms:

1. If A and B are disjoint, A and C are disjoint, and P(B)=P(C), then P(A ∪ B)=P(A ∪ C)

2. P(Ω − A)=P(Ω − B) if and only if P(A)=P(B).

Then P(A)=P(∅) for every singleton A.

In other words, we cannot have regularity (non-empty sets having different probability from empty sets) if we have the additivity-type condition (1), the complement condition (2) and rotational invariance.

Proof: Fix an irrational number r and let B be the set of points at angles in degrees r, 2r, 3r, .... Let x₀ be the point at angle 0. Then B and C = B ∪ {x₀} are rotationally equivalent (you get the former from the latter by rotating by r degrees). So, P(B)=P(C). Let A = Ω − C. Then A and B are disjoint as are A and C. Hence, P(A ∪ B)=P(A ∪ C). But A ∪ C = Ω. So, P(A ∪ B)=P(Ω) by axiom 1. But A ∪ B = Ω − {x₀}. So, P({x₀}) = P(∅) by axiom 2. But all singletons are rotationally equivalent so they all have the same measure.

This result is a variant of the results here.

Causation and Thomism

Assume a Thomistic metaphysics, including the primary/secondary causation model from Aquinas. Thus, whenever a created cause has an effect, it has the effect it does only because God, through primary causation, cooperates with the created cause. If God did not cooperate with the created cause, the creature’s secondary causal power would be impotent to produce the effect. On the other hand, God can directly cause something by primary causation without the secondary causes doing anything.

Suppose that I strike a match, but God doesn’t cooperate in the frictional causing of fire. Then the match is struck, and does everything a struck match does, except that no fire results. Now imagine these two scenarios:

1. I strike a match which, in the ordinary way and with God’s cooperation, causes fire.

2. I strike a match, but God does not cooperate with me; however, God miraculously causes a fire just like the one in (1).

These two scenarios are different. So they must differ in something. They cannot differ in God, since that would violate divine simplicity, a core commitment of Thomistic metaphysics. So they must differ on the side of creatures. If so, they differ in the match striking or in the fire (or, more precisely, in the match and in that which is on fire, given a substance-accident ontology), God’s cooperation or lack thereof making the match-striking or the fire different.

Suppose God’s cooperation makes the match-striking different. Then in scenario (1), created reality includes the event of divinely-cooperated-match-striking. This event surely doesn’t need any further divine cooperation, or else we’d have a regress. But no item in created reality is sufficient on its own to produce an effect witout God’s cooperation being added to it on the primary/secondary causation model.

So, it is the fire that must be made different by God’s cooperation. In scenario (1), the fire is caused by the match and God while in (2), it is caused by God alone, and that makes the fire different between the scenarios. I would like to say that the esse of the fire is different in the two cases: in the ordinary case its esse is at least in part being caused by the match with God’s cooperation while in the other case the match doesn’t enter into its esse. But the details don’t matter for this post: what matters is that the fire is different between scenarios (1) and (2).

But this has an unfortunate consequence: If the fire must be different in some metaphysical way in cases (1) and (2), it follows that God cannot directly and independently of creation cause the same effect as the match caused. And this violates the Thomistic principle that whatever a finite cause suffices for can be produced by God directly. God cannot directly produce a fire-caused-by-the-match; that would be a contradiction.

So we have a conflict between a number of Thomistic principles:

3. Divine simplicity

4. Divine omnipotence

5. The primary/secondary causation model

6. God can directly cause anything he can cause in cooperation with a creature.

It seems to me that 3-5 are more central to Thomism than 6. So, I am inclined to reject 6, perhaps replacing it with the weaker principle that for any item x that God can cause in cooperation with a creature, God can cause an item x^* which is qualitatively just like x.

Perhaps I was too quick when I said that (1) and (2) must differ in the match or the fire. Perhaps they differ in something “in between” the match and the fire, a token causal relation. I think this is a problematic solution for two reasons. First, it is central to Aristotelianism that all that exists are substances and their accidents. The token causal relation, if it’s not “in” any creature, would violate this. Second, it seems that the match strike plus this “in between” thingy are now sufficient to produce the fire, or else we can run the above argument with the match strike and the “in between” thingy in place of the match strike. But no mere creature is sufficient to produce an effect without God’s cooperation.

Ataraxia

The stoics, the academic sceptics and the epicureans all to various degrees basically agreed—or at least largely lived as if they agreed—that happiness was ataraxia, imperturbable calm and tranquility. This is a useful and important corrective to our busy work and busy “leisure”. But at the sme time, it’s really a quite empty and negative picture of life’s fulfillment. It’s more like a picture of how to get done with life without too much misery.

Perhaps they had a part of the truth: perhaps what is truly worth having is imperturbably, calmly and tranquilly doing certain things, such as enjoying the companionship of those we love—God above all. But the ataraxia is just a mode of the worthwhile activity rather than the center of it.

Furthermore, perhaps these ancients were extensionally right: for perhaps the only way to have ataraxia is by being with God, since our hearts are restless apart from him. In that case, ataraxia isn’t happiness, or worth pursuing for its own sake, but is a sign of happiness.

Hangboard build

With our climbing gym still closed, I made a hangboard for myself and my son, a quick and inferior clone of the Lyons Edge Hideout. My build instructions are here (with kind permission from Lyons Edge).

Avoiding Dutch Books Despite Inconsistent Credences

Preprint is available here. Just accepted by Synthese.

Does supererogation always deserve praise?

Suppose that Bob spent a month making a birthday cake for Alice that was only slightly better than what was available in the store, and Bob did not enjoy the process at all. One can fill out the case in such a way that what Bob did was permissible. Moreover, it is was more burdensome to him than buying the slightly less good cake would have been, and it was better for Alice, so it looks like the action was supererogatory. Nonetheless, we wouldn’t praise this action: We would say that the action was insufficiently prudent. So, it seems that not every supererogatory action is praiseworthy.

Perhaps the problem is with my understanding of supererogation. If we add the necessary condition for supererogation that the action is on balance better than the relevant alternative, then we can avoid saying that Bob’s action is supererogatory, because it is not better on balance than the alternative. But I would rather avoid adding that a supererogatory action is on balance better than the alternative. For then it becomes mysterious how it can be permissible to do the alternative.

I am inclined to just bite the bullet and deny the supererogation always deserves praise.

Generalizing supererogation

My preferred way of understanding supererogation is that an action is supererogatory provided that it is permissible and more burdensome than some permissible alternative (see here for a defense). This suggests an interesting generalization. Let J denote an individual or a group (perhaps described relative to the agent). Then an action is J-supererogatory provided that it is is permissible and more burdensome for J than some permissible alternative.

Then supererogatory actions are, in the new terminology, agent-supererogatory. On the other hand, we have a new category of actions, others-supererogatory. These actions are permissible but more burdensome to others than some permissible alternative. An action can be both agent-supererogatory and others-supererogatory. For instance, suppose that by sacrificing two arms I can save two people from losing two arms each, but by sacrificing one arm I can save one person from losing one arm. And suppose I have no special duties here, so it is permissible for me to make no sacrifice at all. Then, the action of sacrificing one arm is agent-supererogatory (it is more burdensome than the permissible alternative of no sacrifice) and others-supererogatory (it is less burdensome than sacrificing both arms).

Supererogation and determinism

1. If at most one action is possible for one, that action is not supererogatory.

2. If determinism is true, then there is never more than one action possible for one.

3. So, if any action is supererogatory, determinism is false.

There is controversy over (2), but I don’t want to get into that in this post. What about (1)? Well, the standard story about supererogation is something like this: A supererogatory action is one that is better than, or perhaps more burdensome, that some permissible alternative. In any case, supererogatory actions are defined in contrast to a permissible alternative. But that permissible alternative has got to be possible for one to count as a genuine alternative. For instance, suppose I stay up all night with a sick friend. That’s better than going to sleep. But if there is loud music playing which would make it impossible for me to go to sleep and I am tied up so I can’t go elsewhere, then my staying up all night with the friend is not supererogatory.

Do promises sometimes make otherwise wrong actions permissible?

Consider a variant of my teenage Hitler case. You’re a hospital anesthetist and teenage Hitler is about to have an emergency appendectomy. The only anesthetic you have available is one that requires a neutralizer to take the patient out of anesthesia—without the neutralizer, the patient dies. You know (an oracle told you) that if teenage Hitler survives, he’ll kill millions. And you’re the only person who knows how to apply anesthesia or the neutralizer in this town.

You’re now asked to apply anesthesia. You have two options: apply or refuse. If you refuse, the surgeon will perform the appendectomy without anesthesia, causing excruciating pain to a (still) innocent teenager, who will still go on to kill millions. Nobody benefits from your refusal.

But if you apply anesthesia, you will put yourself in a very awkward moral position. Here is why. Once the surgery is over, standard practice will be to apply the neutralizer. But the Principle of Double Effect (PDE) will forbid you from applying the neutralizer. For applying the neutralizer is an action that has two effects: the good effect of saving teenage Hitler’s life and the evil effect of millions dying. PDE allows you to do actions that have a foreseen evil effect only when the evil effect is not disproportionate to the good effect. But here the evil effect is disproportionate. So, PDE forbids application of the neutralizer. Thus if you know yourself to be a morally upright person, you also know that if you apply the anesthesia, you will later refuse to apply the neutralizer. But surely it is wrong to apply the anesthesia to an innocent teenage while expecting not to apply the neutralizer. For instance, it would be clearly wrong to apply the anesthesia if one were out of neutralizer.

So, it seems you need to refuse to apply anesthesia. But your reasons for the refusal wiil be very odd: you must refuse to apply anesthesia, because it would be morally wrong for you to neutralize the anesthesia, even though everyone is no worse or better off in the scenario where you apply anesthesia and neutralize it than in the scenario where the operation happens without anesthesia. To make the puzzle even sharper, we can suppose that if teenage Hitler has the operation without anesthesia, he will blame you for the pain, and eventually add your ethnic group—which otherwise he would have no prejudice against—to his death lists. So your refusal to apply anesthesia not only causes pain to an innocent teenager but causes many deaths.

The logical structure here is this: If you do A, you will be forbidden from doing B. But you are not permitted to do A if you expect not do B. And some are much better off and no one is worse off if you do both A and B than if you do neither.

Here is a much more moderate case that seems to have a similar structure. Bob credibly threatens to break all of Carl’s house windows unless Alice breaks one of Carl’s windows. It seems that it would be right for Alice to break the window since any reasonable person would choose to have one window broken rather than all of them. But suppose instead Bob threatens to break all of Carl’s windows unless Alice promises to break one of Carl’s windows tomorrow. And Alice knows that by tomorrow Bob will be in jail. Alice knows that if she makes the promise, she would do wrong to keep it, for Carl’s presumed permission of one window being broken to save the other windows would not extend to the pointless window-breaking tomorrow. And one shouldn’t make a promise one is planning not to keep (bracketing extreme cases, which this is not one of). So Alice shouldn’t make the promise. But no one would be worse off if Alice made the promise and kept it.

I wonder if there isn’t a way out of both puzzles, namely to suppose that in some cases a promise makes permissible something that would not otherwise be permissible. Thus, it would normally be wrong to apply the neutralizer to teenage Hitler. But if you promised to do so (e.g., implicitly when you agree to perform your ordinary medical duties at the hospital, or explicitly when you reassured his mom that you’ll bring him out of anesthesia), then it becomes permissible, despite the fact that many would die if you kept the promise. Similarly, if Alice promised Bob to break the window, it could become permissible to do so. Of course, we better not say in general that promises make permissible things that would otherwise be impermissible.

The principle here could be roughly something like that:

1. If it would be permissible for you to now intentionally ensure that a state of affairs F occurs at a later time t, then it is permissible for you to promise to bring about F at t and then to do so if no relevant difference in the circumstances occurs.

Consider how (1) applies to the teenage Hitler and window-breaking cases.

It would be permissible for you to set up a machine that would automatically neutralize Hitler’s anesthesia at the end of the operation, and then to administer anesthesia. Thus, it is now—i.e., prior to your administering the anesthesia—permissible for you to ensure that Hitler’s anesthesia will be neutralized. Hence, by (1) it is permissible for you to promise to neutralize the anesthesia and then to keep the promise, barring some relevant change in the circumstances.

Similarly, it would be permissible for you to throw a rock at Carl’s window from very far away (out in space, say) so that it would only reach the window tomorrow. So, by (1) it is permissible for you to promise to break the window tomorrow and then to keep the promise.

On the other hand, take the case where an evildoer asks you to promise to kill an innocent tomorrow or else she’ll kill ten today, and suppose that tomorrow the evildoer will be in jail and unable to check up on what you did. It would be wrong for you to now intentionally ensure the innocent dies tomorrow, so (1) does not apply and does not give you permission to make and keep the promise. (Some people will think it’s OK to make and break this promise. But no one thinks it’s OK to make and keep this promise.)

Principle (1) seems really ad hoc. But perhaps this impression is reduced when we think of promises as a way of projecting our activity forward in time. Principle (1) basically says that if it would be permissible to project our activity forward in time by making a robot—or by self-hypnosis—then we should be able to accomplish something similar by a promise.

The above is reminiscent of cases where you promise to ignore someone’s releasing you from a promise. For instance, Alice, a staunch promoter of environmental causes, lends Bob a large sum of money, on the condition of Bob making the following promise: Bob will give the money back in ten years, unless Alice’s ideals shift away from environmentalism in which case he will give it to the Sierra Fund, notwithstanding any pleas to the contrary from Alice. The current context—Alice’s requirements at borrowing time—becomes normative at the time for the promise to be kept, notwithstanding some feared changes.

I am far from confident of (1). But it would let one escape the unhappy position of saying that in cases with the above structure one is required to let the worst happen. I expect there are counterexamples to (1), too. But perhaps (1) is true ceteris paribus.

Pluralism in public life

Consider this formulation of the central problem of a pluralist democracy:

1. How to have a democracy where there is a broad plurality of sets of values?

Assuming realism about the correct set of values, this is roughly equivalent to:

2. How to have a democracy where most people are wrong in different ways about the values?

But when we think about (1) and (2), we are led to thinking about the problem in different ways. Formulation (1) leads us to think the problem is with the state, which should somehow accommodate itself to the plurality of values. Formulation (2) points us, however, to the idea that the problem is with the people (including perhaps ourselves) who have the wrong set of values.

My own view is that there is partial but incomplete realism about values. Specifically, there is such a thing as the correct set of values. But there is a legitimate plurality of rankings between the values, though even there not everything goes—some rankings violate human nature. As a result, the problem is both with us, in that most of us have the wrong set of values and have some prioritizations that violate human nature, and with the state which needs to accommodate a legitimate plurality of prioritizations.