Part II: The glass isn’t half-empty or half-full. It's just complex or simple

In the previous article, I presented the problem of gut instincts and personal preferences in decision-making and argued that we need a more scientific model of the basis for risk-taking and risk-aversion in decision-making. In this final part of the article I will explain how we can begin to construct a theory of rational risk-aversion and risk-taking based on the children’s game 20 Questions.

20 Questions, A Recap

In one version of game ‘20 Questions’, which I used to play as a child, one player writes down the name of a celebrity, alive or dead, and the other player has to guess the celebrity. The guesser is only allowed to ask questions with a ‘Yes’ or ‘No’ answer and is only allowed 20 questions in total before the game is over. If they guess the celebrity within 20 questions they have won, if not, they have lost. Now, how do you want to play?

Risk-taking versus risk-averse players

The usual trick with this game is to not play in too ‘risky’ a way. In the more cautious approach you divide the world of celebrities you know the names of, into two roughly evenly populated categories. For example, we may say that roughly half the celebrities we can name are alive and the other half are dead. We may expect that roughly half are female and half are male, etc. Then we ask questions using these binary categories so that half the possibilities we know about are eliminated, whatever the answer. This approach can take a bit of mental effort to do, because the categories that split the remaining set of celebrities in half might not be that obvious. Nevertheless, this strategy normally wins eventually. It is ‘dependable’ even given the uncertainty which is integral to the game. In contrast, more risky approaches, involve trying to guess in a lot less than 20 questions, and these strategies can pay off if there are several players and the first one to guess right wins the game.

The game of 20 questions is deceptive, it appears very simple, but a principle of the mathematical theory of information by Claude Shannon says that by splitting the celebrities into halves we are maximising the ‘surprise’ that we get from the answer to the questions we ask. This means essentially, that we are getting more information on average, when we say ‘Are they alive or dead?’ than if we ask more risky questions like ‘Is it Superman?’. This is interesting, because it relates risk-attitudes to gathering more, or less information in a rational way.

Explaining the two approaches: risky and less risky

The cautious approach to 20 questions means we move towards our goal in a more predictable way and we don’t assume we know the answers already. Each question, if based on a binary category moves us predictably one ‘step’ closer to our goal of the answer, but none gets us all the way at once. In contrast, the more risky strategy to guess the answer in one question may move us all the way to our goal if we think we probably already have all the information we need. However, the movement towards the goal in this more optimistic view of our current information is less predictable. We think that each time we may get all the way to our goal in one step, so the move will be high value, but most of the time we in fact get nowhere. The pattern of progress is usually less consistent and predictable than in the cautious approach when the game is actually played.

Optimism and pessimism as a complexity inference

In the story of The Tortoise and the Hare, one over-confident hare was eventually beaten by one slower but steadier tortoise as the Hare takes an over-long ‘nap’ halfway through the race. This means that the Hare thought the race was easy, and in the end it was a little closer than he thought. 20 questions, however, is about where you think you are in relation to the finish line, in terms of how much information you already have, versus how much you still need. This estimate of how much information you have relative to your goal is a crucial assumption that informs your strategy, and it looks very similar to the ‘risk-taking’ versus the ‘risk-averse’ approaches to many decisions. Interestingly, in 20 Questions, it potentially has nothing to do with subjective ideas about costs and benefits, it can be just about how much information you already have about something. That is still partly subjective, but it in principle, (and I think in reality) it can be measured, or at least estimated.

This is interesting, so it seems to me, because central to dealing with the notion of a personality for risk-taking or risk-aversion is actually an inference of the complexity of your position. This complexity estimate is actually just an estimate of how much information we already have relative to our goal. The less information we have, the more complex the problem, the more information we have, the simpler the problem. This means we can improve our decision about whether to be ‘risk-takers’ or ‘risk-averse’ in an informed way by estimating how much information we have, more accurately. If we more accurately estimate how much information we have relative to our goal before we start, we will make a better decision about whether to be ‘risk-averse’ or ‘risk-takers’. In that case the decision is a more rational, informed choice, and not merely a personal preference or subjective belief.

Future research

My research project will be filling in some of the details of the 20 Questions example, to help people, businesses and organisations make better informed decisions about risk. I will be spelling out what informed strategy choices might mean for different types of situation. I will explain in more detail how we can choose so called ‘risk-averse’ decision in a rational way, and conversely, how we can rationally decide to be more ‘risk-taking’ too. I will also relate 20 questions to the notion of rational agility which I wrote about in another blog. I will show that when things get too complex relative to our current information, it will often be more rational for agents to be more ‘risk-averse’, and like the tortoise, to proceed slowly by gathering more information, because we know we have less than we need. In other situations, when we know we already have a lot of information relative to our task, we can be more like the hare, and proceed quickly, and simply, taking risks to maximise our gains. This way we can use the notion of complexity in these terms, to be more rational about our decisions. I hope you enjoyed the discussion, and look forward to providing more to think about.

Bibliography

Weber, Elke U., Ann‐Renee Blais, and Nancy E. Betz. "A domain‐specific risk‐attitude scale: Measuring risk perceptions and risk behaviors." Journal of behavioral decision making 15.4 (2002): 263-290.