8 Mental accounting

Imagine that you have decided to see a play and paid the admission price of $10 per ticket. As you enter the theater, you discover that you have lost the ticket. The seat was not marked, and the ticket cannot be recovered.

Would you pay $10 for another ticket?

Imagine that you have decided to see a play where admission is $10 per ticket. As you enter the theater, you discover that you have lost a $10 bill.

Would you still pay $10 for a ticket for the play?

When Kahneman and Tversky (1984) asked experimental participants these questions, 46% said they would pay for another ticket in the first instance, and 88% said they would pay for a ticket in the second.

The behaviour of those who will not buy a replacement ticket in the first instance, but will in the second, involves mental accounting. Mental accounting was named by Richard Thaler (2008), who described several different ways that we form mental accounts. These include putting labels on different pots of money, and creating mental accounts that are linked to a topic or temporary occasion.

In the case of the first potential theatre attendees, $10 has already been spent in the entertainment account. They are not willing to increase their expenditure to $20.

In the second, nothing has yet been spent on the entertainment account. The loss of the $10 note does not change that, so they are willing to increase their expenditure in that account to $10.

8.1 Coding gains and losses

Mental accounting provides a hook for the application of prospect theory. Gains and losses are assessed within mental accounts. The reference point is shaped by the mental account, not their entire financial position.

Thaler (2008) asks what happens when an agent experiences two outcomes. For example, what of the following scenario:

Mr. A bought his first New York State lottery ticket and won $100. Also, in a freak accident, he damaged the rug in his apartment and had to pay the landlord $80.

Mr. B bought his first New York State lottery ticket and won $20.

Who was happier?

Suppose an agent realises a joint outcome (x, y), such as Mr. A’s outcomes of ($100, -$80). Through the lens of prospect theory, we have four scenarios to consider:

Multiple gains: If $x>0$ and $y>0$, then $v(x)+v(y)>v(x+y)$ due to diminishing sensitivity to gains. An agent will be happier experiencing separate gains of $x$ and $y$ than a single gain of $x+y$. They will be happier with the gains segregated.
Multiple losses: If $x<0$ and $y<0$, then $v(x)+v(y)<v(x+y)$ due to diminishing sensitivity to losses. An agent will be happier experiencing a single loss of $x+y$ than separate losses of $x$ and $y$. They will be happier with the losses integrated.
Mixed gain: If $x>0$ and $y<0$ and $x+y>0$, then $v(x)+v(y)<v(x+y)$. An agent will be happier experiencing a single gain of $x+y$ than a gain of $x$ and a loss of $y$. They will be happier with the loss integrated with the gain so that they do not feel the pain of the loss.
Mixed loss: If $x>0$ and $y<0$ and $x+y<0$, we cannot determine whether $v(x)+v(y)$ is less than or greater than $v(x+y)$. With a large loss $y$ and a small gain $x$, segregation might be preferred due to the diminishing sensitivity of losses. For a loss $y$ marginally greater than the gain $x$, integration is likely preferred due to the effect of loss aversion.

In the scenario above involving the lottery ticket, we have Mr. A experiencing a mixed gain. Integration is preferred to segregation: hence most people believe Mr B. will be happier.