The Economics of Hard Choices

In economics, there are two types of numbers that we use. Cardinal numbers express amounts. For example, “one”, “two”, “three”, etc. are all cardinal numbers. You can add them, subtract them, or even take them to an exponent.

Money prices are cardinal, which is why you can calculate precise profits and loss.

On the other hand, ordinal numbers express ranks. For example “first, “second”, “third”, etc. are all ordinal numbers. It doesn’t really make sense to talk about adding (or subtracting or exponentiating) ranks.

Almost all economists believe that utility is ordinal. This means your preferences are ranked: first most preferred, second most preferred, and so on. Here is a made up value scale:

1st. Having a slice of pizza
2nd. Having $2 in cash
3rd. Having a cyanide pill

Someone with the above preferences would give $2 in cash in order to get a slice of pizza. But would rather keep their $2 than to have a cyanide pill. By the same principle, they would also prefer to have a slice of pizza to a cyanide pill.

This is in contrast to cardinal utility, which requires the existence of something like “utils”. It’s just as nonsensical to say that “Sally gets twice as many utils from her first preferred good than the next best thing,” as it is to say “I like my first best friend twice as much as my second best friend.”

Usually, this is where most discussions of ordinality as it applies to economics end. But I believe I have a new extension of this concept that affect utility theory.

A New Perspective on Ordinal Preferences

Some people are dissatisfied with the ordinal approach to utility. “Sure, I prefer pizza over cyanide,” they’ll say, “but I really, really prefer pizza. You can’t show this intensity of preferences ordinally!” In other words, they believe the ordinal approach is lacking something real that a cardinal approach could approximate.

Well, it’s true that in a specific moment when I observe you choosing pizza over cyanide, I can’t really tell “how much” you preferred it.

But one way I can model it is that in your mind, you have a value scale of all things you wanted in that moment. And that the thing that you “really, really” wanted is ranked “much, much” higher relative to the other thing.

Let’s say pizza was first on your value scale, and cyanide was 1000th. So while it’s wrong to say you preferred pizza “one thousand times” as much as cyanide, it would be correct to say you would have preferred 999 other things to cyanide.

In other words, you would rather have any one of these 999 other things instead of instead cyanide—with pizza being chief among them. This is the sense in which you “really, really” prefer pizza to cyanide. We’ve been able to express the “intensity” sentiment without resorting to cardinal numbers.

Let’s extend the example. If your choice was between pizza and sushi, and sushi was your 2nd ranked good, then we can say several equivalent things: (i) you’re closer to indifference (i.e., viewing them as the same good) between pizza and sushi than pizza and cyanide; (ii) your preference for pizza over cyanide is stronger than your preference for pizza over sushi; (iii) you prefer pizza less intensely to sushi than to cyanide; and (iv) it’s easier for you to choose between pizza and cyanide than it is to choose between pizza and sushi.

Of course, we don’t walk around with an exhaustive list of all the goods we could possibly want at any time. This fact may make it virtually impossible to empirically test this account of psychology. But this way of thinking about “intensity of preferences” is at least consistent with ordinal preferences, meaning we can better understand this phenomena using mental tools we’re already familiar with.

I believe this way of thinking is also useful in interpreting “hard choices”. Everyone is familiar with being in a situation where you don’t know what to choose between to seemingly attractive alternatives. An easily relatable example might be choosing a drink at the self-serve cola machines that are in most fast food restaurants now. You might really like both Vanilla Coke and Cherry Coke, but you can only choose one. Because you feel as though you like both of them equally, this is what makes it a hard choice.


In other words, I’m proposing the reason that this is a hard choice is because these two goods are positioned very close together on your value scale. So close, in fact, that you have a difficult time determining which outranks the other. This is what makes the choice hard.

Applications of this framework

You might object. “This might be fun to think about, it might even be a contribution to psychology. But what implication does this have for economics—that is, the science of human action?”

My answer is this: when presented with a difficult choice, a person will choose to wait instead of choosing instantly. Waiting allows them to collect more information, deliberate more, and consider other options.

(More formally: a person facing a choice between two goods that are indistinguishably close on their value scale will not choose either good in the present period; instead, they will postpone the choice to a future period where they expect to have a larger information set.)

How can we apply this framework to the real world? Before we begin, note well that hesitation is itself an action. And as an action, it has a place on the individual’s value scale. For an entrepreneur, this has at least two implications.

First, the entrepreneur’s consumers may be facing hesitation because they can’t choose between the goods on sale. Think back to the cola examples. It’s possible that you’re in such a rush that the hesitation is not worth your time. The consumer may choose not to buy cola at all.

Second, I believe this approach can shed new light on the issue of so-called “transfer pricing”. While transfer pricing typically is used in the context of tax ramifications to a firm that is trying to buy or sell assets from a subsidiary, we can generalize the concept by considering how a either a very large firm that has “horizontally integrated” by buying and selling inputs for its final product from itself, either because it has grown so large that it’s merged with all its competitors and suppliers, or it has a government monopoly where no other firm is allowed to produce that input. In short, if a firm has monopolized the production of inputs to the extent where no market prices exist for them, how should he calculate his own costs (and therefore profits)?

Murray Rothbard was the first to observe that in effect a firm that has grown so large where this is a problem has become a socialist economy. And just as how a socialist economy can’t produce efficiently without market prices, neither can this hypothetical firm. (For more on this point, see pp. 659-660 of Murray Rothbard’s Man, Economy, and State with Power and Market.)

And so while the standard story of why a socialistic economy can’t rationally calculate profits and losses is based on the cardinal notions of money—without money prices, you literally cannot subtract costs from revenues—I approach from a different angle. Namely, action becomes “harder” because the lack of a market does not allow the firm (or socialist government) to observe its own ordinal rankings for its inputs. And so, the firm faces a “hard choice” in how to optimize its own production schedule.

Firms and governments also demonstrate that they’re engaging in hard choices, by establishing bureaucracies. Firms hire “transfer pricing specialists”, governments set up councils that “determine” prices, and so on. This is analogous to an indecisive person hiring a consultant to help them pick between Vanilla Coke and Cherry Coke.


In summary, a “hard choice” is when a person cannot distinguish where two heterogeneous goods rank on their own value scale. This can be demonstrated through hesitation and/or deliberation. The harder it is to establish a market price for goods, the more hesitation and deliberation will be required.

I believe this approach, if correct, can be insightful for both entrepreneurs and research. A new question that is raised is, “how do individuals, firms, and governments respond under different circumstances when faced with a hard choice?”

In a future post, I hope to extend this framework of ambiguous ordinal rankings to probabilities as well. In the meantime, I look forward to any feedback on this post.


On Capitalism and Slavery : Pêle-Mêle Comments

Last week, a debate was initiated via an article in the Chronicle of Higher Education that relates to the clash between historians and economists over the topic of slavery. The debate seems acrimonious given the article and at the reading of a special issue of the Journal of Economic History regarding the Half has never been told by Edward Baptist, its hard to conclude otherwise. Pseudoerasmus published comments on the issue in a series of posts and a Trumpian twitterstorm (although the quality is far from being Trumpian). I find myself largely in agreement with him in response to the historians, but there are some pêle-mêle points that I felt I needed to add.

On Historians Versus Economists

To be honest, when I took my first classes in economic history, it seemed clear that there were important points that were agreed upon in the literature on slavery. The first was that the accounting profitability of slavery was not the same as the economic profitability (think opportunity cost here) of slavery. Thus, it was possible that (concentrating on the US here) the peculiar institution could more or less thrive regardless of the social costs it imposed (i.e. slavery is a tax on leisure which also increases the expropriation rate from slaves, and non-slaveowners often had to shoulder the cost of enforcing the institution). This argument is not at all new; in fact it is basically a public choice argument that Gordon Tullock and Anne Krueger could have signed on to without skipping a heartbeat (see Sheilagh Ogilvie – one of my favorite economist who does history in equality with Jane Humphries). The second point of agreement is that no one agreed on how to measure the productivity of slavery in the United States and the distribution of its costs and gains. The second point has been a very deep methodological debate which related to the method of measuring productivity (CES vs Translog TFP – stuff that would make your head blow and which also lead to the self-invitation of the Cambridge Capital Controversy to the debate). The quality of the data has been at the centre-stage as well, and datasets on slave prices, attributes, tasks and many other variables are still being collected (see notably the breathtaking work of Rhode and Olmsted here and here).

Thus, I will admit to being unimpressed by the use of oral histories to contest that literature. In addition, the absence of theory in Baptist’s work yields an underwhelming argument. Oral histories are super-duper important. The work of Jane Humphries on child labor is a case in point of the need to use oral histories. She very carefully used the tales told by children who worked during the industrial revolution to document how labor markets for children worked. The story she told was nuanced, carefully argued and supported by other primary evidence. This is economic history at its best – a merger of cliometrician and historian. In fact, while this is an evaluation that is subjective, the best economists are also historians and vice-versa. The reason for that is the mix of theory with multiple forms of evidence. But they key is to have a theory to guide the analysis.

Unexpectedly for some, the best exposition of this argument comes from Ludwig von Mises in his unknown book Theory and HistoryI was made aware of that book in a discussion with Chris Coyne of George Mason University and I proceeded to reading it. I was surprised how many similarities there were between the Mises who wrote that book and the Douglass Norths and the Robert Fogels of this world. The core argument of Theory and History is that axiomatic statements can be applied to historical events. The goal of historians and economic historians is to sort which theory applies. For example, the theory of signaling and the theory of asymmetric information are both axiomatically true. Without the need for evidence, we know that they must exist. The question of an economic historian becomes to ask “did it matter”? Both theories can compete to offset each other: if signaling is cheap, then asymmetric information can be solved; if it is not, asymmetric information is a problem. Or both may be irrelevant to a given historical development. To explain which two axiomatic statements apply to the event (and in what dosage), you need data (quantitative and qualitative). Thus, Theory and History actually proposes the use of econometrics and statistical methods because it does not try to predict as much as it tries to a) sort which axiomatic statements applied; b) the relative strengths of competing forces; c) the counterfactual scenario.

Without theory, all you have is Baptist’s descriptions which tell us very little and can, incidentally, be distorted by he who recounts the tales he read.

On the Culture of Peasants/Slaves/Slaveowners

When I started my PhD dissertation Canadian economic history, the most annoying thing I saw was the claim that the French-Canadians had “different mentalities” or “more conservative outlooks”. This was basically the way of calling them stupid. This has recently evolved to say that they “maximized goals other than wealth”. Regardless, this was basically: the French-Canadian was not culturally suited for economic development.

But culture is not a fixed variable, it is not an exogenous variable. Culture is basically the coherent framework built by individuals who share certain features to “cut out” the noise. Everyday, we are bombarded with tons of pieces of information and there is no way that the human brain can process them all. Thus, we have a framework – culture (ideology does the same thing) – which tells us what is relevant and what is irrelevant and what interpretation to give to relevant information.

People can cling to old beliefs for a long time, but only if there is no cost to them. I can persist in terrible farming practices if I am not made aware of the proper valuation of the opportunity I am foregoing. For example, British farmers who arrived in Quebec in the 19th century tended to use oxen as they did in England for tilling the soil. They had probably been taught to do that by their parents who learnt it from their grandparents because it was part of the farming culture of England. The behavior was culturally inherited. However, when they saw that the French-Canadians were using horses and that horses – in the Canadian hinterland – got the job done better, they shifted. The culture changed at the sight of how important was the foregone opportunity by continuing to use oxen. Where the British and the French co-existed, both were equally good farmers. Where they could not observe each other, they were all sub-optimal farmers. Seeing the other methods forced changes in culture.

The same applies to slaveowners and slaves! Slaveowners were a more or less tightly knit group that frequented similar circles and were constantly on the lookout to increase productivity. If some master had noticed that he could increase production by whipping more slaves, why would he not adopt this method? Why would he leave 100$ bill on the street? Why did the masters growing cotton in South Carolina not adopt the method of whipping adopted by growers in Louisiana? Without a theory of how culture changes (and what purposes it serves beyond the simplistic Marxist power structure argument), there is no answer to this question. With the work of Rhode and Olmstead, there is an answer: the type of cotton that had higher yields was not suited for growing everywhere! In this case, we are applying my comment from the section above on Historians versus Economists. There are competing theories of explaining increasing output: either some slave masters were unable to observe the other slave masters and adopt the torture methods they had (which would need to be the case for Baptist to be right) or there were biological limitations to growing the better crops in some areas (Rhode and Olmstead).

Two competing theories (they are not mutually exclusive though) that can be tested with data and they set a counterfactual. That is why you need theory to make good history.

One last thing: slave owners were not capitalists

This is probably the most childish thing to come out of works like those of Baptist: to assert that because slaves were capital assets, that the owners were capitalists. That is true if you want to adhere to the inconsistent (and self-contradicting) Marxist approach to capital. In fact, as Phil Magness pointed out to me, slave owners were not free market types. They were very much anti-capitalists. Slavery apologists like Fitzhugh and Carlyle were even more anti-capitalists than that. It’s not because you own capital that you are a capitalist unless you adhere to Marxist theory.

But, capital is just a production input. Its value depends on what it can produce. As Jeffrey Hummel pointed out, there is a deadweight loss from slavery: enforcement costs, the overproduction of cotton because slavery is basically a tax on leisure and the implicit taxation of the output produced by slaves. All three of these factors would have slowed down economic growth in the south. Thus, as capital assets, slaves were relatively inefficient.