The Lottery-Insurance Paradox

September 6th, 2020 by 

Why would a rational person purchase insurance yet also play the lottery? It's a great question - let's discuss the lottery-insurance paradox.

Insurance and Lotteries are Opposites

This is a paradox that has puzzled economists for a long time. Think about it, a lottery is the exact opposite of insurance.

When it comes to insurance, a person purchases coverage to hedge against risks.  In a lottery, sums are spent for a long-shot chance at the 'risk' of a payoff. 

People are risk-seeking when it comes to playing the lottery yet risk-averse when it comes to purchasing insurance. What gives?

A Primer on Insurance

There are all sorts of types of insurance:

  • auto
  • home
  • life
  • health
  • death
  • even body-part insurance
  • and a universe of many more.

In exchange for a recurring or one-time fee, a policy's holder hedges against some event occurring - say, in the case of body-part insurance, damage to a limb. If that event occurs, the policy's issuer will pay out according to the details of the policy. This might be a lump sum in the case of life insurance, or the cost to repair damage to a vehicle in car insurance. 

In the insurer - insured relationship, the insured reduces risk by buying the policy while the insurer spreads risk by issuing many policies. The insurer attempts to collect total premiums or lump sum payments in excess of the cost of a negative event, and invest any money collected in the meantime.

To explain why a risk-seeking person might acquire insurance, it's best to keep a few things in mind.

First, some forms of insurance come with a job, commonly health and life insurance. Other forms of insurance are required - for example, home insurance is required for a mortgage, and car insurance is required to operate a car in many states.

All of that doesn't quite get to the heart of the issue - take car insurance, for example. 

Car insurance laws come with mandated policy minimums. In many cases, you can purchase cheap car insurance and set your coverage to the lowest allowable amount. In some states, you can even self-insure with sufficient reserves.

However, in many cases even people with risk-seeking personalities will get more insurance than mandated.

Winning the Lottery-Insurance Paradox

The Lottery-Insurance Paradox, illustrated by a 1995 Saab 900s
My Old Saab 900s... Only Had Cheap Insurance on It!

The lottery (and gambling in general) is the opposite. 

The 'risk' event is actually a benefit to the holder of a fractional claim on the prize.

In a lottery, a claim holder pays an agreed upon amount for a fractional share of a prize. The lottery itself generally has some defined payout which goes to a certain number of people at the end of the lottery. 

A gambler purchases a ticket or some other claim, and the lottery makes money by setting the total payout of the lottery to less than is collected in claims and administrative and advertising costs.

It's a big business - in many cases governments will actually run lotteries.

An Economic Conundrum! Risk-Seeking Behavior

See the problem? 

Lottery playing and gambling is inherently risk seeking. The games guarantee that you pay something into the system, while placing risk on the holder of the lottery and transferring risk to you. 

On the other side of the coin, insurance guarantees you pay some amount for a policy but it will transfer your risk to the policy writer.

How can we rectify a rational actor both participating in a lottery and buying insurance?

Our friend (the Nobel Prize Winning) Daniel Kahneman and his colleague Amos Tversky developed Prospect Theory in part because of this conundrum. Recent studies point to a genetic connection with risk preferences, which even suggests that one gene can make folks tend towards more lottery playing (and less insurance buying) or the opposite.

If the lottery-insurance paradox is enough to get the Nobel committee to toss out Nobels, it's enough for us to think about. Here are some questions for you to think about:

  • Why do gamblers buy insurance?
  • Do you think that people are, in general, over or under insured?
  • How do you think moral hazard affects the behavior of insurance purchasers, especially the risk-seeking variety?
  • How do you explain the lottery-insurance paradox?


PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.

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