Identifying “Choice” Problems

An introduction to a particular type of decision

You may have seen or heard a reference to choice problems as a particular type of decision, whether here on The Tradespace or elsewhere. What do we mean by that? Don’t all decisions involve choices? The short answer is yes, but the longer answer is that not all choices are created equal.

When we talk about decisions, we always need to talk about alternatives: the things being decided between, be they physical objects or courses of action (or both at once!). Alternatives are defined by a set of alternative variables: if given a value for each alternative variable, you could picture a corresponding unique potential solution for the problem. For a generic decision, we generate the set of alternatives by either creatively or computationally enumerating many combinations of different individual choices about the alternative variables. Some combinations may be impossible or nonfunctional, but we are limited only by our ability to imagine and then evaluate new possibilities. We sometimes refer to decisions that are not choice problems as “design problems” to indicate that we are able to design new alternatives to suit our purposes by making different choices about the individual alternative variables.

In contrast, a choice problem is a type of decision for which we cannot create new alternatives and instead must choose from a list of predefined alternatives. The alternatives as a whole are our only choice: not the levels of the individual alternative variables.

Peanut butter can be smooth or chunky, and it can be natural or artificial. But if the grocery store only has jars of smooth+artificial and chunky+natural, then I can’t buy a chunky+artificial jar: I have to take one of the choices offered.

If this person has to pick one of these two baskets of food and can’t build their own by mixing-and-matching the contents, they are facing a choice problem.

Just because choice problems are a subset of all decisions doesn’t mean they are uncommon. Like in the example above, the purchase of a basic consumer good, which typically entails selecting one product from a list of available choices, is a decision that many people solve every single day. If we want, we can still define the alternatives using multiple alternative variables to capture how they differ (e.g., chunkiness, all-natural-ness), but this is strictly an organizational aid — the alternatives could all be reduced to a single variable (e.g., a product name or number) with no loss of information because we are not allowed to customize them or create new combinations.

At this point, another concrete example is in order. Let’s think about a hypothetical situation where I am taking a day trip to Hollywood: there are too many sights to see for me to hit all of them in one day, so what landmarks should I visit on my mini vacation? Depending on the alternatives we consider, this decision could be a design problem or a choice problem:

• If I am willing to rent a car, I can design my own itinerary. I can choose which landmarks I want to visit and in what order (the alternative variables). I can create my own combinations and then evaluate them, both in terms of my satisfaction (i.e. how many sights did I see and did I see the ones I was most excited about) as well as their cost (i.e. rental and gas money, any admission fees). Not all combinations may be valid: for example, if I put too many landmarks on my itinerary, I won’t have enough time in the day to complete it!
• Or, I could limit my decision to choosing one of the many local Hollywood tour buses. These tours could be defined by the same parameters (which landmarks in what order) but I do not have the ability to call up a tour company and demand a custom itinerary. I could use the name of the tour as the only alternative variable if I didn’t want to record all their individual itineraries, because it is a unique identifier that can be used to look up that information later.

Designing vs. Choosing: two approaches to the same decision

Design and Choice alternatives aren’t mutually exclusive: there’s nothing stopping me from considering both custom itineraries and tour buses as alternatives in my tradespace. If I do, I may need to add some new metrics to my evaluation that differentiate them (e.g., the ease of planning and being chauffeured around might give a small edge to the tour buses that offsets a non-ideal itinerary). However, once I open the door to custom itineraries it is not strictly a choice problem anymore: remember, the choice problem is a case where I have only predefined choices as alternatives.

So what do you do when you find yourself solving a choice problem? Is that a good thing or a bad thing? Should it impact your decision making process beyond the creation of the alternatives? To finish, here are some quick tips about choice problems that might help you the next time you tackle one:

• Take it easy: you deserve it — Choice problems are often considered “easier” than design problems when it comes to populating the tradespace. With no ability to make your own alternatives, there is a much lower burden of creativity required. Your only responsibility is to do your due diligence collecting the available choices, rather than determining what is feasible and what’s not. Don’t overthink this part, at least for your first pass!
• It’s all right in front of you — It is much more common for choice problems to have a “complete” tradespace than design problems. Many design problems technically have an infinite number of potential alternatives; essentially as long as any of the alternative variables is a continuous number, it could take infinite values and therefore there can be infinite different alternatives. The inability to test every alternative is a big part of the motivation for many optimization-based decision making techniques: finding the “sweetspot” of those continuous variables. In contrast, choice problems are capped by the number of existing alternatives. Sometimes that number can be extremely large and it is impossible to compare them all (as anyone who has tried to buy something on Amazon can attest), but it is common to have a much more reasonably sized set of alternatives. This makes tradespace exploration uniquely well-suited to choice problems: there’s no need to second-guess if the best solution is actually “in-between” two of the alternatives in your tradespace and no need to do analyses that estimate what is happening in those gaps (e.g. regression, Kriging).
• Stick to the fundamentals, even when no choices look good — Sometimes the constrained nature of a choice problem means there aren’t any desirable alternatives and you’ll have to choose the lesser of some number of evils. The difference between “choosing the least bad option” and “choosing the best option” is primarily psychological: don’t get in your own head about it! Use the same techniques you normally do when exploring the tradespace and attempt to figure out where the tradeoffs between your value criteria are most in your favor.
• Don’t trap yourself in a box — What if, after exploring the tradespace, you really really don’t like any of your alternatives? Consider how you could break out of the box outlined by the choices. Are there other sources of alternatives that you didn’t check yet: a different website, a different search term, a different way of accomplishing the same goal? Think about how to push the boundaries of the choices you’ve already collected. And finally, could you possibly design your own alternative instead? You might be surprised at how many things can be customized down to the studs, and leaving the box of a choice problem altogether can unlock new highly-valuable possibilities.