States with high probabilities and medium returns in the population

Yesterday I suggested that when there is a state with a very tiny probability occurs, many people are betting against the existence of the state; therefore, when the state becomes the reality, it causes greater impacts than the difference of the expected outcome and the state outcome. Today I want to further discuss this topic.

The expected outcome is the accumulation of the products of each state's probability and its outcome. However, when it comes to individual decisions, in some cases, individuals have to make their choices between several states and the expected outcomes are not guaranteed. Each individual has his/her personal risk preference and based on their risk preferences, they choose their preferred states. It is commonly believed that the majority of the population has risk averse risk preferences. If I assume that all individuals in the population have risk averse risk preferences, when a state has a higher probability, the number of people choosing this state becomes larger. When more people choose one particular state, the price for this state rises as the demand increases, so the return for the state decreases. Vice verse, the returns for states with lower probabilities become larger.

In addition, if assuming it is a zero-sum game, the overall outcome does not change, so the average return does not change and is meaningless. The median outcome or return in the population changes when we assume risk averse risk preferences or risk neutral risk preference, as the number of people choosing states with high probabilities under the risk averse risk preference assumption is greater than the number under the risk neutral risk preference assumption, the returns for states with high probabilities under the risk averse risk preference assumption are lower than the returns for the same states under the risk neutral risk preference assumption. Therefore, the median return of individuals when the general risk preference of the population is risk averse is lower than the median return and the expected return of individuals when the general risk preference of the population is risk neutral.