What is it about “risk” that makes it so hard for people to evaluate?

I've thought about this for a long time, but it came to head recently while listening to a conversation about, of all things, lottery tickets. Here's the simple scenario – People pay for a lottery ticket in the hopes of winning prizes, even though the probability of winning is extremely low.

Let's deal with this question by introducing a concept many people may not be familiar with - "Expected Value." If something costs a dollar, a rational consumer should expect at least a dollar of value from it. Often, the object purchased is one where the rational consumer applies some personal judgment in establishing the value. For example, one person might feel that a dollar for a small chocolate bar at the local quick-mart is too costly and refrain from purchasing it; whereas, another person might be in the throes of an irresistible urge for a chocolate fix and happily pays the price. The same thing applies to just about any purchase of this kind, from a loaf of bread to an SUV. (This is not an appropriate time to discuss the difference between a necessity and a luxury. In principal, this applies to anyone with any money to spend, even if deciding between food and prescription drugs.)

Sometimes though, the value may be intrinsic, that is integral to the object such as a readily exchangeable commodity like gold or silver (though that would usually cost more than a dollar.) Another type of purchase that may be considered to have an intrinsic value is the “significant” business purchase or investment, where various aspects of the purchase and use of the object can be analyzed and quantified, then presented in a way that helps the rational consumer (business owner, in this case) make a decision about the purchase.

… which brings us back to the lottery ticket.

Lotteries usually have clearly stated conditions and procedures that make the probabilities of winning equally clear. As an example, the multi-state Mega-Millions game in the United States offers a grand prize with the odds of winning fixed at about 175 million to one. By way of contrast, given that on average 1,000 people in the United States are struck by lighting each year, then the odds of an individual getting hit by lightning on a given day is approximately 109 million to one. So, on the day they do the lottery drawing, you’re more likely to get hit by lightning than to win the grand prize.

The neat thing about the lottery though is the fact that you can actually work out the actual – or I should say the “expected” value of a one dollar selection of numbers (with of course some margin for error.) Let’s keep it simple for the moment and think about flipping a coin, where the odds are two to one for either heads or tails. Without going into all the theory behind it, if you were to make bets of one dollar on each flip, you would want to be paid two dollars for every win so that over time you’d at least come out even. You get paid two dollars, but there are two possible outcomes or odds of two to one. Divide the prize ($2) by the odds (the 2 outcomes) and you get one dollar – the “expected value” of any given flip of the coin. 

The same logic holds for the lottery. If the odds of winning the Mega-Millions grand prize are 175 million to one, you would want the grand prize to be at least 175 million dollars! (Beyond this simple analysis, it gets really complicated. For example, would you want to add in the “expected values” of all the other smaller prizes? Or, what if you decided to consider that as the prize gets larger more people will play? How many people have to play before the probability of more than one person choosing the winning numbers becomes significant and you would have to share the prize?)

The Issue of Rational Decision Making

If it’s only rational to buy a lottery ticket if the expected value equals or exceeds the cost, why is it that people buy lottery tickets when prizes are much too small to justify on an expected value basis? More to the point of this discussion: Why wouldn’t a business owner make all purchase decisions based on an “expected value” approach? One reason, which probably applies more to a lottery ticket than a business decision is the emotional component of the decision. Dreams of becoming an overnight multi-millionaire can have a way of affecting your decision making process. Alternatively, it’s probably more likely that the cost of the investment has an impact on the decision. At a dollar a chance, the bargain seems so cheap compared to the possible payoff (not the expected value!) that people will play the game.

A parallel business decision might be the relatively minimal costs of say, office supplies. Getting involved in every decision to buy a box of paper at the best price would cost more than the possible savings. The decision process allows for some leeway in minimizing every cost because of the possibility you’d incur additional unexpected costs somewhere else in the business, like the loss of productive time of highly paid resources (supervisors, managers, the owner, …)

Then the questions become: How do you balance the need to make important decisions vs. the unknown costs of getting too deeply involved in every decision? The answer lies in the science/art of Risk Management, another subject I've thought about for a long time, though that will have to wait for another entry at another time.