âone person stops eating chickensâ to âfuture chicken production is lower in expectationâ we donât currently have any idea what that number is (Iâve looked into this somewhat carefully)
Canât we make informed estimates, even if they have wide ranges? We multiply the demand shift by Ï”SÏ”SâÏ”D (based on equilibrium displacement models, or this), with long-run elasticity estimates from the literature.
(FWIW, Iâm also sympathetic to diet change being net negative in the near term, mostly because of the impacts on wild invertebrates and maybe fish. So I mostly focus on welfare.)
Iâm a professor of economics, but thanks for the link explaining elasticity :)
The answer is no, we canât just do that, since those approaches assume nontrivial changes (and/âor they assume everything is continuous, which the real world isnât). One plausible simple model of supermarket (or restaurant) purchasing behavior is that when observed demand goes above/âbelow a certain threshold relative to predicted demand, they buy more/âless of the input next cycle. From an individual point of view, the expected aggregate demand of other agents in any time period will be a Gaussian distribution (by the law of large numbers), and the threshold will be away from the mean (doesnât make sense to update every time), which implies that oneâs probability of being the marginal buyer at the threshold declines exponentially (not linearly, as it would be for macro-level shifts and as you are implicitly assuming). From the ACE link: âwe can approximate the supply and demand curves in this region by straight linesââno, you canât do that (for individual behavior) without substantive additional assumptions or a lot of legwork into how these decisions actually get made.
In any case I have no idea if thatâs the right model, because I havenât studied supermarket supply chain management. As far as I can tell (but Iâd love to see this somewhere), nobody in either the econ lit or animal welfare lit has tried to do this at the level required to make what I would consider an informed estimate; weâre not just talking about a factor of 2 or 3 here. That knowledge gap doesnât seem to stop the latter group from making very strong claims; they mostly donât even seem to understand or acknowledge the high uncertainty and strong assumptions.
This sounds like Budolfsonâs buffer model. Have you seen the response by McMullen and Halteman? They describe supply chains and management practices in the section âEfficient Responsive Supply Chains and Causal Efficacyâ.
I agree that itâs probably true most people donât know the right reasons to believe that their individual purchase decisions make much difference on average, because most people know basically nothing about supply chain management.
I had seen some of this, but not the specific paper (ungated) by McMullen & Haltemanâthanks!
First of all note that the two sources you cite directly contradict one another: the first-hand anecdotal account says there is essentially no meat waste even in very small groceries, while M&H (p.12) say there is a modest constant unavoidable waste that is in fact higher in smaller /â local stores than for big outfits. Indeed M&H are internally inconsistent: they say that the market is highly competitive (although they only give a very incomplete reference for this on p.14, which I couldnât find any trace of; my googling found this source suggesting a net profit margin for farming/âagriculture of 5.7%, which is middlingâbetter than aerospace/âdefense or healthcare), but then they also state (p.23) that larger firms have up to 60% lower costs than smaller onesâso how do the latter survive if the industry is so competitive? All of these are bad signs right off the bat.
Second note that none of these sources actually do any data analysis or try to examine original data about the markets or supply chains; they are armchair papers. My whole point is that depending on which of several reasonable assumptions one makes, different conclusions will be drawn. The only way to adjudicate this is to actually figure out whatâs going on in the real world, and neither of these sources attempts to do that. Hint: neither of them gives an empirically-derived concrete estimate for individual-level elasticity.
Third (to finally answer your question!), no my hypothetical model is not the same as the way they are using the term âbufferâ (which seems to be more about maintaining a minimum level of excess in the system; mine is simply about the optimal tradeoff between stockouts vs excess/âwaste). For instance M&H say (p.25) âif there is some probability (1/ân) that any given purchase will occur on a threshold, then the threshold action will trigger a reduction in production of around n units, yielding an expected impact equal to 1âł (and from the reducing suffering page: âThe probability that any given chicken is the chicken that causes two cases instead of three to be purchased is 1/â25â). Well yesâif itâs linear then the expected effect is the same order of magnitude as the input. My model was precisely one where the probability is plausibly not linear: in any given cycle, total sales are much more likely to be near the mean than near the threshold, so every individual would correctly believe that their own actions are very unlikely to change anything, which is not inconsistent with the (obviously correct) claim that large changes in demand are roughly linear and do influence things according to whatever macro-level elasticity has been estimated for chickens.
Or my 30-second model might be wrongâIâm not claiming itâs correct. Iâm claiming that we donât know, and the fact that none of these sources seems to have even considered it (or any other ones), and donât even realize the nature of the assumptions theyâre making, and nevertheless draw such strong conclusions, is again a bad sign.
Second note that none of these sources actually do any data analysis or try to examine original data about the markets or supply chains; they are armchair papers. My whole point is that depending on which of several reasonable assumptions one makes, different conclusions will be drawn. The only way to adjudicate this is to actually figure out whatâs going on in the real world, and neither of these sources attempts to do that. Hint: neither of them gives an empirically-derived concrete estimate for individual-level elasticity.
This seems fair and seems like the strongest argument here. Even M&H only say they âbriefly sketch the contours of a positive argument for consumer efficacyâ.
While I think this doesnât undermine your point that people could come to reasonable differing conclusions about this case, itâs worth pointing out the same is true about counterfactuals for basically all charity and altruistic work based on similar arguments, so this case doesnât seem categorically special. Some level of guesswork is basically always involved, although to different degrees, and levels of ârobustnessâ can differ:
GiveWell has estimates for the value of counterfactual spending by other actors, but it mostly only reflects government actors, plus the Global Fund. What about Open Phil and smaller donors? (Maybe they can be ignored based on Open Philâs own statements, and assuming smaller donors donât pay attention to these funding levels, and so donât respond.) Some of the numbers they do use are also just guesses. They go further than basically anyone else, but is it far enough? How much less cost-effective could they be?
For individuals doing altruistic work, if they didnât do it (e.g. they didnât take the job), what would others have done differently, and with what value? (âReplaceabilityâ.)
There are other effects on things we donât or canât measure. Does the charity undermine governance and do harm in the long run as a result? What about the effects on nonhuman animals, farmed and wild? What about the potential impacts much further into the future, through economic growth, climate change or space colonization? This gets into cluelessness and the McNamara fallacy.
Yes all fair, and Iâd say it goes beyond counterfactuals. Iâm not sure people fully realize how sensitive many conclusions are to all sorts of assumptions, which are often implicit in standard models. I am on record disagreeing strongly with John Halstead about the likely cost-effectiveness of advocating for economic growth, and I feel similarly about much of the longtermist agenda, so this isnât specific to animals. My personal sense is that if you can save an existing human life for a few thousand dollars (for which the evidence is very clear, although point taken that the marginal impact isnât definitively pinned downâhowever Iâd guess within a factor of two,), thatâs an extremely high bar to overcome.
First of all note that the two sources you cite directly contradict one another: the first-hand anecdotal account says there is essentially no meat waste even in very small groceries, while M&H (p.12) say there is a modest constant unavoidable waste that is in fact higher in smaller /â local stores than for big outfits.
Fair. I think the anecdotal account is a limiting case of M&H where the waste is very close to 0, though, so the arguments in M&H would apply to the anecdote. M&Hâs argument doesnât depend on there being modest constant unavoidable waste rather than essentially none.
Indeed M&H are internally inconsistent: they say that the market is highly competitive (although they only give a very incomplete reference for this on p.14, which I couldnât find any trace of; my googling found this source suggesting a net profit margin for farming/âagriculture of 5.7%, which is middlingâbetter than aerospace/âdefense or healthcare), but then they also state (p.23) that larger firms have up to 60% lower costs than smaller onesâso how do the latter survive if the industry is so competitive? All of these are bad signs right off the bat.
This doesnât show theyâre internally inconsistent.
They probably meant the market is highly competitive in absolute terms, not among the very most competitive markets in the US. The argument they make isnât meant to depend on the relative competitiveness of the industry among industries, and it wouldnât be valid if it did.
Small farms can survive by product differentiation and competing in different submarkets. They can sell niche, specially labelled/âdescribed products, like organic, free range or locally raised, and they can charge premiums this way. They can sell in different places, like farmers markets, to small local grocers or to restaurants trying to appear more responsible/âethical, and charge more this way. Broiler farms producing fewer than 100,000 broilers/âyear only made up around 5% of the market in 2001 (Fig 2), so itâs pretty plausible and Iâd guess itâs the case that small broiler farms with much higher production costs sell differentiated products.
I wasnât gesturing toward the relative competitiveness because itâs important per se (youâre right that it isnât) but rather as a way to gauge absolute competitiveness for those who donât already know that a net profit margin of 5.7% isnât bad at all. My intuition is that people realize that both defense and healthcare firms make decent profits (as they do) and hence that this fact would help convey that farmers (whether large or small; and if your point is that they can differentiate themselves and do some monopolistic competition then youâre already on my side vs M&H) are not typically right on the edge of survival.
However I donât personally think the level of competition is crucial to anything here. M&H believe that itâs necessary for their argument (in the abstract they say their case rests on it), so I was pointing out that (a) itâs actually not that competitive; and (b) if they do think itâs truly competitive (i.e. not differentiated) then that is indeed inconsistent with their own claim on p.23, which is a bad sign for their analysis.
My main point (which you donât seem to have responded to) remains that these are all conceptual arguments making various particular assumptions rather than actually trying to estimate an individual-level impact with a combination of a concrete well-defined model and empirics.
Instead, the threshold-triggered event is a particular growerâs failure to get a contract to raise birds at all, or a delay in the next shipment of birds, a switch to a different type of agriculture, or a rancherâs choice to sell her land to a developer.
And even if their net profit margins were 5.7% on average, many farms could still be on the edge of survival. Also from M&H:
Even in industries that are vertically integrated, like the market for chickens, âgrowersâ often operate with heavy debt, barely above poverty, and parent firms give them only short-term contracts (J. MacDonald 2008).
Net farm income is the difference between gross farm income and operating expenses, and it amounts to 25-27 percent of gross farm income in each size class. Net farm income, however, varies widely among broiler operations, where a quarter of farms experience lossesânegative net farm income. Poor productive performance may be one source of negative net income since, on average, operations with negative net farm income receive fees of 4.8 cents per pound, compared with 5.1 cent per pound for those with positive net income. Depreciation is a more important factor explaining differences in net income. On farms with negative net farm income, depreciation expenses account for 39 percent of gross income, on average, compared with 13 percent for other operations. Farms with recent major capital expenditures will usually record substantial depreciation expenses, often large enough to generate negative net farm incomes. Correspondingly, older operations with fully depreciated assets rarely report negative net incomes.
Furthermore, the 20th percentile of household income[1] across broiler farmers was $18,782 in 2011, according to the USDA, and so close to the poverty line at the time. However, the household income for chicken farmers is relatively high recently, in 2020 (USDA).
Also, about differentiation, I donât see what the existence of some small high-cost farms selling to small niche submarkets tells you about the behaviour or competitiveness of the conventional large farms, which account for almost all of the combined market. I donât think itâs a case of monopolistic competition; these are just a few separate submarkets, like free range and organic. Maybe those selling locally are acting nearly monopolistically, with the âlocalâ label or by selling to farmers markets, but it also doesnât really matter, because theyâre selling to a tiny submarket and their supply is very limited. If a kid sets up a lemonade stand in their neighbourhood and sells lemonade above grocery store prices, you wouldnât conclude from this that an individual lemonade company can set higher prices for grocery stores (or distributors?), where almost all of the lemonade is bought, without being pushed out of the market.
Household income measures the cash income flowing to a household and available for expenditures during a year. For farmers, household income combines the income that the household receives from off-farm activities with the income that the household receives from the farm business, net of expenses and payments to other stakeholders in the business.
Third (to finally answer your question!), no my hypothetical model is not the same as the way they are using the term âbufferâ (which seems to be more about maintaining a minimum level of excess in the system; mine is simply about the optimal tradeoff between stockouts vs excess/âwaste). For instance M&H say (p.25) âif there is some probability (1/ân) that any given purchase will occur on a threshold, then the threshold action will trigger a reduction in production of around n units, yielding an expected impact equal to 1âł (and from the reducing suffering page: âThe probability that any given chicken is the chicken that causes two cases instead of three to be purchased is 1/â25â).
Sorry, I could have been more explicit in my comment. I wasnât referring to the rest of the Reducing Suffering article, and I didnât mean that any of that article referred to your model. M&H refer to a model similar to yours (Budolfsonâs buffer model), but not in the section that I referred to (and from which you quote). What I meant is that both propose more plausible models of markets (more plausible based on observations of how grocery stores behave), and I was pointing to those alternative proposals.
M&H summarizes the main takeaway from Budolfsonâs buffer model:
If a person is facing a decision with this kind of uncertainty, and they have good information about the probability of being near a threshold, this can dramatically alter the expected impact calculation. (...) Similarly, if a person knew that their purchase of a chicken was not near the threshold, they could, he argues, purchase the chicken without worry about consequences for animals.
Budolfson is correct in claiming that expected impact calculations cannot always assume that an action, on the margin, would be the same as the average effect of many such actions. The standard expected utility response given by Singer and Kagan can depend crucially on the kind of information that a person has about the location of thresholds.
This is an illustration of Budolfsonâs buffer model, directly from Budolfson, 2018:
Richard makes paper T-shirts in his basement that say âHOORAY FOR CONSEQUENTIALISM!â, which he then sells online. The T-shirts are incredibly cheap to produce and very profitable to sell and Richard doesnât care about waste per se, and so he produces far more T-shirts than he is likely to need each month, and then sells the excess at a nearly break-even amount at the end of each month to his hippie neighbor, who burns them in his wood-burning stove.Footnote10 For many years Richard has always sold between 14,000 and 16,000 T-shirts each month, and heâs always printed 20,000 T-shirts at the beginning of each month. Nonetheless, there is a conceivable increase in sales that would cause him to produce more T-shirtsâin particular, if he sells over 18,000 this month, heâll produce 25,000 T-shirts at the beginning of next month; otherwise heâll produce 20,000 like he always does. So, the system is genuinely sensitive to a precise tipping pointâin particular, the difference between 18,000 purchases and the âmagic numberâ of 18,001.
Presumably there could also be a conceivable decrease in sales that would cause Richard to produce fewer T-shirts, too. Richard has a historical monthly demand range that serves essentially the same purpose as your predicted demand, with thresholds for setting alternative future procurement/âproduction decisions far enough away from the centre of the historical range, or in your case, predicted demand.
EDIT: so your last paragraph seems wrong:
Iâm claiming that we donât know, and the fact that none of these sources seems to have even considered it (or any other ones), and donât even realize the nature of the assumptions theyâre making, and nevertheless draw such strong conclusions, is again a bad sign.
Interestingâthanks for the extra info re Budolfson. I did in fact read all of M&H, and they give two interpretations of the buffer model, neither of which is related to my model, so thatâs what I was referring to. [Thatâs also what I was referring to in my final paragraph: none of the sources you cited on that side of the causal efficacy argument seems to have considered anything like my model, which remains true given my current knowledge.] In fact if Budolfson was saying something more like my model, which does seem to be the case, then thatâs an even worse sign for M&H because they must not have understood it.
The paragraph you quote from Budolfson is indeed more similar to my model, except that in my case the result follows from profit-maximizing behavior (in a competitive industry if you like!) rather than ad hoc and unusual assumptions.
Suppose that I consider a threshold (for increasing or decreasing production next cycle) right at the mean of expected sales (15,000 in the example): half the time Iâll stockout and have disappointed customers; half the time Iâll have extra stock and have to sell it on a secondary market, or give it away, or waste it. Which is worse for business? Plausibly stocking out is worse. So my threshold will be higher than the mean, reducing the probability of stocking out and increasing the prob of excess. The optimal level will be set just so that at the margin, the badness of stocking out (larger) multiplied by the prob of stocking out (smaller) will exactly offset the badness of excess times the prob of excess. Because it is above the mean, which is in fact the true best-guess state of the world (ignoring any individual consumer), and because the distribution around the mean will plausibly be Gaussian (normal), which declines exponentially from the meanânot linearly! - every individual consumer should rationally believe that their decision is less than 1/ân likely to be taking place at the threshold. QED.
Iâm not sure what you mean by M&H not understanding Budolfson. They give a brief overview of the model, but the section from M&H I referred to (âEfficient Responsive Supply Chains and Causal Efficacyâ) describes the market as they understand it, in a way thatâs not consistent with Budolfson. The implicit reply is that Budolfsonâs model does not match their observations of how the market actually works.
I think how theyâd respond to your model is:
stores do use explicit demand predictions to decide procurement,
they are constantly making new predictions,
these predictions are in fact very sensitive to recent individual purchase decisions, and actually directly so.
Suppose the store makes stocking decisions weekly. If demand is lower one week than it would have otherwise been, their predictions for the next week will be lower than they would have otherwise been. Of course, thereâs still a question of how sensitive: maybe they give little weight to their actual recent recorded purchases[1] relative to other things, like othersâ market forecasts or sales the same time in past years.[2] But M&H would contend that actually they are very sensitive to recent purchases, and I would guess thatâs the case, too, because it probably is one of the most predictive pieces of information they can use, and plausibly the most predictive. They donât provide direct estimates of the sensitivity based on empirical data and maybe they donât back these claims with strong enough evidence at all (i.e. maybe stores donât actually usually work this way), and itâs fair to point out these kinds of holes in their arguments if someone wants to use their paper to make a strong case.
Here are relevant quotes:
For example, modern grocery stores have check-out procedures that track the sale of each product and automatically order replacements from the parent companies. Even in industries that are not vertically integrated, standard information technology allows firms to track sales in great detail, down to individual transactions (Salin 2000). In addition, these companies track the rates of orders to optimize shipping and refrigeration times and to minimize waste. (...) In this kind of system, the large distributors that contract with farms actually do know the rate at which chickens are being purchased throughout their network.
(...)
Given this description of the way these markets function, we can now describe the causal chain that connects an individualâs purchase to a farmerâs production decision. When a person decides to stop purchasing chickens, the result is that their local grocery store automatically starts ordering chickens more slowly, to reflect the decreased rate of sale. The distributor (perhaps Chickens R Us) will automatically adjust their shipments of chickens to that store. Since some shipments will require preset bundles of chickens, there will be a threshold at which a delivery of meat comes a day later, to reflect the slower demand. This âthresholdâ does not mean, however that the information going down the supply chain is less precise. As Chickens R Us is managing their supply of chickens in the distribution network, they are also managing the rate at which they send contracts of birds to their âgrowersâ and the number of growers that get contracts.
I would correct the one sentence to âWhen a person decides to stop purchasing chickens, the result is that their local grocery store automatically starts ordering chickens more slowly than they otherwise would have, to reflect the lower than otherwise rate of sale.â
I still havenât read Budolfson, so Iâm not claiming that M&H misinterpret him. As I said, I did read their entire paper, and in the section specifically about him they describe two interpretations of âbufferâ, neither of which matches my model. So if his model is similar to mine, they got it wrong. If his model is different than mine, then they donât seem to have ever considered a model like mine. Either way a bad sign.
Everything you write about how you think they might respond to me (i.e. your three bullet points and the subsequent paragraph) is 100% consistent with my model and doesnât change any of its implications. In my model stores use predicted demand and can update it as often as they want. The point is that purchasing is in bulk (at least at some level in the supply chain); therefore there is a threshold; and the optimal threshold (every single time) will be chosen to be away from the mean prediction. This can still be extremely sensitive, and may well be. [Apologies if my brief descriptions were unclear, but please do take another look at it before responding if you donât see why all this is the case.]
To the final point, yes of course if someone decides to stop purchasing then the store [probabilistically] starts ordering fewer chickens [than otherwise]; I didnât disagree with that sentence of theirs, and it is also 100% consistent with my model. The question is the magnitude of that change and whether it is linear or not, crucial points to which they have nothing to contribute.
EDIT: I did misunderstand at this point, as you pointed out in your reply.
Ok, I think I get your model, but I donât really see why a grocery store in particular would follow it, and it seems like a generally worse way to make order decisions for one. I think itâs more plausible for earlier parts of the supply chain, where businesses may prefer to produce consistent volumes, because there are relevant thresholds (in revenue) for shutting down, downsizing, expanding and entering the market, and itâs costly to make such a decision (selling/âbuying capital, hiring/âfiring staff) only to regret it later or even flip-flop.[1] It takes work to hire someone, so hiring and firing (in either order) is costly. Capital assets lose value once you purchase or use them, so buying and selling (in either order) is costly. If changes in a businessâ production levels often require such a decision, that business has reason to try to keep production more consistent or stick with their plans to avoid accumulating such costs. But not all changes to production levels require such decisions.
(I donât mean to imply you donât understand all of the above; this is just me thinking through it, checking my understanding and showing others interested.)
I donât think a grocery store has to adjust its capital or staff to order more or less, or at least not for the vast majority of marginal changes in order size. Same for distributors/âwholesalers.
Iâm not sure about broiler farms. Theyâd sometimes just have to wait longer for a contract (or never get one again), or maybe theyâd get a smaller contract and raise fewer broilers (the market is contract-based in the US, and the farms donât own the broilers[2]), so it often just wouldnât be their decision. But on something like your model, if a farm was planning to enter the market or expand, and contracts or revenues (or market reports) come only slightly worse than expected (still above the threshold in your model, and which is far more likely than coming below the threshold), theyâd enter/âexpand anyway. For farms not planning to expand/âenter the market, maybe theyâd even take on a contract they donât expect to pay for its variable costs, just to get more favour from the companies contracting them in the future or to push out competitors. Or, just generally, the contracts would very disproportionately be above their thresholds for shutdown, as they expect them to be. Also, many individual farmers are probably subject to the sunk cost fallacy.
Then there are the integrator/âprocessor companies like Tyson that contract the farms. A small number of companies control a large shares of this part of the supply chain, and theyâve been caught price-fixing (see here and here), which undermines the efficiency (and of course competitiveness) of the market. Below their predictions, maybe theyâd want to keep giving farms contracts in order to keep them from shutting down or to keep them from switching to competitors, because itâll be harder/âslower to replace them if demand recovers, or just to hurt competitors. Or, if they were already planning to expand production, but sales come in below expectation, theyâd do it anyway for similar reasons.
Hereâs an example for a grocery store:
Suppose, to avoid stockouts (like you propose they should), as a rule, they order 7 more units than (the expected value of) their predicted sales.
Suppose they would have predicted 123 sales for the next period had you not abstained. Because you abstained, they instead predict 122. So, as a result of your abstention, they order 129 instead of 130, and you make a difference, at least at this level.
Now, maybe they need to order in specific multiples of units. Say they need to order in multiples of 10, and they order the minimum multiple of 10 thatâs at least 7 over what they predict.
In the above case, your abstention makes no difference, and they would order 130 either way, but thatâs just one case. The threshold to order 10 fewer is when the prediction modulo 10 would have been 4 and your abstention drops it below that.[3] If you look at a randomly sampled period where they need to order, thereâs not really any reason to believe that their prediction modulo 10 will be especially unlikely to be 4 compared to any of the other digits.[4]
Broiler production contracts add another risk aside from the way in which compensation is determined. Traditionally, broiler contracts have not required strong commitments by integrators. In 2006, about half of broiler contracts were âflock to flockâ; that is, the integrator made no specific commitment to provide birds beyond the current flockâs placement. Those contracts that specified a longer duration (usually 1 to 5 years) rarely committed the integrator to a specified number of birds or flocks in a year.
I guess one way would be if they have sufficiently consistent purchases and choose a supplier based on the multiple to get their prediction modulo the multiple away from the threshold. I think itâs very unlikely theyâd switch suppliers just to get their predictions in a better spot with respect to multiples.
Hiâthanks again for taking more time with this, but I donât think you do understand my model. It has nothing to do with capital assets, hiring/âfiring workers, or switching suppliers. All that it requires is that some decisions are made in bulk, i.e. at a level of granularity larger than the impact of any one individual consumer. I agree this is less likely for retail stores (possibly some of them order in units of 1? wouldnât it be nice if someone actually cared enough to look into this rather than us all arguing hypothetically...), but it will clearly happen somewhere back up the supply chain, which is all that my model requires.
Your mistake is when you write âSay they need to order in multiples of 10, and they order the minimum multiple of 10 thatâs at least 7 over what they predict.â Thatâs not what my model predicts (I think itâs closer to M&Hâs first interpretation of buffers?), nor does it make economic sense, and it builds in linearity. What a profit-maximizing store will do is to balance the marginal benefit and marginal cost. Thus if they would ideally order 7 extra, but they have to order in multiples of 10 and x=4 mod10, theyâll order x+6 not x+16 (small chance of one extra stock-out vs large chance of 10 wasted items). They may not always pick the multiple-of-10 closest to 7 extra, but they will balance the expected gains and losses rather than using a minimum. From there everything that Iâm suggesting (namely the exponential decline in probability, which is the key point where this differs from all the others) follows.
And a quick reminder: Iâm not claiming that my model is the right one or the best one, however it is literally the first one that I thought of and yet no one else in this literature seems to have considered it. Hence my conclusion that theyâre making far stronger claims than are possibly warranted.
(Iâve edited this comment, but the main argument about grocery stores hasnât changed, only some small additions/âcorrections to it, and changes to the rest of my response.)
Thanks for clarifying again. Youâre right that I misunderstood. The point as I now understand is that they expect the purchases (or whatever theyâd ideally order, if they could order by individual units) to fall disproportionately in one order size and away from each threshold for lower and higher order sizes, i.e. much more towards the middle, and theyâve arranged for their order sizes to ensure this.
Iâll abandon the specific procedure I suggested for the store, and make my argument more general. For large grocery stores, I think my argument at the end of my last comment is still basically right, though, and so you should expect sensitivity, as I will elaborate further here. In particular, this would rule out your model applying to large grocery stores, even if they have to order in large multiples, assuming a fixed order frequency.
Letâs consider a grocery store. Suppose they make purchase predictions p (point estimates or probability distributions), and they have to order in multiples of K, but Iâll relax this assumption later. We can represent this with a function f from predictions to order sizes so that f(p)=Kâg(p), where g is an integer-valued function.f can be the solution to an optimization problem, like yours. Iâm ignoring any remaining stock they could carry forward for simplicity, but they could just subtract it from p and put that stock out first. Iâm also assuming a fixed order frequency, but M&H mention the possibility of âa threshold at which a delivery of meat comes a day laterâ. I think your model is a special case of this, ignoring what Iâm ignoring and with the appropriate relaxations below.
I claim the following:
Assuming the store is not horrible at optimizing, f should be nondecreasing and scale roughly linearly with p. What I mean by âroughly linearly with pâ is that for (the vast majority of possible values of) p, we can assume that f(p+K)=f(p)+K, and that values of p where f(p+1)=f(p)+K, i.e. the thresholds, are spaced roughly K apart. Even if different order sizes didnât differ in multiples of some fixed number, something similar should hold, with spacing between thresholds roughly reflecting order size differences.
A specific store might have reason to believe their predictions are on a threshold much less than 1/K of the time across order decisions, but only for one of a few pretty specific reasons:
They were able to choose K the first time to ensure this, intentionally or not, and stick with it and f regardless of how demand shifts.
The same supplier for the store offers different values of K (or the store gets the supplier to offer another value of K), and the store switches K or uses multiple values of K simultaneously in a way that avoids the thresholds. (So f defined above isnât general enough.)
They switch suppliers or products as necessary to choose K in a way that avoids the thresholds. Maybe they donât stop offering a product or stop ordering from the same supplier altogether, but optimize the order(s) for it and a close substitute (or multiple substitutes) or multiple suppliers in such a way that the thresholds are avoided for each. (So f defined above isnât general enough.)
If none of these specific reasons hold, then you shouldnât expect to be on the threshold much less than 1/K of the time,[1] and you should believe E[f(pâ1)]âE[f(p)]â1, where the expectation is taken over your probability distribution for the storeâs prediction p.
How likely are any of these reasons to hold, and what difference should they make to your expectations even if they did?
The first reason wouldnât give you far less than 1/K if the interquartile range of their predictions across orders over time isnât much smaller than K, but they prefer or have to keep offering the product anyway. This is because the thresholds are spaced roughly K apart, p will have to cross thresholds often with such a large interquartile range, and if p has to cross thresholds often, it canât very disproportionately avoid them.[2]
Most importantly, however, if K is chosen (roughly) independently of p, your probability distribution for pmodK for a given order should be (roughly) uniform over 0,..., Kâ1,[3] so p should hit the threshold with probability (roughly) 1/K. It seems to me that K is generally chosen (roughly) independently of p. In deciding between suppliers, the specific value of K seems less important than the cost per unit, shipping time, reliability and a lower value of K.[4] In some cases, especially likely for stores belonging to large store chains, there isnât a choice, e.g. Walmart stores order from Walmart-owned distributors, or chain stores will have agreements with the same supplier company across stores. Then, having chosen a supplier, a store could try to arrange for a different value of K to avoid thresholds, but I doubt theyâd actually try this, and even if they did try, suppliers seem likely to refuse without a significant increase in the cost per unit for the store, because suppliers have multiple stores to ship to and donât want to adjust K by the store.
Stores similarly probably wouldnât follow the strategies in the second and third reasons because they wouldnât be allowed to, or even if they could, other considerations like cost per unit, shipping time, reliability and stocking the same product would be more important. Also, if the order quantities vary often enough between orders based on such strategies, youâd actually be more likely to make a difference, although smaller when you do.
So, I maintain that for large stores, you should believe E[f(pâ1)]âE[f(p)]â1.
And a quick reminder: Iâm not claiming that my model is the right one or the best one, however it is literally the first one that I thought of and yet no one else in this literature seems to have considered it. Hence my conclusion that theyâre making far stronger claims than are possibly warranted.
Fair. I donât think they should necessarily have considered it, though, in case observations they make would have ruled it out, but it seems like they didnât make such observations.
but it will clearly happen somewhere back up the supply chain, which is all that my model requires.
I donât think this is obvious either way. This seems to be a stronger claim than youâve been making elsewhere about your model. I think youâd need to show that itâs possible and worth it for those at one step of the supply chain to choose K or suppliers like in a way I ruled out for grocery stores and without making order sizes too sensitive to predictions. Or something where my model wasnât general enough, e.g. I assumed a fixed order frequency.
It could be more than 1/K, because weâve ruled out being disproportionately away from the threshold by assumption, but still allowed the possibility of disproportionately hitting it.
I would in fact expect lower numbers within 0, âŠ, Kâ1 to be slightly more likely, all else equal. Basically Benfordâs law and generalizations to different digit positions. Since these are predictions and people like round numbers, if K is even or a multiple of 5, I wouldnât be surprised if even numbers and multiples of 5 were more likely, respectively.
Except maybe if the minimum K across suppliers is only a few times less than p, closer to p or even greater, and they canât carry stock forward past the next time they would otherwise receive a new shipment.
Canât we make informed estimates, even if they have wide ranges? We multiply the demand shift by Ï”SÏ”SâÏ”D (based on equilibrium displacement models, or this), with long-run elasticity estimates from the literature.
(FWIW, Iâm also sympathetic to diet change being net negative in the near term, mostly because of the impacts on wild invertebrates and maybe fish. So I mostly focus on welfare.)
Iâm a professor of economics, but thanks for the link explaining elasticity :)
The answer is no, we canât just do that, since those approaches assume nontrivial changes (and/âor they assume everything is continuous, which the real world isnât). One plausible simple model of supermarket (or restaurant) purchasing behavior is that when observed demand goes above/âbelow a certain threshold relative to predicted demand, they buy more/âless of the input next cycle. From an individual point of view, the expected aggregate demand of other agents in any time period will be a Gaussian distribution (by the law of large numbers), and the threshold will be away from the mean (doesnât make sense to update every time), which implies that oneâs probability of being the marginal buyer at the threshold declines exponentially (not linearly, as it would be for macro-level shifts and as you are implicitly assuming). From the ACE link: âwe can approximate the supply and demand curves in this region by straight linesââno, you canât do that (for individual behavior) without substantive additional assumptions or a lot of legwork into how these decisions actually get made.
In any case I have no idea if thatâs the right model, because I havenât studied supermarket supply chain management. As far as I can tell (but Iâd love to see this somewhere), nobody in either the econ lit or animal welfare lit has tried to do this at the level required to make what I would consider an informed estimate; weâre not just talking about a factor of 2 or 3 here. That knowledge gap doesnât seem to stop the latter group from making very strong claims; they mostly donât even seem to understand or acknowledge the high uncertainty and strong assumptions.
This sounds like Budolfsonâs buffer model. Have you seen the response by McMullen and Halteman? They describe supply chains and management practices in the section âEfficient Responsive Supply Chains and Causal Efficacyâ.
Also, this short first-hand account for grocery stores in an older article from the EA community on the issue, quoted from a comment on a post in an EA Facebook group on the issue.
I agree that itâs probably true most people donât know the right reasons to believe that their individual purchase decisions make much difference on average, because most people know basically nothing about supply chain management.
I had seen some of this, but not the specific paper (ungated) by McMullen & Haltemanâthanks!
First of all note that the two sources you cite directly contradict one another: the first-hand anecdotal account says there is essentially no meat waste even in very small groceries, while M&H (p.12) say there is a modest constant unavoidable waste that is in fact higher in smaller /â local stores than for big outfits. Indeed M&H are internally inconsistent: they say that the market is highly competitive (although they only give a very incomplete reference for this on p.14, which I couldnât find any trace of; my googling found this source suggesting a net profit margin for farming/âagriculture of 5.7%, which is middlingâbetter than aerospace/âdefense or healthcare), but then they also state (p.23) that larger firms have up to 60% lower costs than smaller onesâso how do the latter survive if the industry is so competitive? All of these are bad signs right off the bat.
Second note that none of these sources actually do any data analysis or try to examine original data about the markets or supply chains; they are armchair papers. My whole point is that depending on which of several reasonable assumptions one makes, different conclusions will be drawn. The only way to adjudicate this is to actually figure out whatâs going on in the real world, and neither of these sources attempts to do that. Hint: neither of them gives an empirically-derived concrete estimate for individual-level elasticity.
Third (to finally answer your question!), no my hypothetical model is not the same as the way they are using the term âbufferâ (which seems to be more about maintaining a minimum level of excess in the system; mine is simply about the optimal tradeoff between stockouts vs excess/âwaste). For instance M&H say (p.25) âif there is some probability (1/ân) that any given purchase will occur on a threshold, then the threshold action will trigger a reduction in production of around n units, yielding an expected impact equal to 1âł (and from the reducing suffering page: âThe probability that any given chicken is the chicken that causes two cases instead of three to be purchased is 1/â25â). Well yesâif itâs linear then the expected effect is the same order of magnitude as the input. My model was precisely one where the probability is plausibly not linear: in any given cycle, total sales are much more likely to be near the mean than near the threshold, so every individual would correctly believe that their own actions are very unlikely to change anything, which is not inconsistent with the (obviously correct) claim that large changes in demand are roughly linear and do influence things according to whatever macro-level elasticity has been estimated for chickens.
Or my 30-second model might be wrongâIâm not claiming itâs correct. Iâm claiming that we donât know, and the fact that none of these sources seems to have even considered it (or any other ones), and donât even realize the nature of the assumptions theyâre making, and nevertheless draw such strong conclusions, is again a bad sign.
This seems fair and seems like the strongest argument here. Even M&H only say they âbriefly sketch the contours of a positive argument for consumer efficacyâ.
While I think this doesnât undermine your point that people could come to reasonable differing conclusions about this case, itâs worth pointing out the same is true about counterfactuals for basically all charity and altruistic work based on similar arguments, so this case doesnât seem categorically special. Some level of guesswork is basically always involved, although to different degrees, and levels of ârobustnessâ can differ:
GiveWell has estimates for the value of counterfactual spending by other actors, but it mostly only reflects government actors, plus the Global Fund. What about Open Phil and smaller donors? (Maybe they can be ignored based on Open Philâs own statements, and assuming smaller donors donât pay attention to these funding levels, and so donât respond.) Some of the numbers they do use are also just guesses. They go further than basically anyone else, but is it far enough? How much less cost-effective could they be?
For individuals doing altruistic work, if they didnât do it (e.g. they didnât take the job), what would others have done differently, and with what value? (âReplaceabilityâ.)
There are other effects on things we donât or canât measure. Does the charity undermine governance and do harm in the long run as a result? What about the effects on nonhuman animals, farmed and wild? What about the potential impacts much further into the future, through economic growth, climate change or space colonization? This gets into cluelessness and the McNamara fallacy.
Yes all fair, and Iâd say it goes beyond counterfactuals. Iâm not sure people fully realize how sensitive many conclusions are to all sorts of assumptions, which are often implicit in standard models. I am on record disagreeing strongly with John Halstead about the likely cost-effectiveness of advocating for economic growth, and I feel similarly about much of the longtermist agenda, so this isnât specific to animals. My personal sense is that if you can save an existing human life for a few thousand dollars (for which the evidence is very clear, although point taken that the marginal impact isnât definitively pinned downâhowever Iâd guess within a factor of two,), thatâs an extremely high bar to overcome.
Fair. I think the anecdotal account is a limiting case of M&H where the waste is very close to 0, though, so the arguments in M&H would apply to the anecdote. M&Hâs argument doesnât depend on there being modest constant unavoidable waste rather than essentially none.
This doesnât show theyâre internally inconsistent.
They probably meant the market is highly competitive in absolute terms, not among the very most competitive markets in the US. The argument they make isnât meant to depend on the relative competitiveness of the industry among industries, and it wouldnât be valid if it did.
Small farms can survive by product differentiation and competing in different submarkets. They can sell niche, specially labelled/âdescribed products, like organic, free range or locally raised, and they can charge premiums this way. They can sell in different places, like farmers markets, to small local grocers or to restaurants trying to appear more responsible/âethical, and charge more this way. Broiler farms producing fewer than 100,000 broilers/âyear only made up around 5% of the market in 2001 (Fig 2), so itâs pretty plausible and Iâd guess itâs the case that small broiler farms with much higher production costs sell differentiated products.
I wasnât gesturing toward the relative competitiveness because itâs important per se (youâre right that it isnât) but rather as a way to gauge absolute competitiveness for those who donât already know that a net profit margin of 5.7% isnât bad at all. My intuition is that people realize that both defense and healthcare firms make decent profits (as they do) and hence that this fact would help convey that farmers (whether large or small; and if your point is that they can differentiate themselves and do some monopolistic competition then youâre already on my side vs M&H) are not typically right on the edge of survival.
However I donât personally think the level of competition is crucial to anything here. M&H believe that itâs necessary for their argument (in the abstract they say their case rests on it), so I was pointing out that (a) itâs actually not that competitive; and (b) if they do think itâs truly competitive (i.e. not differentiated) then that is indeed inconsistent with their own claim on p.23, which is a bad sign for their analysis.
My main point (which you donât seem to have responded to) remains that these are all conceptual arguments making various particular assumptions rather than actually trying to estimate an individual-level impact with a combination of a concrete well-defined model and empirics.
The edge of survival is not the only relevant threshold here. Chicken farmers donât own the birds they raise and only raise them when given a contract, so itâs not entirely their choice whether or not and when they raise any chickens. From M&H:
And even if their net profit margins were 5.7% on average, many farms could still be on the edge of survival. Also from M&H:
From MacDonald, 2008:
Furthermore, the 20th percentile of household income[1] across broiler farmers was $18,782 in 2011, according to the USDA, and so close to the poverty line at the time. However, the household income for chicken farmers is relatively high recently, in 2020 (USDA).
Also, about differentiation, I donât see what the existence of some small high-cost farms selling to small niche submarkets tells you about the behaviour or competitiveness of the conventional large farms, which account for almost all of the combined market. I donât think itâs a case of monopolistic competition; these are just a few separate submarkets, like free range and organic. Maybe those selling locally are acting nearly monopolistically, with the âlocalâ label or by selling to farmers markets, but it also doesnât really matter, because theyâre selling to a tiny submarket and their supply is very limited. If a kid sets up a lemonade stand in their neighbourhood and sells lemonade above grocery store prices, you wouldnât conclude from this that an individual lemonade company can set higher prices for grocery stores (or distributors?), where almost all of the lemonade is bought, without being pushed out of the market.
The USDAâs definition:
Sorry, I could have been more explicit in my comment. I wasnât referring to the rest of the Reducing Suffering article, and I didnât mean that any of that article referred to your model. M&H refer to a model similar to yours (Budolfsonâs buffer model), but not in the section that I referred to (and from which you quote). What I meant is that both propose more plausible models of markets (more plausible based on observations of how grocery stores behave), and I was pointing to those alternative proposals.
M&H summarizes the main takeaway from Budolfsonâs buffer model:
This is an illustration of Budolfsonâs buffer model, directly from Budolfson, 2018:
Presumably there could also be a conceivable decrease in sales that would cause Richard to produce fewer T-shirts, too. Richard has a historical monthly demand range that serves essentially the same purpose as your predicted demand, with thresholds for setting alternative future procurement/âproduction decisions far enough away from the centre of the historical range, or in your case, predicted demand.
EDIT: so your last paragraph seems wrong:
Interestingâthanks for the extra info re Budolfson. I did in fact read all of M&H, and they give two interpretations of the buffer model, neither of which is related to my model, so thatâs what I was referring to. [Thatâs also what I was referring to in my final paragraph: none of the sources you cited on that side of the causal efficacy argument seems to have considered anything like my model, which remains true given my current knowledge.] In fact if Budolfson was saying something more like my model, which does seem to be the case, then thatâs an even worse sign for M&H because they must not have understood it.
The paragraph you quote from Budolfson is indeed more similar to my model, except that in my case the result follows from profit-maximizing behavior (in a competitive industry if you like!) rather than ad hoc and unusual assumptions.
Suppose that I consider a threshold (for increasing or decreasing production next cycle) right at the mean of expected sales (15,000 in the example): half the time Iâll stockout and have disappointed customers; half the time Iâll have extra stock and have to sell it on a secondary market, or give it away, or waste it. Which is worse for business? Plausibly stocking out is worse. So my threshold will be higher than the mean, reducing the probability of stocking out and increasing the prob of excess. The optimal level will be set just so that at the margin, the badness of stocking out (larger) multiplied by the prob of stocking out (smaller) will exactly offset the badness of excess times the prob of excess. Because it is above the mean, which is in fact the true best-guess state of the world (ignoring any individual consumer), and because the distribution around the mean will plausibly be Gaussian (normal), which declines exponentially from the meanânot linearly! - every individual consumer should rationally believe that their decision is less than 1/ân likely to be taking place at the threshold. QED.
Iâm not sure what you mean by M&H not understanding Budolfson. They give a brief overview of the model, but the section from M&H I referred to (âEfficient Responsive Supply Chains and Causal Efficacyâ) describes the market as they understand it, in a way thatâs not consistent with Budolfson. The implicit reply is that Budolfsonâs model does not match their observations of how the market actually works.
I think how theyâd respond to your model is:
stores do use explicit demand predictions to decide procurement,
they are constantly making new predictions,
these predictions are in fact very sensitive to recent individual purchase decisions, and actually directly so.
Suppose the store makes stocking decisions weekly. If demand is lower one week than it would have otherwise been, their predictions for the next week will be lower than they would have otherwise been. Of course, thereâs still a question of how sensitive: maybe they give little weight to their actual recent recorded purchases[1] relative to other things, like othersâ market forecasts or sales the same time in past years.[2] But M&H would contend that actually they are very sensitive to recent purchases, and I would guess thatâs the case, too, because it probably is one of the most predictive pieces of information they can use, and plausibly the most predictive. They donât provide direct estimates of the sensitivity based on empirical data and maybe they donât back these claims with strong enough evidence at all (i.e. maybe stores donât actually usually work this way), and itâs fair to point out these kinds of holes in their arguments if someone wants to use their paper to make a strong case.
Here are relevant quotes:
I would correct the one sentence to âWhen a person decides to stop purchasing chickens, the result is that their local grocery store automatically starts ordering chickens more slowly than they otherwise would have, to reflect the lower than otherwise rate of sale.â
Or, indirectly, through leftover stocks or stockouts.
Although eventually that should get picked up.
I still havenât read Budolfson, so Iâm not claiming that M&H misinterpret him. As I said, I did read their entire paper, and in the section specifically about him they describe two interpretations of âbufferâ, neither of which matches my model. So if his model is similar to mine, they got it wrong. If his model is different than mine, then they donât seem to have ever considered a model like mine. Either way a bad sign.
Everything you write about how you think they might respond to me (i.e. your three bullet points and the subsequent paragraph) is 100% consistent with my model and doesnât change any of its implications. In my model stores use predicted demand and can update it as often as they want. The point is that purchasing is in bulk (at least at some level in the supply chain); therefore there is a threshold; and the optimal threshold (every single time) will be chosen to be away from the mean prediction. This can still be extremely sensitive, and may well be. [Apologies if my brief descriptions were unclear, but please do take another look at it before responding if you donât see why all this is the case.]
To the final point, yes of course if someone decides to stop purchasing then the store [probabilistically] starts ordering fewer chickens [than otherwise]; I didnât disagree with that sentence of theirs, and it is also 100% consistent with my model. The question is the magnitude of that change and whether it is linear or not, crucial points to which they have nothing to contribute.
EDIT: I did misunderstand at this point, as you pointed out in your reply.
Ok, I think I get your model, but I donât really see why a grocery store in particular would follow it, and it seems like a generally worse way to make order decisions for one. I think itâs more plausible for earlier parts of the supply chain, where businesses may prefer to produce consistent volumes, because there are relevant thresholds (in revenue) for shutting down, downsizing, expanding and entering the market, and itâs costly to make such a decision (selling/âbuying capital, hiring/âfiring staff) only to regret it later or even flip-flop.[1] It takes work to hire someone, so hiring and firing (in either order) is costly. Capital assets lose value once you purchase or use them, so buying and selling (in either order) is costly. If changes in a businessâ production levels often require such a decision, that business has reason to try to keep production more consistent or stick with their plans to avoid accumulating such costs. But not all changes to production levels require such decisions.
(I donât mean to imply you donât understand all of the above; this is just me thinking through it, checking my understanding and showing others interested.)
I donât think a grocery store has to adjust its capital or staff to order more or less, or at least not for the vast majority of marginal changes in order size. Same for distributors/âwholesalers.
Iâm not sure about broiler farms. Theyâd sometimes just have to wait longer for a contract (or never get one again), or maybe theyâd get a smaller contract and raise fewer broilers (the market is contract-based in the US, and the farms donât own the broilers[2]), so it often just wouldnât be their decision. But on something like your model, if a farm was planning to enter the market or expand, and contracts or revenues (or market reports) come only slightly worse than expected (still above the threshold in your model, and which is far more likely than coming below the threshold), theyâd enter/âexpand anyway. For farms not planning to expand/âenter the market, maybe theyâd even take on a contract they donât expect to pay for its variable costs, just to get more favour from the companies contracting them in the future or to push out competitors. Or, just generally, the contracts would very disproportionately be above their thresholds for shutdown, as they expect them to be. Also, many individual farmers are probably subject to the sunk cost fallacy.
Then there are the integrator/âprocessor companies like Tyson that contract the farms. A small number of companies control a large shares of this part of the supply chain, and theyâve been caught price-fixing (see here and here), which undermines the efficiency (and of course competitiveness) of the market. Below their predictions, maybe theyâd want to keep giving farms contracts in order to keep them from shutting down or to keep them from switching to competitors, because itâll be harder/âslower to replace them if demand recovers, or just to hurt competitors. Or, if they were already planning to expand production, but sales come in below expectation, theyâd do it anyway for similar reasons.
Hereâs an example for a grocery store:
Suppose, to avoid stockouts (like you propose they should), as a rule, they order 7 more units than (the expected value of) their predicted sales.
Suppose they would have predicted 123 sales for the next period had you not abstained. Because you abstained, they instead predict 122. So, as a result of your abstention, they order 129 instead of 130, and you make a difference, at least at this level.
Now, maybe they need to order in specific multiples of units. Say they need to order in multiples of 10, and they order the minimum multiple of 10 thatâs at least 7 over what they predict.
In the above case, your abstention makes no difference, and they would order 130 either way, but thatâs just one case. The threshold to order 10 fewer is when the prediction modulo 10 would have been 4 and your abstention drops it below that.[3] If you look at a randomly sampled period where they need to order, thereâs not really any reason to believe that their prediction modulo 10 will be especially unlikely to be 4 compared to any of the other digits.[4]
I see papers on sunk-cost hysteresis and entry and exist decisions under uncertainty, like Baldwin, 1989, Dixit, 1989, Gschwandtner and Lambson, 2002.
Also:
For their prediction x, if x mod10=4, then they order x+16. If x mod10=3, then they order x+7.
I guess one way would be if they have sufficiently consistent purchases and choose a supplier based on the multiple to get their prediction modulo the multiple away from the threshold. I think itâs very unlikely theyâd switch suppliers just to get their predictions in a better spot with respect to multiples.
Hiâthanks again for taking more time with this, but I donât think you do understand my model. It has nothing to do with capital assets, hiring/âfiring workers, or switching suppliers. All that it requires is that some decisions are made in bulk, i.e. at a level of granularity larger than the impact of any one individual consumer. I agree this is less likely for retail stores (possibly some of them order in units of 1? wouldnât it be nice if someone actually cared enough to look into this rather than us all arguing hypothetically...), but it will clearly happen somewhere back up the supply chain, which is all that my model requires.
Your mistake is when you write âSay they need to order in multiples of 10, and they order the minimum multiple of 10 thatâs at least 7 over what they predict.â Thatâs not what my model predicts (I think itâs closer to M&Hâs first interpretation of buffers?), nor does it make economic sense, and it builds in linearity. What a profit-maximizing store will do is to balance the marginal benefit and marginal cost. Thus if they would ideally order 7 extra, but they have to order in multiples of 10 and x=4 mod10, theyâll order x+6 not x+16 (small chance of one extra stock-out vs large chance of 10 wasted items). They may not always pick the multiple-of-10 closest to 7 extra, but they will balance the expected gains and losses rather than using a minimum. From there everything that Iâm suggesting (namely the exponential decline in probability, which is the key point where this differs from all the others) follows.
And a quick reminder: Iâm not claiming that my model is the right one or the best one, however it is literally the first one that I thought of and yet no one else in this literature seems to have considered it. Hence my conclusion that theyâre making far stronger claims than are possibly warranted.
(Iâve edited this comment, but the main argument about grocery stores hasnât changed, only some small additions/âcorrections to it, and changes to the rest of my response.)
Thanks for clarifying again. Youâre right that I misunderstood. The point as I now understand is that they expect the purchases (or whatever theyâd ideally order, if they could order by individual units) to fall disproportionately in one order size and away from each threshold for lower and higher order sizes, i.e. much more towards the middle, and theyâve arranged for their order sizes to ensure this.
Iâll abandon the specific procedure I suggested for the store, and make my argument more general. For large grocery stores, I think my argument at the end of my last comment is still basically right, though, and so you should expect sensitivity, as I will elaborate further here. In particular, this would rule out your model applying to large grocery stores, even if they have to order in large multiples, assuming a fixed order frequency.
Letâs consider a grocery store. Suppose they make purchase predictions p (point estimates or probability distributions), and they have to order in multiples of K, but Iâll relax this assumption later. We can represent this with a function f from predictions to order sizes so that f(p)=Kâg(p), where g is an integer-valued function.f can be the solution to an optimization problem, like yours. Iâm ignoring any remaining stock they could carry forward for simplicity, but they could just subtract it from p and put that stock out first. Iâm also assuming a fixed order frequency, but M&H mention the possibility of âa threshold at which a delivery of meat comes a day laterâ. I think your model is a special case of this, ignoring what Iâm ignoring and with the appropriate relaxations below.
I claim the following:
Assuming the store is not horrible at optimizing, f should be nondecreasing and scale roughly linearly with p. What I mean by âroughly linearly with pâ is that for (the vast majority of possible values of) p, we can assume that f(p+K)=f(p)+K, and that values of p where f(p+1)=f(p)+K, i.e. the thresholds, are spaced roughly K apart. Even if different order sizes didnât differ in multiples of some fixed number, something similar should hold, with spacing between thresholds roughly reflecting order size differences.
A specific store might have reason to believe their predictions are on a threshold much less than 1/K of the time across order decisions, but only for one of a few pretty specific reasons:
They were able to choose K the first time to ensure this, intentionally or not, and stick with it and f regardless of how demand shifts.
The same supplier for the store offers different values of K (or the store gets the supplier to offer another value of K), and the store switches K or uses multiple values of K simultaneously in a way that avoids the thresholds. (So f defined above isnât general enough.)
They switch suppliers or products as necessary to choose K in a way that avoids the thresholds. Maybe they donât stop offering a product or stop ordering from the same supplier altogether, but optimize the order(s) for it and a close substitute (or multiple substitutes) or multiple suppliers in such a way that the thresholds are avoided for each. (So f defined above isnât general enough.)
If none of these specific reasons hold, then you shouldnât expect to be on the threshold much less than 1/K of the time,[1] and you should believe E[f(pâ1)]âE[f(p)]â1, where the expectation is taken over your probability distribution for the storeâs prediction p.
How likely are any of these reasons to hold, and what difference should they make to your expectations even if they did?
The first reason wouldnât give you far less than 1/K if the interquartile range of their predictions across orders over time isnât much smaller than K, but they prefer or have to keep offering the product anyway. This is because the thresholds are spaced roughly K apart, p will have to cross thresholds often with such a large interquartile range, and if p has to cross thresholds often, it canât very disproportionately avoid them.[2]
Most importantly, however, if K is chosen (roughly) independently of p, your probability distribution for p mod K for a given order should be (roughly) uniform over 0,..., Kâ1,[3] so p should hit the threshold with probability (roughly) 1/K. It seems to me that K is generally chosen (roughly) independently of p. In deciding between suppliers, the specific value of K seems less important than the cost per unit, shipping time, reliability and a lower value of K.[4] In some cases, especially likely for stores belonging to large store chains, there isnât a choice, e.g. Walmart stores order from Walmart-owned distributors, or chain stores will have agreements with the same supplier company across stores. Then, having chosen a supplier, a store could try to arrange for a different value of K to avoid thresholds, but I doubt theyâd actually try this, and even if they did try, suppliers seem likely to refuse without a significant increase in the cost per unit for the store, because suppliers have multiple stores to ship to and donât want to adjust K by the store.
Stores similarly probably wouldnât follow the strategies in the second and third reasons because they wouldnât be allowed to, or even if they could, other considerations like cost per unit, shipping time, reliability and stocking the same product would be more important. Also, if the order quantities vary often enough between orders based on such strategies, youâd actually be more likely to make a difference, although smaller when you do.
So, I maintain that for large stores, you should believe E[f(pâ1)]âE[f(p)]â1.
Fair. I donât think they should necessarily have considered it, though, in case observations they make would have ruled it out, but it seems like they didnât make such observations.
I donât think this is obvious either way. This seems to be a stronger claim than youâve been making elsewhere about your model. I think youâd need to show that itâs possible and worth it for those at one step of the supply chain to choose K or suppliers like in a way I ruled out for grocery stores and without making order sizes too sensitive to predictions. Or something where my model wasnât general enough, e.g. I assumed a fixed order frequency.
It could be more than 1/K, because weâve ruled out being disproportionately away from the threshold by assumption, but still allowed the possibility of disproportionately hitting it.
For realistic distributions of p across orders over time.
I would in fact expect lower numbers within 0, âŠ, Kâ1 to be slightly more likely, all else equal. Basically Benfordâs law and generalizations to different digit positions. Since these are predictions and people like round numbers, if K is even or a multiple of 5, I wouldnât be surprised if even numbers and multiples of 5 were more likely, respectively.
Except maybe if the minimum K across suppliers is only a few times less than p, closer to p or even greater, and they canât carry stock forward past the next time they would otherwise receive a new shipment.