One commonly known tendency of humans is that we are often more afraid of loss than we are motivated by the possibility of gain. While this feature of humans often works in our favor, there are many times when it prevents us from making optimal decisions. In order to make the best decisions, it is important to identify when risk aversion is wise, and when it is works against us. Let’s consider how this tendency towards loss aversion plays out in various situations:
Coin Flip Bet
Option A: Flip Coin: Heads, you win $100 and Tails, you lose $100
⫸ Probable Value: ($100 x 0.5) + (-$100 x 0.5) = $0
OR
Option B: Keep your current money
⫸ Probable Value: $0
Consistent with the tendency of risk aversion, most people would choose to simply keep their current money rather than risk the chance of losing $100, even though mathematically the options in this situation are equal:
$0 = $0
What If the Odds Are in Your Favor?
What’s interesting is that people tend to pick the more certain option even when the alternative has a higher probable value. Such is the case in the below example:
Option A: 90% chance of winning $1,000 (10% chance of winning nothing)
⫸ Probable Value: ($1,000 x 0.9) + ($0 x 0.1) = $900
OR
Option B: Guaranteed $800
⫸ Probable Value: $800
$900 > $800… but people tend to choose option B, despite it having a lower probable value.
How Framing Can Influence Decisions
Another component that can influence perceived risk is the manner in which two alternatives are framed. Consider the following study in which a hypothetical example was proposed to a sample of respondents:
Scenario: Imagine that the U.S. is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows:
Framing One
If Program A is adopted, 200 people will be saved.
If Program B is adopted, there is a one-third probability that 600 people will be saved and a two-thirds probability that no people will be saved.
Which of the two programs would you favor?
⫸72% chose Program A and 28% chose Program B (152 polled)
Framing Two
If Program A is adopted, 400 people will die.
If Program B is adopted, there is a one-third probability that nobody will die and a two-thirds probability that 600 people will die.
Which of the two programs would you favor?
⫸This time only 22% chose Program A and 78% chose Program B (155 polled)
Kahneman, D., & Tversky, A. (1984).
As you can see, framing the alternatives as either “saved lives” or “deaths” resulted in a drastically different choice for the groups, despite the fact that the two pairs of programs led to an identical number of saved lives and deaths.
What Explains This Human Tendency For Loss Aversion?
There are several proposed reasons for the human tendency for loss aversion many of which have their route in the social sciences. There does, however, seem to be one commonality between these explainations…
Law of Diminishing Marginal Utility
Marginal Utility is the economic observation that the first unit of something tends to yield the most utility, while each additional unit provides less additional utility than the one before it.
Let’s imagine you’re eating pizza in an apartment with friends. Your first slice of pizza might provide you with a hypothetical 10 units of satisfaction, while your second slice might only give you 8. If you continue this logic, by the time you make it to your 7thpiece of pizza, it may only provide you with 1 unit of satisfaction, or possibly even negative units of satisfaction, in the case that you are uncomfortably full.
Below is a hypothetical list of the marginal satisfaction (utility) one may derive from various amounts of pizza:
A logical conclusion of the law of marginal utility is that the units that you already possess will almost always provide you with more utility per unit than you can expect from any new any additional units.
Let’s say that everyone was allotted 5 pieces of pizza and you and I each only had one piece left. Imagine I then proposed a bet:
Flip a Coin For Pizza
Option A: Heads, and you can have my last slice of pizza (6 slices for you & 4 for me) but if tails, I take your last slice. (4 slices for you & 6 for me)
⫸ Probable Value: (0.5 x 6) + (0.5 x 4) = 5 slices of pizza expected
OR
Option B: Or you reject the bet and we both just eat our last slice. (5 Slices each)
⫸ Probable Value: 5 slices of pizza
5 slices = 5 slices… it would appear that both alternatives are equal, however, this assumes that every slice provides identical utility, but this simply is not the case…
If we really want to make the optimal decision, we should actually be focusing on the utility gained or lost. By considering the utility, rather than the units, we are able to factor in how much the additional units are actually worth to you in that given situation. For instance, you might be upset to lose a slice of pizza if you only had three, but if you have just eaten ten, you’d probably be completely fine losing a slice.
Not considering any possible utility that you might derive from the excitement of the bet itself, the logical decision would actually be to reject the bet. In this case, your human tendency towards risk aversion is your ally. The calculated expected utility for the two choices below should illustrate why:
Expected Probable Utility for Both Options
Option A: Accept the bet
⫸(0.5 x 6 units) + (0.5 x 0 units) = 3 marginal units of satisfaction
⫸(0.5 x 39 units) + (0.5 x 33 units) = 36 total units of satisfaction
Option B: Reject the Bet
⫸ 4 marginal units of satisfaction
⫸ 37 total units of satisfaction (5 total slices)
As illustrated mathematically above, you are better off rejecting the bet because the value of what you could lose, is greater than the value that you could potentially gain by winning the bet. In fact, assuming you value your pizza, in this situation, you would be wise to reject the bet unless you had a 67% chance or above at winning:
Break-Even Probability Point
4 units satisfaction = (0.666 x 6 units) + (0.333 x 0 units)= 4
⫸ Expected marginal utility for both options equal 4 at 66.66%
&
37 total units satisfaction = (0.666 x 39 units) + (0.333 x 33 units) = 37
⫸ Expected total utility for both options equal 37 at 66.66%
Thus you should turn the bet back on your friend and propose that you flip the coin five times. If it lands on heads on at least 2 out of the 5 flips, you win, but if it lands on tails 4 times or more, they win…. Touche
An Obvious Example Where Risk Aversion is Wise
Here’s another example in which marginal utility is clearly more important than marginal units. Imagine that we happen to meet up at a gas station and I propose another coin flip bet…
If heads, you can have one of the four tires on my car, but if tails, I will take one of your four tires.
Option A. Accept the bet: (3 tires x 0.5) + (5 tires x 0.5) =
⫸ 4 tires
Option B. Reject the bet:
⫸ 4 tires
Mathematically, these to options are equal: the average probable outcome for both is 4 tires, but no one in his or her right mind would take this bet. Without 4 tires you can’t even drive, thus, the marginal utility for the fourth tire is very high, let’s say 100 units. Conversely, acquiring a fifth tire is a burden if anything, therefore, the marginal utility of a fifth tire is around 0. Let’s look at this mathematically:
Option A. Accept bet: (-100 units utility x 0.5) + ( near 0 units utility x 0.5) = ⫸ -100 units marginal utility Option B. Reject the bet: ⫸ 0 units marginal utility
There are many other examples in nature where loss aversion is wise. Here’s another:
Winning a bet for an extra pound of meat from a fellow caveman might be nice, but the possibility of starving if you lose the bet and end up with
Option A. Reject the Bet:
⫸ keep 1 lb meat
Option B. Accept Bet: (2 lb meat x 0.5) + (0 lb meat x 0.5) + (chance of starvation)
⫸ 1 pound meat & chance of starvation
This illustrates that loss aversion is often not as irrational as most people believe: for many of the decisions made in nature, it is wise to be risk or loss averse. This doesn’t explain, however, why people tend to display loss aversion beyond the point where it is logical. That is, the degree to which people are loss averse cannot be completely explained by the law of marginal utility. For instance, humans display similar risk aversion to money– a resource with a utility curve so steep than most will never come close to its diminishing marginal returns. For example, the difference in the utility of your 999th dollar is almost indistinguishable from you 1001th.
I propose that this incongruency is the result of humans evolving to access the utility of concrete goods such as food or offspring. Our wiring is not fully equipped to make a highly accurate, intuitive risk analysis for abstract concepts such as money.
Implication
By considering what we stand to lose or gain in terms of marginal utility, we are able to overcome our often irrational human tendency towards risk aversion and optimize our decisions.
References:
Kahneman, D., & Tversky, A. (1984). Choices, values, and frames. American Psychologist, 39(4), 341-350. http://dx.doi.org/10.1037/0003-066X.39.4.341
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