Tuesday, 13 April 2021

What we together risk: three vignettes in search of a theory

For a PDF version of this post, see here.

Many years ago, I was climbing Sgùrr na Banachdich with my friend Alex. It's a mountain in the Black Cuillin, a horseshoe of summits that surround Loch Coruisk at the southern end of the Isle of Skye. It's a Munro---that is, it stands over 3,000 feet above sea level---but only just---it measures 3,166 feet. About halfway through our ascent, the mist rolled in and the rain came down heavily, as it often does near these mountains, which attract their own weather system. At that point, my friend and I faced a choice: to continue our attempt on the summit or begin our descent. Should we continue, there were a number of possible outcomes: we might reach the summit wet and cold but not injured, with the mist and rain gone and in their place sun and views across to Bruach na Frìthe and the distinctive teeth-shaped peaks of Sgùrr nan Gillean; or we might reach the summit without injury, but the mist might remain, obscuring any view at all; or we might get injured on the way and either have to descend early under our own steam or call for help getting off the mountain. On the other hand, should we start our descent now, we would of course have no chance of the summit, but we were sure to make it back unharmed, for the path back is good and less affected by rain.

Alex and I had climbed together a great deal that summer and the summer before. We had talked at length about what we enjoyed in climbing and what we feared. To the extent that such comparisons make sense and can be known, we both knew that we both gained exactly the same pleasure from reaching a summit, the same additional pleasure if the view was clear; we gained the same displeasure from injury, the same horror at the thought of having to call for assistance getting off a mountain. What's more, we both agreed exactly on how likely each possible outcome was: how likely we were to sustain an injury should we persevere; how likely that the mist would clear in the coming few hours; and so on. Nonetheless, I wished to turn back, while Alex wanted to continue.

How could that be? We both agreed how good or bad each of the options was, and both agreed how likely each would be were we to take either of the courses of action available to us. Surely we should therefore have agreed on which course of action would maximise our expected utility, and therefore agreed which would be best to undertake. Yes, we did agree on which course of action would maximise our expected utility. However, no, we did not therefore agree on which was best, for there are theories of rational decision-making that do not demand that you must rank options by their expected utility. These are the risk-sensitive decision theories, and they include John Quiggin's rank-dependent decision theory and Lara Buchak's risk-weighted expected utility theory. According to Quiggin's and Buchak's theories, what you consider best is not determined only by your utilities and your probabilities, but also by your attitudes to risk. The more risk-averse will give greater weight to the worst-case scenarios and less to the best-case ones than expected utility demands; the more risk-inclined will give greater weight to the best outcomes and less to the worst than expected utility does; and the risk-neutral person will give exactly the weights prescribed by expected utility theory. So, perhaps I preferred to begin our descent from Sgùrr na Banachdich while Alex preferred to continue upwards because I was risk-averse and he was risk-neutral or risk-seeking, or I was risk-neutral and he was risk-seeking. In any case, he must have been less risk-averse than I was.

Of course, as it turned out, we sat on a mossy rock in the rain and discussed what to do. We decided to turn back. Luckily, as it happened, for a thunderstorm hit the mountains an hour later at just the time we'd have been returning from the summit. But suppose we weren't able to discuss the decision. Suppose we'd roped ourselves together to avoid getting separated in the mist, and he'd taken the lead, forcing him to make the choice on behalf of both of us. In that case, what should he have done?

As I will do throughout these reflections, let me simply report by own reaction to the case. I think, in that case, Alex should have chosen to descend (and not only because that was my preference---I'd have thought the same had it been he who wished to descend and me who wanted to continue!). Had he chosen to continue---even if all had turned out well and we'd reached the summit unharmed and looked over the Cuillin ridge in the sun---I would still say that he chose wrongly on our behalf. This suggests the following principle (in joint work, Ittay Nissan Rozen and Jonathan Fiat argue for a version of this principle that applies in situations in which the individuals do not assign the same utilities to the outcomes):

Principle 1  Suppose two people assign the same utilities to the possible outcomes, and assign the same probabilities to the outcomes conditional on choosing a particular course of action. And suppose that you are required to choose between those courses of action on their behalf. Then you must choose whatever the more risk-averse of the two would choose.

However, I think the principle is mistaken. A few years after our unsuccessful attempt on Sgùrr na Banachdich, I was living in Bristol and trying to decide whether to take up a postdoctoral fellowship there or a different one based in Paris (a situation that seems an unimaginable luxury and privilege when I look at today's academic job market). Staying in Bristol was the safe bet; moving to Paris was a gamble. I already knew what it would be like to live in Bristol and what the department was like. I knew I'd enjoy it a great deal. I'd visited Paris, but I didn't know what it would be like to live there, and I knew the philosophical scene even less. I knew I'd enjoy living there, but I didn't know how much. I figured I might enjoy it a great deal more than Bristol, but also I might enjoy it somewhat less. The choice was complicated because my partner at the time would move too, if that's what we decided to do. Fortunately, just as Alex and I agreed on how much we valued the different outcomes that faced us on the mountain, so my partner and I agreed on how much we'd value staying in Bristol, how much we'd value living in Paris under the first, optimistic scenario, and how much we'd value living there under the second, more pessimistic scenario. We also agreed how likely the two Parisian scenarios were---we'd heard the same friends describing their experiences of living there, and we'd drawn the same conclusions about how likely we were to value the experience ourselves to different extents. Nonetheless, just as Alex and I had disagreed on whether or not to start our descent despite our shared utilities and probabilities, so my partner and I disagreed on whether or not to move to Paris. Again the more risk-averse of the two, I wanted to stay in Bristol, while he wanted to move to Paris. Again, of course, we sat down to discuss this. But suppose that hadn't been possible. Perhaps my partner had to make the decision for both of us at short notice and I was not available to consult. How should he have chosen?

In this case, I think either choice would have been permissible. My partner might have chosen Paris or he might have chosen Bristol and either of these would have been allowed. But of course this runs contrary to Principle 1.

So what is the crucial difference between the decision on Sgùrr na Banachdich and the decision whether to move cities? In each case, there is an option---beginning our descent or staying in Bristol---that is certain to have a particular level of value; and there is an alternative option---continuing to climb or moving to Paris---that might give less value than the sure thing, but might give more. And, in each case, the more risk-averse person prefers the sure thing to the gamble, while the more risk-inclined prefers the gamble. So why must someone choosing for me and Alex in the first case choose to descend, while someone choosing for me and my partner in the second case choose either Bristol or Paris?

Here's my attempt at a diagnosis: in the choice of cities, there is no risk of harm, while in the decision on the mountain, there is. In the first case, the gamble opens up a possible outcome in which we're harmed---we are injured, perhaps quite badly. In the second case, the gamble doesn't do that---we countenance the possibiilty that moving to Paris might not be as enjoyable as remaining in Bristol, but we are certain it won't harm us! This suggests the following principle:

Principle 2  Suppose two people assign the same utilities to the possible outcomes, and assign the same probabilities to the outcomes conditional on choosing a particular course of action. And suppose that you are required to choose between those courses of action on their behalf. Then there are two cases: if one of the available options opens the possibility of a harm, then you must choose whatever the more risk-averse of the two would choose; if neither of the available options opens the possibility of a harm, then you may choose an option if at least one of the two would choose it. 

So risk-averse preferences do not always take precedence, but they do when harms are involved. Why might that be?

A natural answer: to expose someone to the risk of a harm requires their consent. That is, when there is an alternative option that opens no possibility of harm, you are only allowed to choose an option that opens up the possibility of a harm if everyone affected would consent to being subject to that risk. So Alex should only choose to continue our ascent and expose us to the risk of injury if I would consent to that, and of course I wouldn't, since I'd prefer to descend. But my partner is free to choose the move to Paris even though I wouldn't choose that, because it exposes us to no risk of harm.

A couple of things to note: First, in our explanation, reference to risk-aversion, risk-neutrality, and risk-inclination have dropped out. What is important is not who is more averse to risk, but who consents to what. Second, our account will only work if we employ an absolute notion of harm. That is, I must say that there is some threshold and an option harms you if it causes your utility to fall below that threshold. We cannot use a relative notion of harm on which an option harms you if it merely causes your utility to fall. After all, using a relative notion of harm, the move to Paris will harm you should it turn out to be worse than staying in Bristol.

The problem with Principle 2 and the explanation we have just given is that it does not generalise to cases in which more than two people are involved. That is, the following principle seems false:

Principle 3  Suppose each member of a group of people assign the same utilities to the possible outcomes, and assign the same probabilities to the outcomes conditional on choosing a particular course of action. And suppose that you are required to choose between those courses of action on their behalf. Then there are two cases: if one of the available options opens the possibility of a harm, then you must choose whatever the most risk-averse of them would choose; if neither of the available options opens the possibility of a harm, then you may choose an option if at least one member of the group would choose it.

A third vignette might help to illustrate this.

I grew up between two power stations. My high school stood in the shadow of the coal-fired plant at Cockenzie, while the school where my mother taught stood in the lee of the nuclear plant at Torness Point. And I was born two years after the Three Mile Island accident and the Chernobyl tragedy happened as I started school. So the risks of nuclear power were somewhat prominent growing up. Now, let's imagine a community of five million people who currently generate their energy from coal-fired plants---a community like Scotland in 1964, just before its first nuclear plant was constructed. This community is deciding whether to build nuclear plants to replace its coal-fired ones. All agree that having a nuclear plant that suffered no accidents would be vastly preferable to having coal plants, and all agree that a nuclear plant that suffered an accident would be vastly worse than the coal plants. And we might imagine that they also all assign the same probability to the prospective nuclear plants suffering an accident---perhaps they all defer to a recent report from the country's atomic energy authority. But, while they agree on the utilities and the probabilities, they have don't all have the same attitudes to risk. In the end, 4.5million people prefer to build the nuclear facilities, while half a million, who are more risk-averse, prefer to retain the coal-fired alternatives. Principle 3 says that, for someone choosing on behalf of this population, the only option they can choose is to retain the coal-fired plants. After all, a nuclear accident is clearly a harm, and there are individuals who would suffer that harm who would not consent to being exposed to the risk. But surely that's wrong. Surely, despite such opposition, it would be acceptable to build the nuclear plant.

So, while Principle 2 might yet be true, Principle 3 is wrong. And I think my attempt to explain the basis of Principle 2 must be wrong as well, for if it were right, it would also support Principle 3. After all, in no other case I can think of in which a lack of consent is sufficient to block an action does that block disappear if there are sufficiently many people in favour of the action.

So what general principles underpin our reactions to these three vignettes? Why do the preferences of the more risk-averse individuals carry more weight when one of the outcomes involves a harm than when they don't, but not enough weight to overrule a significantly greater number of more risk-inclined individuals? That's the theory I'm in search of here.


  1. There are some interesting points in time in this article but I don’t know if I see all of them center to heart. There is some validity but I will take hold opinion until I look into it further. Good article, thanks and we want more!

  2. Wow, thanks, great article, but i don't think that I risk much.

  3. This comment has been removed by the author.

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