Understanding Expected Utility with Easy Animations

Welcome to Expected Utility - a powerful tool that helps us make better decisions.When making decisions, we need to consider two key factors.First, the probability - how likely each outcome is to occur. And second, the value - what each outcome is worth to us.Let's see how this works in a simple decision tree.Starting from our decision point, we have two main choices, each leading to different possible outcomes.Each branch has a probability - the chance of that outcome occurring.And each final outcome has both a probability and a value associated with it.Expected Utility combines these probabilities and values to help us make the best choice.Now that we understand the basic concept, let's look at how to calculate Expected Utility.Expected utility combines two key components: probability and utility value.Let's understand this using a simple coin flip example.For a fair coin, the probability of heads is 0.5, or fifty percent.Similarly, the probability of tails is also 0.5.Now let's assign utility values. Winning on heads gives us 10 utility points.While winning on tails gives us 5 utility points.To calculate the expected utility for heads, we multiply its probability by its utility value.For tails, we do the same calculation: probability times utility.Remember, probability always ranges from zero to one, where zero means impossible and one means certain.As we move along the probability scale, we can see how different probabilities affect our expected utility calculation.To measure utility values, we use a scale from zero to one hundred, where zero represents the least desirable outcome and one hundred the most desirable.Let's start with monetary values as an example. Notice how the relationship between dollars and utility isn't always linear.Now, let's look at how we measure utility for free time. The value of additional free time might vary significantly between individuals.Job satisfaction provides another example of how we can measure utility. Different aspects of a job contribute to its overall utility value.Different people may assign different utility values to the same outcome. Let's visualize this using preference curves.Person A values initial gains more highly, showing diminishing returns as values increase.Person B shows a more conservative valuation, requiring larger actual values to achieve the same utility.Several personal factors influence how we assign utility values to different outcomes.Understanding these personal factors is crucial for accurately measuring utility values in decision making.Different people have different attitudes toward risk, which affects how they value money and make decisions.A risk-averse person gets less additional utility from each additional dollar. Their utility curve bends downward, showing diminishing returns.A risk-neutral person values each dollar equally. Their utility increases linearly with money.A risk-seeking person gets more utility from each additional dollar. Their curve bends upward, showing increasing returns.Let's look at how different people might view a one thousand dollar investment with a fifty percent chance of doubling their money.A risk-averse person focuses on the potential loss. They value the guaranteed one thousand dollars more than the uncertain chance of two thousand.A risk-neutral person simply calculates the expected value, treating the potential gain and loss equally.A risk-seeking person is excited by the potential gain, valuing the chance of two thousand dollars more than the secure one thousand.Let's compare how each type of person values the same amounts of money differently.Let's analyze a simple decision: whether to take an umbrella based on the probability of rain.We have two choices: take an umbrella or leave it at home.The weather forecast shows a 40 percent chance of rain, and consequently, a 60 percent chance of no rain.Let's assign utility values to each possible outcome. Having an umbrella when it rains gives us high utility of 80.But carrying an umbrella on a sunny day is somewhat inconvenient, giving us a lower utility of 40.Getting caught in the rain without an umbrella is the worst outcome, with a utility of 0.While having no umbrella on a sunny day gives us maximum utility of 100.Now let's calculate the expected utility for taking an umbrella.And now for not taking an umbrella.Comparing the expected utilities, we see that not taking an umbrella has a slightly higher expected utility of 60, compared to 56 for taking an umbrella.Now we'll explore scenarios with multiple possible outcomes using a more complex decision tree.In this investment scenario, we have three initial market conditions: up, flat, or down, each with their own probability.Each market condition can then lead to different specific outcomes, creating a branching structure of possibilities.Each specific outcome has its own probability, which is conditional on the initial market condition.We assign utility values to each final outcome, ranging from highly positive for the best outcomes to negative for the worst scenarios.To calculate the expected utility for the Market Up branch, we multiply each outcome's probability by its utility and sum them up, then multiply by the branch probability.We do the same for the Market Flat branch, where the outcomes are more moderate.And for the Market Down branch, where we deal with negative utility values.Finally, we sum the expected utilities from all branches to get our total expected utility of twenty five point three.To compare different options using expected utility, we'll examine two investment choices.Each investment has different probabilities and utility values for various outcomes.For Investment A, we multiply each probability by its utility value. The high outcome contributes thirty points, medium adds another thirty, and low adds four, giving us a total expected utility of sixty-four.For Investment B, the high outcome contributes twenty-four points, medium adds thirty, and low adds six, resulting in a total expected utility of sixty.Comparing the expected utilities, we can see that Investment A has a higher value at sixty-four compared to Investment B's sixty.Investment A offers more consistent returns, while Investment B has higher variance in its outcomes.Based on expected utility calculations, Investment A would be the better choice, despite Investment B having a higher maximum potential utility.A common mistake is focusing only on the highest possible value while ignoring probabilities.Consider this lottery example. While the million dollar prize looks attractive, the extremely low probability makes it a worse choice than a guaranteed five hundred dollars.Let's clear this example and look at another common misconception.Another misconception is failing to update decisions when probabilities change.An investment might look good initially with an eighty percent chance of success.But if market conditions change and the probability drops to forty percent, the expected value is significantly lower, even though the potential return hasn't changed.Let's examine our final misconception about ignoring risk attitudes.Two investments might have the same expected value, but be appropriate for different investors based on their risk tolerance.A conservative option offers moderate returns with higher probability, suitable for risk-averse investors.While an aggressive option offers the chance of higher returns but also the possibility of no return, better suited for risk-seeking investors.Understanding these misconceptions helps us make better decisions using expected utility.Let's examine how expected utility helps with investment decisions between stocks and bonds.For stocks, we multiply each potential return by its probability. A thirty percent return has point four probability, ten percent return has point three probability, and a fifteen percent loss has point three probability.For bonds, we calculate similarly with their more conservative returns and higher probabilities of moderate gains.Next, let's look at how expected utility helps choose between insurance deductibles.With a high deductible plan, we consider the certain cost of premiums and the probability of paying the deductible.The low deductible plan has higher premiums but lower out-of-pocket costs if a claim occurs.Finally, let's analyze a career decision between a startup and an established company.The startup offers higher potential returns but with more risk. We calculate the expected utility considering both the upside and downside scenarios.The corporate position offers more stability but potentially lower maximum returns. The expected utility helps quantify this tradeoff.While expected utility is a powerful decision-making tool, it has important limitations we need to consider.Let's examine three major limitations: emotional factors, incomplete information, and changing circumstances.First, emotional decisions, like choosing a life partner, often can't be reduced to pure utility calculations.Second, we often face decisions with incomplete information, where we can't accurately determine probabilities.Third, utility values can change significantly over time, making long-term decisions particularly challenging.Expected utility theory works best when combined with other decision-making approaches, considering both quantitative and qualitative factors.Remember to account for emotional factors, gather as much information as possible, and regularly reassess your utility values as circumstances change.By understanding these limitations, we can use expected utility theory more effectively in our decision-making process.