# 5 Notation

Before we get into our analysis of decision-making under risk and uncertainty, I will introduce some notation.

Suppose we have a lottery L with n possible outcomes x_1, x_2, ..., x_n each with probabilities p_1, p_2, ..., p_n. A shorthand way to write this is:

L=(p_1,x_1; p_2,x_2; ...; p_n,x_n)

For example, suppose you are offered a gamble with a 50% probability of winning $200 and a 50% probability of losing $100. We can write this as:

L=(0.5, −100; 0.5, 200)

The order of each outcome-probability pair does not matter. I could also write:

L=(0.5, 200; 0.5, -100)

You may also see gambles represented with the outcome and probability in a different order, such as:

L=(x_1,p_1; x_2,p_2; ...; x_n,p_n)

Or:

L=(x_1,x_2,...,x_n;p_1,p_2,...,p_n)

It is typically not difficult to determine which is which.