Proxy Measures, Sunk Costs, And Chesterton's Fence

G.K. Chesterton ponders a fence:

In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, "I don't see the use of this; let us clear it away." To which the more intelligent type of reformer will do well to answer: "If you don't see the use of it, I certainly won't let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it."

This paradox rests on the most elementary common sense. The gate or fence did not grow there. It was not set up by somnambulists who built it in their sleep. It is highly improbable that it was put there by escaped lunatics who were for some reason loose in the street. Some person had some reason for thinking it would be a good thing for somebody. And until we know what the reason was, we really cannot judge whether the reason was reasonable. It is extremely probable that we have overlooked some whole aspect of the question, if something set up by human beings like ourselves seems to be entirely meaningless and mysterious. There are reformers who get over this difficulty by assuming that all their fathers were fools; but if that be so, we can only say that folly appears to be a hereditary disease. But the truth is that nobody has any business to destroy a social institution until he has really seen it as an historical institution. If he knows how it arose, and what purposes it was supposed to serve, he may really be able to say that they were bad purposes, that they have since become bad purposes, or that they are purposes which are no longer served. But if he simply stares at the thing as a senseless monstrosity that has somehow sprung up in his path, it is he and not the traditionalist who is suffering from an illusion.

Contrast the sunk cost fallacy, according to one account:

When one makes a hopeless investment, one sometimes reasons: I can't stop now, otherwise what I've invested so far will be lost. This is true, of course, but irrelevant to whether one should continue to invest in the project. Everything one has invested is lost regardless. If there is no hope for success in the future from the investment, then the fact that one has already lost a bundle should lead one to the conclusion that the rational thing to do is to withdraw from the project.

The sunk cost fallacy, according to another account:

Picture this: It's the evening of the Lady Gaga concert/Yankees game/yoga bootcamp. You bought the tickets months ago, saving up and looking forward to it. But tonight, it's blizzarding and you've had the worst week and are exhausted. Nothing would make you happier than a hot chocolate and pajamas, not even 16-inch pink hair/watching Jeter/nailing the dhanurasana.

But you should go, anyway, right? Because otherwise you'd be "wasting your money"?

Think again. Economically speaking, you shouldn't go.

Has Chesterton committed the sunk cost fallacy? Consider the concept of proxy measures:

The process of determining the value of a product from observations is necessarily incomplete and costly. For example, a shopper can see that an apple is shiny red. This has some correlation to its tastiness (the quality a typical shopper actually wants from an apple), but it's hardly perfect. The apple's appearance is not a complete indicator -- an apple sometimes has a rotten spot down inside even if the surface is perfectly shiny and red. We call an indirect measure of value -- for example the shininess, redness, or weight of the apple -- a proxy measure. In fact, all measures of value, besides prices in an ideal market, are proxy measures -- real value is subjective and largely tacit.

Cost can usually be measured far more objectively than value. As a result, the most common proxy measures are various kinds of costs. Examples include:

(a) paying for employment in terms of time worked, rather than by quantity produced (piece rates) or other possible measures. Time measures sacrifice, i.e. the cost of opportunities foregone by the employee

(b) most numbers recorded and reported by accountants for assets are costs rather than market prices expected to be recovered by the sale of assets.

(c) non-fiat money and collectibles obtain their value primarily from their scarcity, i.e. their cost of replacement.

Proxy measures are important because we usually can't measure value directly, much less forecast future value with high confidence. And often we know little of the evidence and preferences that went into an investment decision. You may have forgotten or (if the original decision maker was somebody else) never learned the reason. In which case, the original decision-maker may have had more knowledge than you do -- especially if that decision-maker was somebody else, but sometimes even if that decision-maker was you. In which case it can make a great deal of sense to use the sunk cost as a proxy measure of value.

In the first account of sunk cost, there seems to be no uncertainty: by definition we know that our investment is "hopeless." In such a case, valuing our sunk costs is clearly erroneous. But the second, real-world example, is far less clear: "you've had the worst week and are exhausted.." Does this mean you won't enjoy the concert, as you originally envisioned? Or does it mean that in your exhaustion you've forgotten why you wanted to go to the concert? If it's more likely to mean the latter, then my generalization of Chesterton's fence, using the idea of proxy measures, suggests that you should use your sunk costs as a proxy measure of value, and weigh that value against the costs of the blizzard and the benefits of hot chocolate and pajamas, to decide whether you still will be made happier by going to the concert.

If your evidence may be substantially incomplete you shouldn't just ignore sunk costs -- they contain valuable information about decisions you or others made in the past, perhaps after much greater thought or access to evidence than that of which you are currently capable. Even more generally, you should be loss averse -- you should tend to prefer avoiding losses over acquiring seemingly equivalent gains, and you should be divestiture averse (i.e. exhibit endowment effects) -- you should tend to prefer what you already have to what you might trade it for -- in both cases to the extent your ability to measure the value of the two items is incomplete. Since usually in the real world, and to an even greater degree in our ancestors' evolutionary environments, our ability to measure value is and was woefully incomplete, it should come as no surprise that people often value sunk costs, are loss averse, and exhibit endowment effects -- and indeed under such circumstances of incomplete value measurement it hardly constitutes "fallacy" or "bias" to do so.

In short, Chesterton's fence and proxy measures suggest that taking into account sunk costs, or more generally being averse to loss or divestiture, rather than always being a fallacy or irrational bias, may often lead to better decisions: indeed if it is done in just those cases where substantial evidence or shared preferences that motivated the original investment decision have been forgotten or have not been communicated, or otherwise where the quality of evidence that led to that decision may outweigh the quality of evidence that is motivating one to change one's mind.. We generally have far more information about our past than about our future. Decisions that have already been made, by ourselves and others, are an informative part of that past, especially when their original motivations have been forgotten.

References:

Chesterton's Fence

Sunk Cost Fallacy  (1), (2)

Endowment Effects/Divestiture Aversion: 

Loss Aversion:

Cost as a Proxy Measure of Value