How to quantify intangible costs for decision making In many situations, decision-making requires weighing multiple losses. For example, you might determine the optimal threshold for a churn classification problem by comparing the cost of offering a reduced rate and the cost of losing the customer. In any case, it is necessary to convert both costs into the same unit of measure in order to make a decision. However, some losses are very difficult to quantify and resist being converted to any sort of standard unit. These are intangible or unquantifiable losses.
Despite the challenges, these losses are often evaluated against each other and against quantifiable losses. This is done by organizations (government agencies have to compare economic costs with costs to human-life) and by individuals (people compare comfort, perception, safety, and cost when purchasing a car).
My question is not about any specific case, but about the process of quantifying non-quantifiable costs for the purpose of decision making. To simplify things, I'm asking specifically about the case where you have access to a representative stakeholder (could be an individual, a group, or even yourself) that can answer simple questions. What is the process of translating their thinking into a representative loss function?
Let me give an example.

Your mom is deciding how much food to order for the Christmas
party and she requests your help. Let's say you're given the maximum
likelihood estimate for the amount of food that will be consumed and
the error distribution is known. You want to decide how much food to
purchase in order to minimize your mother's dissatisfaction. Now in
the case of overestimating, you know that a serving of food has a
fixed cost and you might conclude the loss is linearly related to how
much extra food you purchase. However, your mom really hates not
having enough food. You know that the loss of underestimating will be
higher, and likely non-linear, but you have no idea what form it
takes, and you don't want to choose something arbitrarily.
You might
assume a sort of model for the loss exists in your mom's head since
she is capable of making decisions that weigh the two losses against
each other.

My question is, how do you go about translating a stakeholder's
subjective preferences into a quantifiable loss function? What questions do you ask? Does a methodology exist for doing this?

 A: This is maybe a bit of a cheeky response, but you're basically describing the fields of economics, psychology, and many many others :-). Each has their own approaches to the problem, and you can further combine insights from each field. I know relatively more about economics than the other fields, but most of what you wrote in your example in many ways underpin the foundations of utility theory and/or a social planner problem. In fact, in many economic models, one often assumes a representative individual that is representative of the overall economy/country/etc.
So the cheap answer to your question is: the way we go about translating subjective preferences into a quantifiable loss function is by carefully thinking about the problem, and building a model that we think is justifiable and interesting. We may start with a very general model, and then think about what assumptions we are ok adding, and which ones we are not comfortable with. In doing so, we want to remain realistic, but also want to actually learn something. To illustrate this, consider two example regarding, say, a representative individual in an economy, and we want to understand why they work instead of spending leisure time. One approach could be to think that the individual have any function that determines their preferences, and that function is infinite dimensional, and it's completely unknown. Although true, this gets us nowhere. Another approach could be to say that individuals works $5$ hours a day no matter what, so that he always spends $5$ hours working, and $24-5$ hours not working. Here, we instantly get a really precise answer, but again, I claim we learn nothing because the results came from our assumptions directly, and nothing else.
As you probably guessed, the key is to think of assumptions that seem plausible and realistic, but that still provide interesting and novel results. So maybe we assume that the individual prefers leisure to work, but also has some preference for other goods, such as food and a car. Although he prefers leisure to work, working $x$ hours means he will receive $wx$ dollars, where $w$ is the hourly wage of working. So what's the tradeoff here? Well if I work an extra hour, I lose an hour of leisure, but I gain $w$ dollars, which I could use to buy other goods I also enjoy. So we have a function that represents how much I 'like' things (this is called a utility function), and I'll also assume that more things gives me more utility (partial derivative of utility function with respect to each good is positive), but that more of one thing also gives me less and less joy (second derivative is negative). And so on and so forth. Already, we reduced the space of infinite functions to a far smaller space, and with some more assumptions, we can quickly arrive to some classic functional forms that are often used in economics, such as a cobb-douglass function. These functions are not random, but are often the result of a certain set of assumptions. Are they valid? Well that's a separate question, but I can at least explain why I think they are indeed valid for certain cases (though certainly not for all). And in doing so, by refining my class of functions and parameters I am thinking of, I can start considering what I want to ask to fit my model (this is a very simple classic model learned in intro economics courses, and you can easily read more about it online, ie here).
In your Christmas dinner example, we are technically trying to reduce expected losses of failing to host a good party, and so ways we can understand it could include: a question where we ask what percent of weekly budget would someone spend on an important party, a question asking, from a scale of 1-10 (10 is love it, 1 is hate it), how you feel about wasting 1 lb of food, 2 lbs, etc, and then another question asking how you feel about everyone leaving feeling very hungry, slightly hungry, etc...
Through this process, we hopefully learn what are the correct questions to elicit given our model and assumptions. So in some sense, your question is more a question about the entire process of research, and it certainly does not have to start entirely grounded in statistics!
