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Lentil convexity: Difference between revisions
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But in actual fact lentil purchasing decisions are ''not'' independent, as our new friend the [[coronavirus]] pandemic illustrates. They just ''seem'' like it, in most markets. Ninety-five per cent of the sample are connected by a general disposition ''not'' to buy lentils. But this disposition is a function of one’s apprehension of the proximity of [[apocalypse]]. Apocalypses are, in the main, rare, and one does not tend to form an opinion that one is nigh purely through ones’ own deductions from meteorological and astronomical data. Rather, we apprehend oblivion because someone said it on Twitter. Because Owen Jones wrote a thought-piece on it, or because — ''by Jupiter, everyone is suddenly buying lentils and there are hardly any left in Sainsbury’s''. | But in actual fact lentil purchasing decisions are ''not'' independent, as our new friend the [[coronavirus]] pandemic illustrates. They just ''seem'' like it, in most markets. Ninety-five per cent of the sample are connected by a general disposition ''not'' to buy lentils. But this disposition is a function of one’s apprehension of the proximity of [[apocalypse]]. Apocalypses are, in the main, rare, and one does not tend to form an opinion that one is nigh purely through ones’ own deductions from meteorological and astronomical data. Rather, we apprehend oblivion because someone said it on Twitter. Because Owen Jones wrote a thought-piece on it, or because — ''by Jupiter, everyone is suddenly buying lentils and there are hardly any left in Sainsbury’s''. | ||
So, we get ''infected'' with the idea of | So, we get ''infected'' with the idea of [[apocalypse]] ''by each other''. Our legume-buying habits ''are not independent after all''. They are all formed out of a collective consensus about the ''non-imminence'' of the second coming. While each person’s threshold for precautionary lentil purchase in the event of apocalypse will differ, across the group, news of the unchecked spread of [[coronavirus]] will bring each person closer to that threshold and will push some of them over it. | ||
Back to the 95% normals. As they walk past the tinned goods shelf, it only takes a small proportion of | Back to the 95% normals. As they walk past the tinned goods shelf, it only takes a small proportion of them to decide ''this'' is the week to pick up an extra tin to blow the grocer's expectations out the window. Let’s say, unnerved by all this elbow-touching and obsessive-compulsive hand-washing carry on, just 5 of the 95% decide to buy an extra tin. As the hippies, vegans & health nuts who buy lentils for fun are ''also'' buying their regular quota, the supermarket’s lentil supply quickly diminishes. | ||
Then an unexpected second order of dependence emerges. For some of the 95% | Then an unexpected second order of dependence emerges. For some of the 95% — who have not yet crossed the threshold for precautionary lentil purchase — then ''notice'' that the lentil shelf is nearly empty. They reconsider their apprehension of the apocalypse. They move closer to their threshold. Some cross it. Those who do collect a tin. The shelf is cleaned out. | ||
The supermarket management, alarmed at this inexplicable sudden run on lentils, | The supermarket management, alarmed at this inexplicable sudden run on lentils, now intervenes. They impose a 3-item limit for each customer. But limiting most customers, who would not normally be seen dead buying ''one'' tin of lentils, to ''three'', won’t help the problem, since the lentils-for-judgement-day-only contingent only wanted one each in the first place. The problem is not these people bulk buying, but that ''all'' of them are ''single''-item buying. It will also irritate those hippies and rabbit-food munchers who would ordinarily buy more tins than that even when they weren’t panicking. | ||
Not only will it not help, but | Not only will it not help, but it further validates the suspicion among the 95% non-hippies that these are indeed desperate times. After all, one could hardly ask for a clearer sign of imminent implosion of the social order than LENTIL RATIONING — could things ''get'' any more messed up? | ||
The 95%, as one, increase their demand to the maximum permitted. It is only common sense. | The 95%, as one, increase their demand to the maximum permitted. It is only common sense. | ||
[[File:Lentil convexity.png|300px|right|thumb|The [[fat tail]] of the distribution. In the middle of the “bell”, the distributions look quite similar. At the extremes they are very different.]]Still: no panic hoarding, but the shelf is bare. And those latecomers, discovering it is now ''too late'' to buy lentils, head to borlotti beans and Mexican bean fiesta. To their horror they discover ''these have been cleaned out as well''. Every distant fear about a forthcoming final reckoning now confirmed, they stampede for the couscous and quinoa. | [[File:Lentil convexity.png|300px|right|thumb|The [[fat tail]] of the distribution. In the middle of the “bell”, the distributions look quite similar. At the extremes they are very different.]]Still: no panic hoarding, but the shelf is bare. And those latecomers, discovering it is now ''too late'' to buy lentils, head to borlotti beans and Mexican bean fiesta. To their horror, they discover ''these have been cleaned out as well''. Every distant fear about a forthcoming final reckoning now confirmed, they stampede for the couscous and quinoa. | ||
===Implications=== | ===Implications=== | ||
We can see the interconnectedness between human decisions like lentil-buying, at the extremes is not stable. You can’t model it. You can’t predict it. The [[correlation]] ''changes'' on account of the very ''existence'' of each buying decision, and each other people’s reaction to that decision. In ordinary times one person’s buying decision won’t affect another’s. They ''look'' for all the world like truly independent events. What do I care whether you bought lentils? But events which are ''really'' independent ''stay'' independent, however weird things get. The odds of flipping heads on a fair coin stays 0.5 however often you flip it, and whatever the previous results.<ref>Practical point though: the longer your sequence of heads, the greater the probability that the ''coin is not fair''.</ref> This makes the job of modelling independent events much, much easier. | We can see the interconnectedness between human decisions like lentil-buying, at the extremes is not stable. You can’t model it. You can’t predict it. The [[correlation]] ''changes'' on account of the very ''existence'' of each buying decision, and each other people’s reaction to that decision. In ordinary times one person’s buying decision won’t affect another’s. They ''look'' for all the world like truly independent events. What do I care whether you bought lentils? But events which are ''really'' independent ''stay'' independent, however weird things get. The odds of flipping heads on a fair coin stays 0.5 however often you flip it, and whatever the previous results.<ref>Practical point though: the longer your sequence of heads, the greater the probability that the ''coin is not fair''.</ref> This makes the job of modelling independent events much, much easier. Your standard deviation stays put. Modelling dependent events isn’t just a case of more complex maths. It isn’t ''possible''. | ||
Mis-modelling overall lentil demand is a relatively low-stakes game. It is liable to annoy peaceniks — but they are dispositionally unlikely to foment insurrection — and (unless armageddon does arrive after all, in which case a lack of lentils is the least of our problems) actual bodily consumption of lentils won’t change, so the supply-shortage will quickly sort itself out, as the 95% find themselves unexpectedly long more lentils than they know what to do with and their part of the demand curve hits absolute rock bottom. | |||
But it is a nice illustration of how badly a normal curve can serve you when the chips are down. | |||
{{sa}} | {{sa}} | ||