The notions of luck and risk are closely related. Many of the luckiest events we can imagine occur in situations where there is a large amount of risk involved. Being the only survivor in a plane crash or winning roulette after betting one's life savings on one spin are examples of very lucky events that occur in situations where there is a lot of risk involved. In this essay, I aim to investigate the conceptual connection between luck and risk. More specifically, I aim to explain the former in terms of the latter.
Let me start with a quick overview of the philosophical literature on luck so as to frame the discussion. Philosophers who have theorized about luck have characterized the notion using three types of conditions: (1) chance conditions, (2) lack of control conditions, and (3) significance conditions. The core idea of chance conditions is that lucky events are by chance. Lack of control conditions roughly say that an event is lucky for an agent only if the agent lacks control over it, whereas significance conditions say that an event, even if chancy or beyond the agent's control, cannot be regarded as lucky unless it is significant to the agent.
Each type of condition has several versions, depending on how the relevant notions of chance, control, and significance are cashed out. For example, depending on what is thought to determine the chance of an event occurring, the chance condition is or might be formulated in terms of: (1.1) accidentality (the idea is that whatever makes an event accidental is what makes it chancy);1 (1.2) indeterminacy (the idea here is that chancy events are events that were not determined to occur prior to their occurrence);2 (1.3) subjective probability (under this interpretation, the chance component of luck is cashed out in terms of what is expected to occur by the lucky agent);3 (1.4) epistemic probability (this view states that chancy events are events that are not likely to occur given available evidence);4 the notion of being in a position to know (according to this view, luck is a matter of failing to be in a position to know that an event will occur);5 objective probability (chancy events are events whose occurrence is objectively unlikely);6 and (1.7) modality (chancy events are events that would fail to occur in close possible worlds).7
On the other hand, lack of control conditions are formulated in terms of: (2.1) failing to exploit the target lucky event for some purpose (see Riggs 2009); (2.2) not being free to do something that would help produce it and prevent it (see Coffman 2009); and (2.3) there not being a basic action that the lucky agent could perform which she knows would bring about the lucky event (and how it would do so) (see Levy 2011, chap. 2).
Finally, the significance condition is stated in terms of: (3.1) the lucky agent being able to ascribe significance to the lucky event if she were availed of the relevant facts (see Pritchard 2005, 132–33); (3.2) the lucky event having some objective evaluative status for the lucky agent (a sentient being) (see Coffman 2007, 388); and (3.3) the lucky agent having some interest and the lucky event having some objectively positive or negative effect on it (see Ballantyne 2012, 331).
As one can imagine, different definitions of luck result from combining these versions of the significance, chance, and lack of control conditions. We do not need to go into further detail here. It suffices to note that some commentators think that the three types of conditions are necessary (and jointly sufficient) for luck,8 that others drop the lack of control condition from their definitions,9 that some others drop the chance condition and go for a pure lack of control account of luck,10 and that there are alternative accounts that include neither chance nor lack of control conditions.11 It is also worth noting that most commentators think that the significance condition is necessary for luck, although this point has recently been disputed.12
With this overview of the literature in hand, we can now frame the forthcoming discussion. The aim of this essay is mainly positive— namely, to give an account of luck in terms of the notion of risk. This means that I will not argue against the definitions of luck referred to in the preceding paragraph. In addition, I assume (with most commentators) that a properly stated version of the significance condition is necessary for luck. My sympathies are with (3.3) (this is an assumption for which I will give no argument). Finally, I will only discuss those versions of the chance condition that I consider relevant to explaining luck in terms of risk. In particular, I will not address (1.1), (1.2), (1.3), (1.4), and (1.5). However, (1.6) and (1.7) will be relevant. As regards the lack of control condition, I aim to advance my own account of the notion of control. For reasons of space, (2.1), (2.2), and (2.3) will be only tangential to the discussion.
Without further ado, let me indicate how the essay is structured. In section 1, I make a distinction between two senses of risk that serve to account for luck: the event-relative and the agent-relative senses of risk. In section 2, I present two ways of interpreting event-relative risk: in modal and in probabilistic terms. In section 3, I argue that, although both interpretations of event-relative risk seem correct qua accounts of risk, only the modal interpretation correctly accounts for luck. In section 4, I cash out the agent-relative sense of risk in terms of lack of control and I suggest that any significant event that is lucky for an agent is an event with respect to which the agent is at risk. In section 5, I categorize lucky and nonlucky cases by means of the event-relative/agent-relative distinction concerning risk. As a result, I argue that there are two different types of luck (or of fortune): one that does not involve event-relative risk and one that does involve it. I argue that both arise out of agent-relative risk (that is, lack of control over the relevant event). In section 6, I advance an account of the notion of control so as to explain in which sense an agent is at risk with respect to an event and how this bears on luck. In section 7, I summarize my view and offer a reply to several counterexamples to the lack of control account of luck.
1. Two Senses of Risk
The idea that luck can be explained in terms of risk is already in the literature. For example, E. J. Coffman interprets Duncan Pritchard's modal chance condition for luck (the condition that an event E is lucky for S only if E occurs in the actual world but would not occur in nearly, if not all, close possible worlds where the initial conditions for E are the same as in the actual world) (see Pritchard 2005, 128) as being equivalent to the view that luck is a matter of risk, where risk is understood in terms of the notion of easy possibility and easy possibility in terms of closeness between worlds, so that E could easily occur at t′ just in case it would occur at t′ in possible worlds close to actuality as they are at t (Coffman 2007, 390). Pritchard (2015 and manuscript) ratifies this interpretation by explicitly accounting for luck in terms of modal risk.13
Although the possibility of explaining luck in terms of risk is already entertained by Pritchard and Coffman, the considerations they offer on the connection between both notions are limited to only one sense of the notion of risk: the risk that lucky events had of not occurring. To be clear, there is a sense of the notion of risk that can be used to account for the notion of luck that has to do with the possible occurrence or nonoccurrence of an event, as when we say that there is risk that a World War II grenade on the tip of a cone will fall or that a talk to be given by a speaker with flu will be canceled. Let us call this sense of risk the event-relative sense of risk.
My claim (and here comes what I take to be a novel point in the literature) is that there is another interesting application of the notion of risk to the luck debate. In addition to affirming or denying that events are at risk of occurring or not occurring, we also affirm or deny that agents are at risk with respect to the possible occurrence or nonoccurrence of events, as when we say that ...
