Tuesday, September 20, 2011

Robustness and Locke's Wingless Gentleman

Our ancestors have made decisions under uncertainty ever since they had to stand and fight or run away, eat this root or that berry, sleep in this cave or under that bush. Our species is distinguished by the extent of deliberate thought preceding decision. Nonetheless, the ability to decide in the face of the unknown was born from primal necessity. Betting is one of the oldest ways of deciding under uncertainty. But you bet you that 'bet' is a subtler concept than one might think.

We all know what it means to make a bet, but just to make sure let's quote the Oxford English Dictionary: "To stake or wager (a sum of money, etc.) in support of an affirmation or on the issue of a forecast." The word has been around for quite a while. Shakespeare used the verb in 1600: "Iohn a Gaunt loued him well, and betted much money on his head." (Henry IV, Pt. 2 iii. ii. 44). Drayton used the noun in 1627 (and he wasn't the first): "For a long while it was an euen bet ... Whether proud Warwick, or the Queene should win."

An even bet is a 50-50 chance, an equal probability of each outcome. But betting is not always a matter of chance. Sometimes the meaning is just the opposite. According to the OED 'You bet' or 'You bet you' are slang expressions meaning 'be assured, certainly'. For instance: "'Can you handle this outfit?' 'You bet,' said the scout." (D.L.Sayers, Lord Peter Views Body, iv. 68). Mark Twain wrote "'I'll get you there on time' - and you bet you he did, too." (Roughing It, xx. 152).

So 'bet' is one of those words whose meaning stretches from one idea all the way to its opposite. Drayton's "even bet" between Warwick and the Queen means that he has no idea who will win. In contrast, Twain's "you bet you" is a statement of certainty. In Twain's or Sayers' usage, it's as though uncertainty combines with moral conviction to produce a definite resolution. This is a dialectic in which doubt and determination form decisiveness.

John Locke may have had something like this in mind when he wrote:

"If we will disbelieve everything, because we cannot certainly know all things; we shall do muchwhat as wisely as he, who would not use his legs, but sit still and perish, because he had no wings to fly." (An Essay Concerning Human Understanding, 1706, I.i.5)

The absurdity of Locke's wingless gentleman starving in his chair leads us to believe, and to act, despite our doubts. The moral imperative of survival sweeps aside the paralysis of uncertainty. The consequence of unabated doubt - paralysis - induces doubt's opposite: decisiveness.

But rational creatures must have some method for reasoning around their uncertainties. Locke does not intend for us to simply ignore our ignorance. But if we have no way to place bets - if the odds simply are unknown - then what are we to do? We cannot "sit still and perish".

This is where the strategy of robustness comes in.

'Robust' means 'Strong and hardy; sturdy; healthy'. By implication, something that is robust is 'not easily damaged or broken, resilient'. A statistical test is robust if it yields 'approximately correct results despite the falsity of certain of the assumptions underlying it' or despite errors in the data. (OED)

A decision is robust if its outcome is satisfactory despite error in the information and understanding which justified or motivated the decision. A robust decision is resilient to surprise, immune to ignorance.

It is no coincidence that the colloquial use of the word 'bet' includes concepts of both chance and certainty. A good bet can tolerate large deviation from certainty, large error of information. A good bet is robust to surprise. 'You bet you' does not mean that the world is certain. It means that the outcome is certain to be acceptable, regardless of how the world turns out. The scout will handle the outfit even if there is a rogue in the ranks; Twain will get there on time despite snags and surprises. A good bet is robust to the unknown. You bet you!

An extended and more formal discussion of these issues can be found elsewhere.


  1. Could it be, that the moral decisions we make, are based on recollected experience and knowledge, from which we construct our best bets? We have several ways of doing so, only one of which is pure and reliable, unbiased. It is necessary that our knowledge does not influence what we sense about an uncertain situation or a situation before an uncertain outcome. It just needs to accept the facts and what is more, understand them correctly, which in a way is jumping to conclusions, which I will explain now. When our un-influencing, uncompromising knowledge accumulates, we start to know what we know, independent from sensing what we sense (the uncertain situation). Now, and only now, it is possible to 'bet' and draw from that unbiased knowledge, sensing what we know (my definition of intuition). And it is the way that knowledge was formed and is now called for, that can and will make us predict what most likely will happen and where our bet is safe.

  2. One of the interesting conclusions of cognitive science is that we are no good at thinking; our brains will do anything to avoid having to think - retrieving knowledge of similar situations from long term memory in order to make a decision, for example. What makes this interesting is that as a decision making strategy it is not robust to non-stationarity, or in new situations. I agree that our ancestors had to make decisions under uncertainty, but it is interesting to see that those decisions are not necessarily robust ones.

  3. Are situations ever the same or similar enough for comparison, the more when they need to be retrieved from long term memory? Calling that non-stationarity doesn't seem to support it.