How Much is Luck Worth?

Disparity of income is self-generating. Once present, it controls individual choices, which tend to preserve it.


In discussing the value of the time of a gold prospector, operating in a situation like one of the historical gold rushes, it became clear that the most valuable component of what the gold prospector brought to the situation was his secret clues, which could have been obtained by illustrious or nefarious means. In the absence of secret clues, identical gold prospectors would achieve their results through the operation of luck, or chance. The gold prospector with the most luck might obtain a bonanza of gold, able to be exchanged for almost anything else, and the other would have a net negative return on their time, effort, and expense.

Gold prospectors might not ascribe the success of the few to luck, but might maintain it was due to diligence, persistence, hard work, acuity, or some other personal attribute. No matter how these other factors played into the result, there was a large component of luck. Similar, the obtaining of secret clues depended in part on luck as well.

Is it the essence of the Just Deserts economic policy that luck is to be compensated for, and that effort and the quality of the effort that is to be rewarded? Before considering eliminating or reducing the effect of luck on personal success, it might be good to consider its value to society as a whole.

Luck is a motivator. Motivation operates on two levels. One is to induce individuals to participate in some activity. In the gold prospector example, each prospector hopes he has the luck to find a lode of gold and achieve a bonanza of wealth and the accompanying good fortune. Those who had no belief in the possibility of their own luck would have less motivation to commit the time, effort and expenses to the task of gold prospecting. So there is a sorting process as well as a beckoning. Those who are optimistic about their own luck may need the call of the gold rush and head for that area; so also might those who are desperate.

Those who do not but could have are the ones who have some tolerable level of satisfaction with their current situation. They may not have the same utility for large amounts of money, or have a low tolerance for risk and gambling. They may have a low tolerance for the experience that is involved with the activity, which might involve very discomforting situations. They might have a low tolerance for novelty, as this activity is not anything that they were familiar with.

The ones who do go are those with some personal optimism, both that they would be successful and have the luck that was needed, but also that any potential discomforting situations will not be too bad and be tolerable, and that any novelty will not be beyond their ability to adapt and incorporate it into their lives. They also have to have a high utility for money, perhaps a quite false one, as the utility of money for satisfying physical needs is quite limited and saturates at a fairly low value. The excess utility has to arrive from psychological needs, perhaps by allowing them personal interactions, such as respect or love, that they were unable to find in other ways. This expectation of psychological benefits provides the motivation and the optimism.

This sorting process may have a very great value for society. By having a situation, like a gold rush, that makes such individuals separate themselves and undertake the mission to prospect for gold, they are found or rather find themselves, and move to the area where they can begin their quest.

Consider the alternative, which might happen in an era where there was more widespread governance and control by some central authorities. When the first report of gold comes in, the governance figures decide how many people will go and grants licenses to them, with the agreement that they would return all or most found gold to the governing body. In return they would be paid some just amount for their time and effort, and the governing body would cover the expenses.

Provided the bonus of a percentage of the found gold was not too large, the same sorting process that worked in the ‘Wild West’ type of winner-takes-all gold rush would not happen, but instead a very different one. Those who saw this as an opportunity for a higher income that what they were doing previously would be the applicants for the licenses, and essentially for the employment by the government. And this is where the second type of motivation kicks in.

Someone who is being paid for their time, with little benefit for success in the tasks they are attempting, and little expectation of such success, would soon realize that performing that task in the easiest possible way would be the best choice for them. That means the probability of success would be lower, and possibly considerably lower. If a hundred thousand gold prospector years would be necessary under the original gold rush rules to find the majority of gold in a gold rush area, perhaps two or three or four times as many would be required if the gold prospectors each had little interest in success. Perhaps ten times as many would be required. What happens is that by sorting out highly optimistic and highly motivated people by the first type of gold rush rules, the efficiency of the process is maximized. It could be said that in the society as a whole, there is a small subset of people who are willing to make a great personal sacrifice in order to have a chance at high rewards. They are optimistic about the rate of success, and that optimism, false as it may be, causes them to exert themselves to the highest level possible to obtain the rare but large reward.

What would be the effect of the bonus? If the likely bonus were small, none, and if very large, it would make the government-controlled situation almost as desirable as the uncontrolled one. What is very large? This depends on the distribution of incomes and wealth in the existing society. Images of possible futures depend upon example. In a society where there was a limited dispersion of wealth, maybe a factor of five, the bonus required would not nearly have to be so large as if there was a huge dispersion of wealth, perhaps a factor of a hundred or a thousand. Because the psychological utility is what motives the optimistic gold prospectors, rather than physical utility, the scale involved is a matter of what they have observed.

This can be restated. In a society where there is a great dispersion of income and wealth, it would be more costly for a governing body to attract and employ highly motivated gold prospectors. A larger fraction of the value of the gold they found would go to them. In a society where there was only a limited dispersion of wealth and income, the costs would be less, and the governing body would receive more. This could be spent, in a situation where the governance was not so corrupt as to divert most of the receipts of the gold prospecting to the benefit of those in the government or their external associates, there would be more gold and therefore more money available to spend on the goals of the government, such as infrastructure, research support, charity, and defense, or equivalently, less taxes would be levied as the gold income would displace some of that.

The value of luck in a situation where there is governance with extensive control can be much less, in absolute terms, if the society in which it is embedded has few or no examples of very disparate incomes or wealth. This is a peculiarity of how a certain group of individuals, those who are highly optimistic and highly motivated, render their psychological utility. Once they have been impressed by examples of extreme disparity, that becomes the goal, and then the costs to direct them to some task where luck plays a large role becomes much greater, by the same measures as the disparity.

There would be a distribution among this set of highly motivated, highly optimistic individuals, and even in a situation of high disparity, there might be some who would be attracted by a much lower return on their effort. How many depends on some difficult-to-determine factors in the society. This does not change the basic result, that individuals, who think they have a lot of luck and are highly motivated to find opportunities to exploit that situation and turn their position in society from one in the lower levels to one in the higher levels, would need to be rewarded in most cases by something commensurate with the difference between these lower levels and the higher ones.

Time doesn’t play too much of a role here, as once the example is set, if society changes toward a lower disparity, the psychological utility of the individuals who might be motivated to take large risks would not immediately change. Perhaps over a long time, it might, or there might have to be a generational effect. This could be thought of as another feedback effect, where high levels of disparity lead to mechanisms, such as something analogous to gold prospecting, which would tend to keep them that high or raise them higher.

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