I am a generalist quantitative researcher. I am open to volunteering and paid work. I welcome suggestions for posts. You can give me feedback here (anonymously or not).
Vasco Grilođ¸
Karma: 11,724
ConÂsciousÂness doesnât do that
Hi Cynthia and Wladimir. Nice post.
The user inputs a target taxon. The tool then determines, where necessary, two related but distinct scopes: one for the sentience gate and one for the affective-capacity analysis.
You may be interested in the article âEthics Without Sentience: Facing Up to the Probable Insignificance of Phenomenal Consciousnessâ by François Kammerer. Here is a summary. Relatedly, you may like this and this very short posts by Keith Frankish. I agree with Keith that phenomenal consciousness does not exist. In any case, even if it exists, I agree with François it is not significant. Phenomenal consciousness as traditionally defined is not falsifiable (or, to be precise, it is traditionally defined such that one can only know about their own consciousness at the moment). In practice, one always has to come up with empirical proxies for it, but I feel these are largely arbitrary if it is not falsifiable. So I believe it would be better to focus just on what animals can do (as in your affective-capacity analysis), and not on assessing phenomenal sentience.
When I click on a given section of a post on the left pane, the URL shown at the top is still that of the post. It used to be the URL of the section. However, I can still link to a section by opening it in a new tab.
I wonder if the power required by brains is proportional to the number of neurons across very different species. It seems to be so among mammals. From Herculano-Houzel (2011):
Based on glucose and oxygen metabolic rates in awake animals and their recently determined numbers of neurons, here I show that, contrary to the expected, the estimated glucose use per neuron is remarkably constant, varying only by 40% across the six species of rodents and primates (including humans).
Hi Agnes. Thanks for the update.
We tested demand in multiple ways. Apart from running user interviews, we ran a survey on the board asking what people were looking for (now with 800+ responses), and added full-time roles to the role-type filter (before we had any full-time listings), to see whether people would look for them organically. Full-time was the most mentioned role type in the survey and the most used filter. It also turned out 48% of the visitors to the board werenât using other popular boards to find EA roles (such as 80,000 Hours or Probably Good).
Have you considered letting visitors to the EA Opportunities Board know about the boards from 80,000 Hours and Probably Good? To which extent did people who knew about these boards still wanted full time roles in the EA Opportunities Board? If to a significant extent, why?
The missÂing half of AI fuÂturÂism debates
Hi Abraham and Mal. Nice post.
âWelfare per yearâ = âpopulation (animal-years per year)â*âwelfare per animal-yearâ = âdeaths per yearâ*âwelfare per deathâ. It is unclear to me whether âwelfare per animal-yearâ varies more or less than âwelfare per deathâ. So it is also unclear to me whether population is a better or worse proxy for welfare than deaths per year as long as both proxies cover the same life stages.
Using more appropriate units (such as total annual deaths or days of experience) reveals that highly r-selected animals might dominate moral calculus to a greater degree than a naive estimate might suggest.
On the other hand, more r-selected animals will tend to be more abundant, and have a lower moral weight? I agree with the above because I think differences in moral weight may be very small, but I also believe they may be very large.
Standing population size is usually not a reliable proxy for comparing the likely scale of harm between different highly numerous species, due to significant differences in population throughput and life-history.
âadult population sizeâ?
For example, for identical stable populations of ants and aphids, we might expect there to be over 200x as many aphid deaths, and over 7x as many aphid days of experience.
âstable adult populationsâ?
One could argue that 1 and 2 remain incomparable and that I have no reason to favor 2 over 1.
If the absolute value of the expected cost-effectiveness of 1 was astronomically larger than that of intervention 2, I think comparing the interventions would be similar to comparing intervention 1 with one with cost-effectiveness of 0 (burning money). It is very unclear whether the expected cost-effectiveness of 1 is positive or negative. So it would be close to arbitrary which intervention has the highest expected cost-effectiveness.
Another thing, assuming there is no 2-like intervention, is that the criterion to pick could be something other than âact straightforwardly as if you were endorsing SHARPâ. It could instead be some (other) form of bracketing.
Bracketing departs from impartiality, and I find this very unappealing.
I think cost-effectiveness accounting for effects on all organisms spans many orders of magnitude (OOMs) due to large uncertainty about how to compare welfare across species. So I expect something like a loguniform or lognormal distributions would be more appropriate. Ideally, one would model the inputs as distributions instead of assuming a distribution for the cost-effectiveness.
In the context of assessing interventions with very uncertain cost-effectiveness (in my view, practically any context), in which sense would it matter a lot whether one uses sharp or unsharp probabilities? With sharp probabilities, it would be close to arbitrary which interventions should be supported. With unsharp probabilities, it would be indeterminate which interventions should be supported, but one would still end up supporting something based on some criteria. From my perspective, it is unclear which one would lead to greater impact. Given the large uncertainty, it is not even clear to me whether any of the approaches would outperform picking interventions randomly.
So I believe the priority would be decreasing uncertainty. I expect this can be most cost-effectively achieved via research (on comparing welfare across species). However, supporting the interventions under comparison also indirectly decreases uncertainty to some extent. Funders who do not want to fund research directly decreasing the uncertainty might be open to funding research aiming to figure out how to decrease uncertainty via supporting existing interventions. They could then update to some extent towards funding interventions which look better in terms of decreasing uncertainty. I guess ones contributing to moral circle expansion help attracts resources to target more neglected animals, including to study how their welfare compares with that of other less neglected animals.
Right. I think using unsharp probabilities, and expected values is fine to highlight it is unclear which of the interventions being compared has the highest expected cost-effectiveness. However, I do not see what is the advantage of this relative to just getting wide distributions for the cost-effectiveness, and showing these overlap a lot, which would be a sign that decreasing their uncertaity may have a higher expected cost-effectiveness than picking the intervention with the highest expected cost-effectiveness. One can analyse value of information (VOI) using perfectly sharp credences.
Hi Jim. You meant âthe authorâs non-endorsement of Uniquenessâ? You said âthe otherâsâ.
Adam (the author) says âIt is compatible with sharp that for certain batches of evidence, there is more than one probability function it is rationally permissible to have on the basis of that evidenceâ. However, Adam concedes in footnote 11 it may be difficult to accept sharpness, and deny uniqueness.
There may well be difficulties with accepting sharp while denying Uniqueness. But I will not press any such difficulties here. Thanks to Susanna Rinard and John Collins for pressing me on this point.
I endorse sharpness and uniqueness. As far as I can tell, the issues of unsharp probabilities would apply in the same way to non-unique probabilities. Why would this not be the case?
At the same time, I believe there are many reasonable probabilities. Humans have a limited memory, and therefore cannot represent infinitely precise /â sharp probabilities. One would need infinite resources to represent an infinitely precise probability. If I say a given event has a chance of 10 %, I mean the sharp unique probability of a rational being with the evidence I have access to is close to 10 % (how close would depend on the context). I do not mean it is exactly 10 %. So I would convey practically the same information (just in an unnecessarily precise way) if I said that same event has a chance of 10.001 %. Does this make sense?
EDIT: my bad, the problem is that if you donât use commitments, you could be worse off. Using backward induction in the Sally argument actually works fine, doesnât leave you (or Sally) worse off and doesnât require any commitment.
I followed up here.
St Petersburg doesnât require any state to have infinite value. Its value is (canonically) 2^n with probability 1/â2^n for each n at least 1. Always finite actual value, but infinite expected value.
The expected value of the St. Petersburg lottery is 1 + 1 + ⌠= +inf. It involves finite terms, but infinitely many terms. I meant to relate f(x) = x in my comment to the expected value of the St. Petersburg lottery. If this involved an arbitrarily large number of terms, its expected value would be arbitrarily large, but not infinite.
Very interesting. Thanks. Relatedly, you may be interested in this comment.
Here is a video I found useful that explains how to use backward induction. Below is Claudeâs reply to your comment after some iteration between us.
Thanks Michael â the backward-induction framing is the strongest version of the reply, and I want to grant what it gets right before saying where I think itâs still exposed.
It does defuse three things at once. It needs no commitment (you predict the future Bet B choice and fold it back, rather than binding yourself), it needs no complete ordering (it runs on statewise dominance, so the Bet B node can stay genuinely unsharp), and it isnât ad hoc (backward induction is the standard discipline for sequential choice). So this isnât PLAN in disguise. Fair enough.
But I think the argument turns on a step that quietly does more than âjust backward induction.â Here is the full tree, with payoffs written as (if H /â if notâH). Bet A pays â10/â+15 and Bet B pays +15/ââ10, so the four leaves are BOTH +5/â+5, A-only â10/â+15, B-only +15/ââ10, and NEITHER 0/â0:
Notice both Bet B nodes are under-determined: at each, neither action statewise-dominates the other (BOTH vs A-only cross; B-only vs NEITHER cross). That is exactly the optionality unsharpness is meant to preserve, so dominance-pruning removes nothing at a Bet B node. To get a verdict on Bet A, backward induction has to fold each Bet B node back into a single continuation value â and the value of the reject-A branch depends entirely on which of its two (equally maximal) leaves you assume youâll pick.
Crucially, the accept-A node is also under-determined â it can land on BOTH or on A-only. So to compare the two root actions I have to fix a policy over both identical Bet B nodes. There are only three consistent options:
The only statewise-dominance relation anywhere in the tree is BOTH âť NEITHER. In particular A-only vs NEITHER crosses â A-only is worse than NEITHER in the H-state (â10 < 0) â so accepting A does not statewise-dominate rejecting A. Under either consistent policy (always-accept or always-reject), both root actions stay admissible and thereâs no dominance reason to prefer accepting A. And note that under âalways accept B,â NEITHER is never reached on either branch, so thereâs nothing for accepting-A to protect against in the first place.
The recommendation to accept A appears only under the third policy â the one that accepts B after accept-A but rejects B after reject-A. That is what produces the BOTH-vs-NEITHER pairing that makes accepting A look dominant. But that policy isnât backward induction resolving each node on its merits; itâs a rule that makes your Bet B choice depend on whether Bet A preceded it, handing down different verdicts at two Bet B nodes that (for a money-only agent) are identical in every respect she cares about. That is precisely the SEQUENCE/âPLAN pattern Elgaâs Sally case is built to reject.
Put differently: the recommendation to accept A materialises only when you assume youâll reject B specifically on the reject-A branch â i.e. you distrust your future self on one branch but not the other. That asymmetric self-distrust is either the sophisticated-chooser reading (treat your own future permitted choice as a hazard to steer around) or the differential treatment of identical nodes. Both are exactly the concessions at issue: if youâre rationally required to prevent your future self from exercising reject-B, then reject-B was never really optional â which is just SHARPâs verdict reached the long way.
So a sharper version of my earlier question: your derivation of âaccept Aâ resolves the accept-A continuation to BOTH and the reject-A continuation to NEITHER. What consistent policy over the two identical Bet B nodes yields that pair? If âalways accept B,â reject-A gives B-only and the dominance is gone. If âalways reject B,â accept-A gives A-only and the dominance is gone. The only policy that yields it treats the two Bet B nodes differently â which is the thing an imprecise theorist owes an account of, and which Sally says you canât have.
(One aside on âyouâd use backward induction even with sharp probabilities, or be worse offâ: agreed, but with sharp credences backward induction never has to override a nodeâs verdict â it agrees with local EV-maximisation, and the cases where skipping it hurts are cases of myopia, not override. This is the unique setting where the rule must reverse a choice the agentâs own decision rule calls permissible. That asymmetry is the tell.)
Hi Anthony. Readers of this post may be interested in this summary and discussion in the comments of Adam Elgaâs article Subjective Probabilities should be Sharp. I very much agree subjective probabilities should be sharp. So I am not concerned about the unawareness argument for âno impartial altruistic justification for preferring any action over anotherâ, which relies on unsharp probabilities.
Hi Simon. Below is what Claude has to say about that.
Hi Simon. I think youâve actually put your finger on the load-bearing feature rather than missed something â but the tension youâre sensing resolves once you separate two things that âfull disclosureâ runs together in your reading: what the agent knows, and when she chooses.
Full disclosure only fixes the first. At the A-node she knows the whole tree: that B will follow, the payoffs, and that her credence in H wonât move. What it does not do is collapse the two choices into one simultaneous package-choice. She still acts twice, at two separate moments â accept/âreject A, and then, after thatâs settled, accept/âreject B. Foreknowledge isnât simultaneity. So the sequential structure survives full disclosure intact; the agent is fully informed and still makes two timed decisions.
That distinction is exactly why your âjust interpret it as: take both, get $5, so itâs irrational not toâ doesnât invalidate the setup â and hereâs the part that I think will unstick you. That reasoning isnât a competitor to Elgaâs argument; itâs Elgaâs own premise. The paperâs central claim is precisely that a rational agent âwill accept at least one of the betsâ because rejecting both is dominated and she can see this in advance. He is not disagreeing that reject-both is irrational. Heâs asserting it. Your intuition and his premise are the same sentence.
So the question the paper is asking is one notch more subtle than the one youâre answering. Itâs not âis it irrational to reject both?â (everyone says yes). Itâs: âwhat account of how unsharp credences guide action actually delivers that verdict, given that the unsharp agentâs rule makes each bet, taken on its own, merely optional?â With an interval straddling 60%, rejecting A is permitted at the A-node; with the interval straddling 40%, rejecting B is permitted at the B-node. A rule that just evaluates each bet locally therefore licenses reject-both â the two âoptionalâs compose into the dominated outcome, foreknowledge notwithstanding. The challenge is to find a rule that blocks that without wrecking the optionality elsewhere.
Now to your direct question â is your move PLAN or SEQUENCE? Once you try to turn âtake both, itâs $5â from an observation into a decision rule the agent runs, you land in the global-rules family, and closest to SEQUENCE (equivalently, the âtreat it as one choice among {A, B, BOTH, NEITHER} and eliminate the dominated NEITHERâ reframe that Evan proposed in the other thread [here]). That rule does give the right verdict here â Elga grants that. His objection is that as a rule it fails the Sally test: it has to call âreject Bâ impermissible when A-was-just-rejected but permissible when B is offered alone, even though a money-only agent faces identical money-consequences at the B-node in both cases. So your reasoning isnât a fourth escape hatch; itâs a restatement of what a global rule has to deliver, and Elgaâs argument is aimed precisely at whether any such rule survives.
On your suspicion that full disclosure âmust be weaker than Iâm interpretingâ â Iâd say the opposite. Itâs exactly as strong as youâre reading it, and that strength is the point. Full disclosure, plus no-belief-change, plus linear-in-dollars, is Elga removing every excuse the unsharp theorist could offer for reject-both: she wasnât surprised, she didnât learn anything mid-sequence that shifted her credence, and she has no non-monetary reasons. With all the confounders stripped out, any residual permission to reject both traces to the unsharp decision rule alone â which is the whole rhetorical purpose of piling on those stipulations.
One last thing that I think will make the sequential structure feel less suspicious: Elga needs it to be sequential, and this is why he canât just let it be a simultaneous package. If the offer were genuinely one simultaneous choice (âaccept both /â reject both /â mixâ), the puzzle evaporates â even a maximally permissive rule picks BOTH over NEITHER by straight dominance, and the unsharp theorist wins for free. The problem only has teeth in the sequential version, because thatâs the only structure where a local rule can manufacture reject-both out of two individually-permitted rejections. So the sequential framing and full disclosure arenât in tension; theyâre doing complementary jobs â disclosure kills the âshe didnât see it comingâ defense, sequentiality is what generates the difficulty in the first place.
Below is how Claude thinks Adam (the author of the article) would object to your comments. The objections make sense to me. Any reactions?
1. âWhat if I do care about the differences?â
Michaelâs most direct hit: Elgaâs Sally argument needs the two B-situations to be identical in everything she cares about, and Michael asks why the agent canât just care about whether sheâs about to complete a dominated sequence â âwhy canât the fact that sheâd pick a dominated sequence or regret it if she rejects both bets matter to her after rejecting bet A?â
Elga has a ready answer, and itâs the one he actually gives in the paper against the parallel âbut rejecting B would break her planâ rejoinder. It splits into a dilemma:
Either this caring is a genuine, independent source of value for Sally â in which case the case has been changed, not answered. Elgaâs Sally is stipulated to care only about money, with reconsideration costless. If you smuggle in a taste for sequence-completion or an aversion to regret, youâre no longer discussing Elgaâs agent; youâre conceding that a purely money-motivated unsharp agent is stuck, and rescuing a different agent who has been given an extra terminal value precisely engineered to patch the hole. Thatâs ad hoc: the value exists only to deliver the verdict UNSHARP needs.
Or the caring is not an independent value but just tracks âthis would be irrationalâ â in which case itâs viciously circular. âI disprefer rejecting B because rejecting B here is irrationalâ cannot be what makes it irrational; the account owes us a prior reason, and this isnât one. Elgaâs âDonât break plans!â-is-like-âDonât break mirrors!â point applies verbatim: either breaking the sequence is independently costly (then say so, and itâs a different case) or it isnât (then âavoid completing dominated sequencesâ is a bare, unmotivated constraint dressed up as a preference).
The regret variant is especially weak. Regret is backward-looking; at the B-node the money consequences of accept-B and reject-B are fixed and identical across the two situations. If anticipated regret genuinely moves her, itâs doing so as a real (dis)utility â back to horn one, the case is changed. Vascoâs reply on the forum (âit is very counterintuitive that this could matter for Sally for reasons that donât have to do with moneyâ) is exactly Elgaâs point, just stated flatly.
2. Michaelâs âtreat them fairlyâ /â Parfitâs-hitchhiker parity argument
This is Michaelâs best move, and itâs really DiGiovanniâs commitment point [made here] sharpened into a parity charge: there are cases everyone agrees call for binding commitments youâll later be inclined to break â Parfitâs hitchhiker, St. Petersburg with unbounded utility â so the same âcommit and rule out the bad branchâ solution should be available to the unsharp agent, if youâre treating her fairly. And he uses this to answer Vascoâs âbut unsharp probabilities are supposed to allow rejecting Aâ: âThey donât have to in every case. If it were A in isolation, both would be permissible. But thatâs not the case presented to us.â
Elga would grant the parity and then deny it helps â for two reasons.
First, notice what Michael has conceded. He now says the unsharp agent is required to accept A (to zero out the chance of the dominated branch). But that is Elgaâs whole thesis about this case: rationality forces a determinate verdict at the A-node. The disagreement was never âcan she avoid NEITHER?â â of course she can. Itâs whether the unsharp credence leaves A genuinely optional. Michael answers âno, not here,â which means the interval straddling 60% is not translating into optionality on A. So the imprecision is doing no work at the node where it was supposed to; the commitment (or the statewise argument, see below) is doing all of it. Thatâs confirmation of Elgaâs challenge â âhow do unsharp credences constrain action?â â with the answer âthey donât; something bolted on top does.â
Second, the Parfitâs-hitchhiker analogy cuts the wrong way for him. In the hitchhiker case the commitment is valuable because the two situations genuinely differ in a consequence the agent cares about: keep-the-commitment vs break-it have different payoffs (you live vs you die, or the predictorâs reading changes your prospects). Thatâs exactly what legitimizes binding there. In Sallyâs case Elga has stipulated the two B-situations donât differ in any consequence she cares about. So the disanalogy is precisely the feature that makes hitchhiker-style commitment rational: where binding pays, it pays because of a real downstream difference; strip that difference out (as Sallyâs stipulation does) and the rationale for binding evaporates. Michael can restore the rationale only by putting a real difference back in â which is move 1â˛s first horn again, changing the case.
Vascoâs exchange on the hitchhiker actually pins this down: he points out that if you just âcommit as much as possible,â your chance of survival tracks your commitment probability and thereâs no residual puzzle. Michaelâs reply â âthe same solution is available to the unsharp agent if you treat them fairlyâ â is true but double-edged: yes, the resolute solution is available, and invoking it is the concession that local unsharp verdicts had to be overridden.
3. The statewise /â maximality argument for accepting A
Michaelâs most technical contribution (in the top comment) is a way for the unsharp agent to derive âaccept A firstâ without any of NARROW/âPLAN/âSEQUENCE: comparing âaccept A nowâ (call it 1) against âreject A and hope to accept Bâ (2), he says 1 statewise-beats 2 with some probability and theyâre incomparable otherwise â so under maximality 1 is permissible and heâll take it, killing the dominated branch.
Elgaâs objection: look at whatâs actually being compared. Option 2 as Michael frames it is âreject A and if I canât guarantee Iâll accept B, risk the dominated sequence.â To get 1 to dominate 2, he has to treat 2 as carrying a live risk of ending in NEITHER â i.e. he has to already be modeling his own future B-node choice as possibly landing on reject-B. But thatâs the entire question. If the agent could guarantee sheâll accept B after rejecting A (which is just the commitment), then 2 = B-only, which does not dominate 1 = A-only (theyâre incomparable, as their EVs cross at 60%), and the argument for being required to accept A collapses. So the statewise argument works only on the assumption that she cannot bind her future self â in which case Elga simply agrees the sequence is a problem and asks what makes each local rejection rational â or it works by importing the commitment, in which case the imprecise credence is again idle and weâre at move 2â˛s concession [see here]. Either way it doesnât vindicate UNSHARP; it either restates the problem or resolves it by non-credal means.
Thereâs also a subtler point. Maximality, applied node-by-node, is precisely the permissive rule Elga says is too permissive: at the B-node in isolation it licenses reject-B. Michaelâs statewise argument applies maximality to the ex-ante policy comparison instead. Switching the object of maximization from acts to policies is, once more, the SEQUENCE/âPLAN move â so Elga files it there and runs Sally. Michaelâs is the most resourceful version because heâs derived the ex-ante verdict from a dominance relation rather than asserting a plan-norm, but the structural commitment (evaluate policies, not nodes) is identical, and itâs that commitment Sally targets.
4. The âarbitrary precisionâ tu quoque
Michaelâs jab â isnât requiring sharpness âany worse than picking numbers to ensure precision for no better reason than that they occurred to youâ? â is a real objection to SHARP, but Elga would note itâs an objection to the plausibility/âmotivation of sharpness, not to the bet argument. And SHARP has a specific shield here: recall it explicitly does not entail Uniqueness. Elga isnât claiming the evidence picks out one number 45.000%; he allows a range of sharp functions to be permissible responses to the toothpaste evidence. So âyouâre forcing a spuriously exact numberâ misfires â SHARP permits you to adopt any of many precise credences; it just denies that your state can itself be spread out. The charge of false precision is aimed at Uniqueness, which Elga has already disowned. What SHARP does insist is that whatever you land on functions as a sharp probability for the purpose of guiding action â and the bet argument is what supports that, independently of how you chose the number.
The bottom line on Michael
Michael is the only one of the three [Anthony, Evans, and you] who attacks the load-bearing premise directly (âwhat if she cares about the difference?â) rather than trying to route around it, and heâs right that Elgaâs argument stands or falls on the stipulation that the two situations are identical in all respects the agent values. But Elgaâs reply is stable: every way of making the difference âmatterâ either (i) reintroduces a genuine downstream (dis)utility â which changes Sallyâs case and concedes that the money-only unsharp agent is stuck â or (ii) makes the mattering parasitic on âit would be irrational,â which is circular. The Parfitâs-hitchhiker parity and the statewise argument both turn out to require the commitment capacity, and invoking it is precisely the admission Elga wants: that unsharp credences, left to constrain action on their own, deliver the wrong verdict and must be overridden by a resolute policy that behaves like a determinate disposition.
So against all three of your interlocutors the dialectic funnels to the same joint: is a rational ideal agent to be assessed choice-by-choice (Elga) or entitled to bind herself and be assessed over policies (DiGiovanniâs commitment, Evanâs four-option reframe, Michaelâs statewise/âparity argument)? Michael states the crux most honestly â heâll happily say the unsharp agent is required to accept A here â and that very concession is what Elga reads as victory: the imprecision has stopped doing the one thing it was introduced to do.
I see. Thanks for clarifying. Below is how Claude thinks Adam (the author of the article) would object to your comments. The objections make sense to me. Any reactions?
The unifying objection: the four-option reframe is one of the three rules
Evanâs central claim is that he can dissolve the puzzle without NARROW, PLAN, or SEQUENCE: treat the situation not as two decisions (A yes/âno, B yes/âno) but as one choice among four policies â {A-only, B-only, BOTH, NEITHER} â notice BOTH statewise-dominates NEITHER, delete NEITHER, and youâre done. He stresses âI didnât even consider the probability of H.â
Elgaâs first reply is that this is exactly SEQUENCE (or PLAN) wearing plain clothes â and Evan concedes it in his own EDIT (âI think this is close in effect to SEQUENCEâ). Evaluating the pair of choices as a single ex-ante object over sequences is the defining move of the global rules. So âI donât need any of the threeâ is false: heâs using the third. And that matters, because Sally is aimed precisely here. Take Evanâs B-only policy: it requires rejecting A and then accepting B. Compare the agent at the B-node in two situations â one where she reached it by rejecting A, one where B is offered alone. For a money-only agent these are identical in everything she cares about, yet the reframe must call rejecting-B impermissible in the first (it would complete NEITHER) and permissible in the second. That is the SEQUENCE verdict, and it fails for the SEQUENCE reason.
Why âconsider them simultaneouslyâ doesnât reach the actual problem
Evanâs sports example â decline each of the Snofuls/âFleertis bets in isolation, take both together for a sure profit â leans on âwhen we consider our options simultaneously, that changes the calculus.â Elgaâs rejoinder: in his setup the bets are not simultaneous. You settle A, and only then face B. So the live question is what binds you at the B-node, where A is already done and the only comparison is accept-B (+15/ââ10) versus reject-B (0). With an interval straddling 40%, maximality rules both permissible. The ex-ante fact âBOTH dominates NEITHERâ is true but does not, by itself, reach into the B-node and make accepting B required there. Supplying that reach is the whole job of PLAN/âSEQUENCE â which is why Evan canât actually skip them.
And the boast âI didnât even need to consider P(H)â is the tell, not the triumph. Dominance eliminates NEITHER for any credence â a sharp agent excludes it too. So the four-option elimination is entirely neutral between SHARP and UNSHARP; it was never the point in dispute. The dispute is about the sequential assembly of a dominated outcome from two individually-licensed choices, and the reframe simply doesnât engage it.
The EDIT smuggles in comparability â i.e. sharpness
Evan tries to close the âwhat if you plan B, reject A, then reject B?â gap thus: âa rational actor does not change their mind without new information. They would only choose B if they believe B > BOTH > NEITHER. Any rational actor who believes B > NEITHER would end up betting B.â
This quietly assumes a complete ordering over the options â exactly what UNSHARP denies. B-only beats BOTH only when P(H) > 60%; with the interval [10%, 80%], B-only and BOTH are incomparable under maximality, as are A-only and BOTH. So âthey would only choose B if B > BOTHâ presupposes the agent can rank options the way a sharp credence lets her. Grant that comparability and of course she never lands on a dominated outcome â but youâve then imported enough structure that she behaves like a sharp agent, which is Elgaâs strict-rules horn: you buy the right behavior only by reintroducing precision and thereby forfeiting the motivation for going unsharp in the first place.
âRational actors with less information make worse decisionsâ gives the game away
Evan concedes that without foreknowledge an UNSHARP agent can reject A as optional, reject B as optional, land on NEITHER, and shrug it off as an information deficit. Two problems. First, Elgaâs case stipulates full foreknowledge, so the no-foreknowledge scenario isnât the one under discussion. Second, and more damaging, the diagnosis âless informationâ is wrong. A sharp agent â even with a diffuse-but-precise prior, and even with no foreknowledge â never rejects both, because her node-by-node expected-value verdicts are automatically time-coherent (reject A only if P(H) > 60%, accept B only if P(H) > 40%, and these canât jointly fail). The unsharp agentâs node verdicts are not automatically coherent: both nodes say âoptional,â which is what lets her assemble NEITHER. So the pathology is produced by the unsharpness, not by any information gap. Evanâs concession thus admits precisely the foreseeable-domination Elga is prosecuting, and mislabels its source.
The portfolio point isnât an argument for UNSHARP
Vasco already made the core objection and Evan half-conceded it: diversification falls straight out of sharp EV reasoning with diminishing marginal returns and cross-correlations. Elga would add the sharper version: where the portfolio reasoning gives sensible verdicts (âthis combination statewise-beats doing nothingâ), itâs dominance reasoning a sharp agent honors equally; where it gives distinctively unsharp verdicts, it does so by licensing inaction â declining each option in isolation â which is just the reject-both pathology relocated to altruistic choice. (This is the âclueless agent whose intervals stay wide because it never actsâ failure mode, which is live in your own work.)
âCan vs. shouldâ is not a dodge â itâs Elgaâs exact target
Evanâs sign-off â âwhether we should have unsharp probabilities is beside the point; my argument is about whether we can have them without sacrificing rationality, and I believe we canâ â doesnât sidestep Elga. UNSHARP just is the âcanâ claim: it is consistent with perfect rationality to be unsharp. SHARP denies that. So Evan is engaging the thesis head-on, and Elgaâs reply is that the âcanâ fails for the reasons above: every route Evan takes either collapses into SEQUENCE (Sally sinks it) or into sharp-style comparability (motivation lost).
The honest crux
Where Evan has a real point â shared with DiGiovanni and Michael St Jules â is the suspicion that node-by-node âlocalâ evaluation is the wrong model, and that a look-ahead agent who plans the whole tree does fine with wide intervals. Elgaâs whole case does assume that a theory of rational credence must deliver correct verdicts at each actual choice node, not merely over ex-ante policies. Evan is, in effect, denying that assumption. But he hasnât defeated Sally independently; heâs relocated to ex-ante policy choice, which Elga classifies as SEQUENCE/âPLAN and which Evan himself admits is âclose in effect to SEQUENCE.â So the disagreement bottoms out exactly where it did in the DiGiovanni thread [this one]: whether an idealized agent is entitled to bind her future choices (resolute/âsophisticated look-ahead), or whether rationality must already be satisfiable choice-by-choice. Elga bets on the latter; Evan (like DiGiovanni) needs the former â and that is the genuine open question, not something Evanâs four-option reframe settles.
Funny, and relatable.
I would prefer draft comments I deleted not to show up in my private homepage.