What Happens When Your Wants Loop Back on Themselves?

The Ice Cream Trap

You walk up to an ice cream cart with money in your pocket. You know you like chocolate more than vanilla. You also know you like vanilla more than strawberry. No surprises there. But then — and this is the strange part — you find that you like strawberry more than chocolate. Chocolate beats vanilla, vanilla beats strawberry, strawberry beats chocolate. You are spinning in a circle of wants.

Your friend sees this and grins. She offers to trade you a strawberry scoop for your chocolate scoop, if you give her a small candy as a fee. You agree. Then she pulls out vanilla and swaps that for your strawberry, again taking a candy. Then chocolate for vanilla — another candy. Over and over you go, losing candy each time, never settling on a favorite. That is the trap of cyclic preferences, and it raises a deep question: Are some wants simply irrational? And what is a preference anyway? Philosophers and economists have wrestled with this puzzle for over a century.

What Is a Preference, Anyway?

A preference is not just saying “I like this.” It is a comparative evaluation: you judge one thing as better, worse, or equal to another. When you prefer chocolate to vanilla, you are ranking them. That ranking is subjective — it belongs to you, not to the universe. Saying “this ice cream is better than that one” is not like saying “this rock is heavier.” It tells us something about you, not some weight you can measure on a scale.

For a long time, thinkers assumed preferences were driven by a hidden measurer of pleasure, called utility. In the 1800s, many economists believed you could count units of pleasure (sometimes called “utils”) and that people simply chose whatever gave the most. But the Italian economist Vilfredo Pareto, writing in the early 1900s, argued that we cannot actually measure pleasure. We cannot put a number on how much joy a cookie gives. Instead, we can only compare alternatives. You can say “I prefer this cookie to that apple,” but you cannot say “this cookie gives me 7.3 utils.” Pareto turned preference into the basic building block: instead of pleasure determining preferences, preferences came first. That shift launched modern economics and philosophy. Now the central question was: when are preferences rational, and what do they reveal about our minds?

Why Circles Are a Problem

Most of us assume our wants are orderly. If you prefer apples to bananas and bananas to cherries, you should prefer apples to cherries. That is called transitivity. But real life can make transitivity wobble.

Imagine one thousand cups of coffee, numbered from 0 to 999. Cup 0 has no sugar, cup 1 has one grain, cup 2 has two grains, and so on. You cannot taste the difference between cup 998 and cup 999 — they taste equally good to you. The same goes for every pair of cups that are side by side. Step by step, all the way from cup 999 to cup 0, you say each neighboring pair is indifferent (equal in value). Yet you definitely prefer the sugarless cup 0 over the extremely sweet cup 999. That clash — intransitive indifference — challenges the tidy idea that our tastes always follow a straight line.

A second famous example comes from the philosopher George Schumm. Picture three boxes of Christmas tree ornaments. Each box holds three glass balls: one red, one green, one blue. You prefer box 1 to box 2 because its red ball is prettier, even though the green and blue are the same. You prefer box 2 to box 3 because its green ball is nicer. And you prefer box 3 to box 1 because its blue ball is the most beautiful. Result: a perfect preference loop. You are cycling.

So what? The most famous argument against loops is the money pump. The idea was first sketched by F.P. Ramsey in the 1920s. Suppose a stamp collector prefers stamp A to B, B to C, and C to A. She walks into a shop holding stamp A. The dealer offers to swap A for C, if she pays 10 cents. She agrees. Then he offers B for C — another 10 cents. Then A for B — another 10 cents. The collector keeps paying and ends up with the stamp she started with, but lighter in the wallet. A trader can pump money out of her forever, simply because her wants loop.

Ramsey argued that a rational person should never be pumpable. So transitivity of strict preference (if A beats B and B beats C, then A must beat C) is a requirement of rationality. But not everyone agrees. Some philosophers point out that the money pump only works if you can keep paying a small cost for each swap — and maybe in some situations that isn’t possible. Others say that real people sometimes face choices where values genuinely cannot be put on a single scale, and forcing transitivity would be dishonest. The debate is still very much alive.

Do Your Choices Reveal Your Wants?

If preferences are rankings inside your head, can we discover them simply by watching what you pick? The economist Paul Samuelson thought so. In 1938, he proposed wiping mental talk away. Revealed preference would be defined entirely by choice: you prefer X to Y if, when both are available, you choose X. No need to talk about feelings or hidden thoughts.

This behaviourist approach keeps things tidy and measurable. But many philosophers and economists push back. Choosing a college, for example, isn’t just a direct preference — it depends on what you believe each college will lead to. You choose based on how you imagine the future outcomes, not just the college itself. Beliefs and preferences mix together. So pure choice data cannot capture your mental ranking without also knowing what you think is likely.

Moreover, you can have preferences over things you cannot choose directly. You might prefer a certain lottery ticket, or hope for sunny weather tomorrow. You cannot pick those outcomes, but the preference feels real. That is why most researchers today treat preferences as mental states that guide choices, rather than reducing them to choices alone. Functionalism offers a middle path: preferences are real because they play a causal role in explaining and predicting behaviour, even if we cannot see them directly. According to this view, a preference is like a gear in a machine — we know it is there because it makes the whole system work.

Changing Your Wants — and Judging Them

Wants are not frozen. You might care more about a treat next week than a treat next year — that is a time preference. People often discount the future: a dollar today feels better than a dollar in a month. Economists model this with a discount rate, though psychologists have found that we often discount in ways that create odd reversals — like preferring one apple today to two apples tomorrow, yet preferring two apples in 51 days to one apple in 50 days.

Even deeper, your wants can change because you judge them. The philosopher Harry Frankfurt introduced the idea of second-order preferences: you can want to have certain wants. A kid who hates broccoli might still wish she liked it — that is a second-order preference, a want about her own wants. That opens the door to criticizing preferences. The eighteenth-century philosopher David Hume argued that reason alone cannot evaluate our deepest desires. He wrote that reason is, and ought only to be, the slave of the passions. On this view, you can only criticize a preference if it is based on faulty beliefs or is inconsistent. But Frankfurt’s insight suggests another route: if your first-order want (candy) clashes with your second-order want (to be healthy), you have a reason to change.

This matters for welfare. If we try to measure how well someone’s life is going, should we count every preference equally — even foolish or nasty ones? Most philosophers say no. We need to launder preferences: filter out those that are misinformed, self-defeating, or cruel, and ask what the person would want if she were calm, fully informed, and thinking clearly. That is exactly what you do when you decide to train yourself to like a food you do not yet enjoy or to curb a habit you regret.

Why It Matters for You

Every time you pick a snack, a game, or a friend to hang out with, you are using preferences. They are the engine behind your choices. But once you know that wants can loop, you can watch out for traps. Maybe you notice a cycle in your own tastes — video game A over B, B over C, C over A — and you realize a clever trader could trick you into wasting your allowance. You can pause and ask: am I being consistent? Is there something I really value more across all these comparisons?

You can also step back and ask bigger questions. Do I truly want this, or is it just a habit? Can I change what I want, the way I might learn to enjoy a new food? When people argue about what is best for a community — whether to spend money on parks or roads — they are wrestling with how to combine different people’s preferences. The puzzles you met here, from money pumps to second-order desires, are the same puzzles that philosophers, economists, and psychologists still debate in labs, governments, and courtrooms. Understanding them does not give you a perfect answer, but it hands you a sharper map. And it starts with noticing the tiny, everyday fact that you are, right now, ranking one thing above another — and that ranking is never as simple as it first looks.

Think about it

1. Imagine you have three snacks, and you would trade A for B, B for C, and C for A, each time paying one gummy bear. How many trades would you make before you stop? What could break the loop?
2. If a friend says “I hate running, but I wish I loved it,” is that a real want? Can someone truly have wants about their wants?
3. Could a robot have preferences if it always picks the same flavor of slushie? Or does a real preference require feelings inside? What would you need to see to believe a machine genuinely prefers one thing over another?