Please find below a pastiche of Alice’s Adventures in Wonderland that illustrates what it means to choose rationally:
‘Sit down, dear’, said the White Queen.
Alice perched delicately on the edge of a chair fashioned from oyster-shells.
‘Coffee, or tea, or chocolate?’, enquired the Queen.
‘I’ll have chocolate, please.’
The Queen turned to the Unicorn, standing, as ever, behind the throne: ‘Trot along to the kitchen and bring us a pot of chocolate if you would. There’s a good Uni.’
Off he trots. And before you can say ‘jabberwocky’ is back: ‘I’m sorry, Your Majesty, and Miss Alice, but we’ve run out of coffee.’
‘But I said chocolate, not coffee’, said a puzzled Alice.
The Unicorn was unmoved: ‘I am well aware of that, Miss. As well as a horn I have two good ears, and I’m not deaf’.
Alice thought again: ‘In that case’, she said, ‘I’ll have tea, if I may?’
‘Of course you may,’ replied the Queen. ‘But if you do, you’ll be violating a funny little thing that in the so-called Real World is known as the contraction axiom; in Wonderland we never bother about such annoyances. In the Real World they claim that they do, but they don’t.’
‘Don’t they?’ asked Alice.
‘No. I’ve heard it said, though I can scarce believe it, that their politicians ordain that a poor girl like you when faced with the choice between starving or taking out a payday loan is better off if she has only the one option, that of starving. No pedantic worries about contraction there (though I suppose your waist would contract, now I come to think of it). But this doesn’t bother me: like their politicians, I am rich, a Queen in fact, as my name suggests’.
‘On reflection, I will revert to chocolate, please. And do they have any other axes there?’
‘Axioms, child, not axes. And yes, they do. They’re rather keen on what they call their expansion axiom – the opposite, in a sense, of their contraction axiom. What if Uni had returned from the kitchen saying that they also had frumenty – a disgusting concoction, I know – and you had again insisted on tea? Then as well making your teeth go brown you’d have violated that axiom.’
‘I know I’m only a little girl, Your Majesty, but who cares?’
‘Not I, not one whit. But people in the Real World seem to. If they satisfy both of these axiom things they consider their choice to be rational, which is something they seem to value. It means, for example, that if they prefer coffee to tea, and tea to chocolate, then they prefer coffee to chocolate.’
‘Well, I prefer coffee to tea, tea to chocolate, and chocolate to tea. And why shouldn’t I?’
‘Because, poor child, you’ll be even poorer than you are now. You’ll happily pay a groat to that greedy little oyster over there to change from tea to coffee, pay him another groat to change from coffee to chocolate, and pay him yet another groat to change from chocolate to tea. And then where will you be? Back where you started from, but three groats the poorer. That’s why if you’re not going to be rational you should remain in Wonderland, or be a politician.’
This little fable illustrates three points. The first is that rationality is a property of patterns of choice rather than of individual choices. As Hume famously noted in 1738, ‘it is not contrary to reason to prefer the destruction of the whole world to the scratching of my finger; it is not contrary to reason for me to chuse [sic] my total ruin to prevent the least uneasiness of an Indian’. However, it seems irrational to choose chocolate when the menu comprises coffee, tea, and chocolate; and to choose tea when it comprises just tea and chocolate. It also seems irrational to choose chocolate from a menu that includes tea; and to choose tea from a larger menu. The second point is that making consistent choices (satisfying the two axioms) and having transitive preferences (not cycling, as does Alice) are, essentially, the same thing: each is a characterisation of rationality. And the third point is that people are, on the whole, rational, for natural selection weeds out the irrational: Alice would not lose her three groats just once, but endlessly.
These three points are equally relevant to the trivia of our daily lives (coffee, tea, or chocolate) and to major questions of government policy (for example, the regulation of the loan market).
Featured image credit: ‘Drink me Alice’, by John Tenniel. Public domain via Wikimedia Commons