My impression is that each family of person-affecting views avoids the Dutch book here.

Here are four families:

(1) Presentism: only people who presently exist matter.

(2) Actualism: only people who will exist (in the actual world) matter.

(3) Necessitarianism: only people who will exist regardless of your choice matter.

(4) Harm-minimisation views (HMV): Minimize harm, where harm is the amount by which a person's welfare falls short of what it could have been.

Presentists won't make trade 2, because Alice doesn't exist yet.

Actualists can permissibly turn down trade 3, because if they turn down trade 3 then Alice will actually exist and her welfare matters.

Necessitarians won't make trade 2, because it's not the case that Alice will exist regardless of their choice.

HMVs won't make trade 1, because Alice is harmed in World 2 but not World 1.

More generally, Arrhenius proves an impossibility result that applies to all possible population ethics (not just person-affecting views), so (if you want consistency) you need to bite at least one of those bullets.

That result (The Impossibility Theorem), as stated in the paper, has some important assumptions not explicitly mentioned in the result itself which are instead made early in the paper and assume away effectively all person-affecting views before the 6 conditions are introduced. The assumptions are completeness, transitivity and the independence of irrelevant alternatives. You could extend the result to include incompleteness, intransitivity, dependence on irrelevant alternatives or being in principle Dutch bookable/money pumpable as alternative "bullets" you could bite on top of the 6 conditions. (Intransitivity, dependence on irrelevant alternatives and maybe incompleteness imply Dutch books/money pumps, so you could just add Dutch books/money pumps and maybe incompleteness.)

Mod note: I've enabled agree-disagree voting on this thread. This is still in the experimental phase, see the first time we did so here. Still very interested in feedback.

Maybe I have the wrong idea about what “person-affecting view” refers to, but I thought a person-affecting view was a non-consequentialist ideology that would not take trade 3, ie it is neutral about moving from no person to happy person but actively dislikes moving from happy person to no person.

When I said that there isn't any adversarial action, I really should have said that you are safe and your learning process is under your control. By default I'm imagining a reflection process under which (a) all of your basic needs are met (e.g. you don't have to worry about starving), (b) you get to veto any particular experience happening to you, (c) you can build tools (or have other people build tools) that help with your reflection, including by building situations where you can have particular experiences, or by creating simulations of yourself that have experiences and can report back, (d) nothing is trying to manipulate or otherwise attack you (unless you specifically asked for the manipulation / attack), whether it is intelligently designed or natural, (e) you don't have any time pressure on finishing the reflection.

To be clear this is pretty stringent -- the current state of affairs where you regularly go around talking to people who try to persuade you of stuff doesn't meet the criteria.

So to restate, your claim is that in the absence of such adversaries, moral reasoning processes will in fact all converge to the same place.

Given conditions of safety and control over the reflection.

It's also not that I think every such process converge to exactly the same place. Rather I'd say that (a) I feel pretty intuitively happy about anything that you get to via such a process, so it seems fine to get any one of them and (b) there is enough convergence that it makes sense to view that as a target which we can approximate or move towards.

Even if we're exposed to wildly different experiences/observations/futures, the only thing that determines whether there's convergence or divergence is whether those experiences contain intelligent adversaries or not.

Part of the reflection process would be to seek out different experiences / observations, so I'm not sure they would be "wildly different".

What precisely about our moral reasoning process make them unlikely to be attacked by "natural" conditions but attackable by an intelligently designed one? [...] Could natural conditions ever play the equivalent of intelligent adversaries?

If they're attacked by natural conditions that violates my requirements too. (I don't think I ever said the adversarial action had to be "intelligently designed" instead of "natural"?)

In this process fundamentally everything that happens to you is meant to be your own choice. It's still possible that you make a mistake, e.g. you send a simulation of yourself to listen to a persuasive argument and then report back, the simulation is persuaded that <bad thing> is great, comes back and persuades you of it as well. (Obviously you've already considered that possibility and taken precautions, but it happens anyway; your precautions weren't sufficient.)  But it at least feels unlikely, e.g. you shouldn't expect to make a mistake (if you did, you should just not do the thing instead).

I don't actually think Dutch books and money pumps are very practically relevant in charitable/career decision-making. To the extent that they are, you should aim to anticipate others attempting to Dutch book or money pump you and model sequences of decisions, just like you should aim to anticipate any other manipulation or exploitation. EDIT: You don't need to commit to views or decision procedures which are in principle not Dutch bookable/money pumpable. Furthermore, "greedy" (as in "greedy algorithm") or short-sighted EV maximization is also suboptimal in general, since you should in general consider what options will be available in the future depending on your decisions.

Also, it's worth mentioning that, in principle, EV maximization with* unbounded utility/social welfare functions can be Dutch booked/money pumped and violate the sure-thing principle, so if such arguments undermine person-affecting views, they also undermine total utilitarianism. Or at least the typical EV-maximizing unbounded versions, but you can apply a bounded squashing function to the sum of utilities before taking expected values, which will then be incompatible with Harsanyi's theorem, one of the main arguments for utilitarianism. Or you can assume, I think unreasonably, fixed bounds to total value, or that only finitely many outcomes from any given choice are possible, (EDIT) or otherwise assign 0 probability to the problematic possibilities.

*Added in an edit.

Trade 3 is removing a happy person, which is usually bad in a person-affecting view, possibly bad enough to not be worth less than $0.99 and thus not be Dutch booked. 

My post The Moral Uncertainty Rabbit Hole, Fully Excavated seems relevant to the discussion here. 

In that post, I describe examples of "reflection environments" that define ideal reasoning conditions (to specify one's "idealized values"). I talk about pitfalls of reflection environments and judgment calls we'd have to make within that environment. (Pitfalls being things that are bad if they happen but could be avoided at least in theory. Judgment calls are things that aren't bad per se but seem to introduce path dependencies that we can't avoid, which may reduce the chance of convergent outcomes.) 

I talk about "reflection strategies," which describe how someone goes about their moral reflection inside a reflection environment. I distinguish between conservative and open-minded reflection strategies. They differ primarily on whether someone has already formed convictions (it's a gradual difference). I describe how open-minded reflection strategies come at some risk of leading to under-defined outcomes. (I argue that this isn't necessarily problem, but it's something people want to be aware of.) 

Here's a section from somewhere in the middle of the post that summarizes some conclusions: 

Conclusion: “One has to actively create oneself”

“Moral reflection” sounds straightforward – naively, one might think that the right path of reflection will somehow reveal itself. However, as we think of the complexities of setting up a suitable reflection environment and how we’d proceed inside it, what it would be like and how many judgment calls we’d have to make, we see that things can get tricky.

Joe Carlsmith summarized it as follows in an excellent post (what Carlsmith calls “idealizing subjectivism” corresponds to what I call “deferring to moral reflection”):

>My current overall take is that especially absent certain strong empirical >assumptions, idealizing subjectivism is ill-suited to the role some hope it can >play: namely, providing a privileged and authoritative (even if subjective) >standard of value. Rather, the version of the view I favor mostly reduces to the >following (mundane) observations:

• If you already value X, it’s possible to make instrumental mistakes relative to X.
• You can choose to treat the outputs of various processes, and the attitudes of various hypothetical beings, as authoritative to different degrees.

>This isn’t necessarily a problem. To me, though, it speaks against treating your >“idealized values” the way a robust meta-ethical realist treats the “true values.” >That is, you cannot forever aim to approximate the self you “would become”; you >must actively create yourself, often in the here and now. Just as the world can’t >tell you what to value, neither can your various hypothetical selves — unless you >choose to let them. Ultimately, it’s on you.

In my words, the difficulty with deferring to moral reflection too much is that the benefits of reflection procedures (having more information and more time to think; having access to augmented selves, etc.) don’t change what it feels like, fundamentally, to contemplate what to value. For all we know, many people would continue to feel apprehensive about doing their moral reasoning “the wrong way” since they’d have to make judgment calls left and right. Plausibly, no “correct answers” would suddenly appear to us. To avoid leaving our views under-defined, we have to – at some point – form convictions by committing to certain principles or ways of reasoning. As Carslmith describes it, one has to – at some point – “actively create oneself.” (The alternative is to accept the possibility that one’s reflection outcome may be under-defined.)

It is possible to delay the moment of “actively creating oneself” to a time within the reflection procedure. (This would correspond to an open-minded reflection strategy; there are strong arguments to keep one’s reflection strategy at least moderately open-minded.) However, note that, in doing so, one “actively creates oneself” as someone who trusts the reflection procedure more than one’s object-level moral intuitions or reasoning principles. This may be true for some people, but it isn’t true for everyone. Alternatively, it could be true for someone in some domains but not others.

Overall, I think Holden's notion of future-proof values is intelligible and holds up to deeper analysis, but I'd imagine that a lot of people underestimate the degree to which it's useful to already form convictions on some ways of reasoning or some components of one's values, to avoid that the reflection outcome becomes under-defined to a degree we might find unsatisfying. 

I kinda suspect no ethics are future-proof in this sense

Which sense do you mean?

I like Holden's description:

I expect some readers will be very motivated by something like "Making ethical decisions that I will later approve of, after I've done more thinking and learning," while others will be more motivated by something like "Making ethical decisions that future generations won't find abhorrent."

Personally I'm thinking more of the former reason than the latter reason. I think "things I'd approve of after more thinking and learning" is reasonably precise as a definition, and seems pretty clearly like a thing that can be approximated.

In practice, I think those with person-affecting views should refuse moves like trade 1 if they "expect" to subsequently make moves like trade 2, because World 1 ≥ World 3*. This would depend on the particulars of the numbers, credences and views involved, though.

EDIT: Lukas discussed and illustrated this earlier here.

*EDIT2: replaced > with ≥.

I definitely think these processes can be attacked. When I say "what I'd approve of after learning and thinking more" I'm imagining that there isn't any adversarial action during the learning and thinking. If I were forcibly exposed to a persuasive sequence of words, or manipulated / tricked into think that some sequence of words informed of benign facts but were in fact selected to hack my mind, that no longer holds.

Suppose that if I take trade 1, I have a p≤100% subjective probability that trade 2 will be available, will definitely take it if it is, and conditional on taking trade 2, a q≤100% subjective probability that trade 3 will be available and will definitely take it if it is. There are two cases:

1. If p=q=100%, then I stick with World 1 and don't make any trade. No Dutch book. (I don't think p=q=100% is reasonable to assume in practice, though.)
2. Otherwise, p<100% or q<100% (or generally my overall probability of eventually taking trade 3 is less than 100%; I don't need to definitely take the trades if they're available). Based on my subjective probabilities, I'm not guaranteed to make both trades 2 and 3, so I'm not guaranteed to go from World 1 to World 1 but poorer. When I do end up in World 1 but poorer, this isn't necessarily so different from the kinds of mundane errors that EU maximizers can make, too, e.g. if they find out that an option they selected was worse than they originally thought and switch to an earlier one at a cost.
   1. A more specific person-affecting approach that handles uncertainty is in Teruji Thomas, 2019. The choices can be taken to be between policy functions for sequential decisions instead of choices between immediate decisions; the results are only sensitive to the distributions over final outcomes, anyway.
   2. Alternatively (or maybe this is a special case of Thomas's work), as long as you guarantee transitivity within each set of possible definite outcomes from your corresponding policy functions (even at the cost of IIA), e.g. by using voting methods like Schulze/beatpath, then you can always avoid (strictly) statewise dominated policies as part of your decision procedure*. This rules out the kinds of Dutch books that guarantee that you're no better off in any state but worse off in some state. I'm not sure whether or not this approach will be guaranteed to avoid (strict) stochastically dominated options under the more plausible extensions of stochastic dominance when IIA is violated, but this will depend on the extension.

*over a finite set of policies to choose from. Say outcome distribution $A$ (strictly) statewise dominates outcome distribution $B$ given the set of alternative outcome distributions $S=\{X_1,\dots ,X_n\}$ (including $A$ and $B$) if

where the inequality is evaluated statewise by fixing a state for $A$, $B$ and all the alternatives in $S$, i.e. $A\left(\omega \right){\ge }_{\left\{X_1\right(\omega ),\dots ,X_n(\omega \left)\right\}}B\left(\omega \right)$ for state $\omega$, with respect to a probability measure $P$ over $\omega$.

Q. In step 2, Alice was definitely going to exist, which is why we paid $1. But then in step 3 Alice was no longer definitely going to exist. If we knew step 3 was going to happen, then we wouldn't think Alice was definitely going to exist, and so we wouldn't pay $1.

If your person-affecting view requires people to definitely exist, taking into account all decision-making, then it is almost certainly going to include only currently existing people. This does avoid the Dutch book but has problems of its own, most notably time inconsistency. For example, perhaps right before a baby is born, it take actions that as a side effect will harm the baby; right after the baby is born, it immediately undoes those actions to prevent the side effects.

Do you mean in the case where we don't know yet for sure if we'll have the option to undo the actions after the baby is born?

If we do know for sure the option will be available, we'll be required to undo them, and the net welfare of those who will definitely exist anyway will be worse if we do the actions and then undo them than not taking them at all, then we wouldn't take the actions that would harm the baby in the first place, because it's worse for those who will definitely exist anyway.

A solution to time inconsistency could be to make commitments ahead of time, which is also a solution for some other decision-theoretic problems, like St. Petersburg lotteries for EU maximization with unbounded utility functions. Or, if we're accepting time inconsistency in some cases, then we should acknowledge that our reasons for it aren't generally decisive, and so not necessarily decisive against time inconsistent person-affecting views in particular.

Maybe this is a little off topic, but while Dutch book arguments are pretty compelling in these cases, I think the strongest and maybe one of the most underrated arguments against intransitive axiologies is Michael Huemer's in "In Defense of Repugnance"

https://philpapers.org/archive/HUEIDO.pdf

Basically he shows that intransitivity is incompatible with the combination of:

If x1 is better than y1 and x2 is better than y2, then x1 and x2 combined is better than y1 and y2 combined

and

If a state of affairs is better than another state of affairs, then it is not also worse than that state of affairs

By giving the example of:

A>B>C>D>A

A+C

>

B+D

>

C+A

My nitpicky analytic professor pointed out that technically this form of the argument only works on axiologies in which cycles of four states exist, not all intransitive axiologies, but it's simple to tweak it to work for any number of states by lining them up in order, and comparing the same state shifted over once and then twice, leading to the even more absurd conclusion that a state of affairs can be both better and worse than itself:

A>B>C>D>E>A

A+B+C+D+E

>

B+C+D+E+A

>

C+D+E+A+B

In a way, I think this result is even more troubling than the dutch book, Because it prevents you from ranking worlds even relative to a single other world in a way that isn't sensitive to just the way the same world is described.