Efficient Markets and the Wisdom of Crowds
Efficient markets and the Wisdom of Crowds
In lecture, we discussed the idea of the the Wisdom of Crowds in the context of horse races. We began by outlining a model of betters (1…n) each with different beliefs and different wealth (w1… wn). The total wealth, then, becomes the sum of the wealth of each of these betters (which we define as w). We then said that the inverse odds (of a horse winning) in the market is the summation of taking each better’s beliefs and multiplying it by that better’s wealth share in the market. Thus, we are building our model around the assumption that everyone is essentially betting their beliefs. Qualitatively, we come to the conclusion that the equilibrium inverse odds is equal to the wealth share weighted average of beliefs. This mechanism of computing market beliefs computes the wisdom of the crowd by summing independent beliefs centered on true probability and wealth shares.
We now turn to the attached article. It posits a quantitative method that says the crowd’s prediction is made more educated by the diversity of individual predictions as long as adding more individual guesses does not increase the average individual error by too much. After this quantitative introduction, the article provides useful commentary on this concept of wisdom of the crowd as it relates to way in which people choose stocks. In this context, we see that most people will underperform the stock market but each individual prediction will be even worse than the average of all investors’ predictions.
Just as we concluded in class, this real-world example of the stock market deduces the importance of each investor’s prediction being independent in order for the wisdom of crowds phenomenon to take effect. When we are able to average each person’s intrinsic perception of the value of stock we are able to estimate with incredible accuracy the true valuation of a company. However, when discussing financial markets we find that it is intrinsically a market based on dependence spewing from discussion, day to day analysis of the markets, and constant speculation. People often pick stocks solely based on what others are doing or recommending in the moment, creating a dangerous domino effect of people making non-independent decisions, undermining the powerful accuracy that the wisdom of the crowds phenomenon is capable of having.
This feedback loop- whereby we make constantly changing decisions of buying and selling- are what create the fluctuations endemic to capital markets. This apparent irrationality in buying behavior creates a useful case study of the effects of how the concept of the wisdom of crowds can become inaccurate when we take away the crucial detail that individual predictions must be independent. This leads us to an important consideration for financial markets as aggregate- are short term stock prices nothing more than guesses? and is short term trading no better than a gamble? Maybe. But regardless, we learn an important fact- things go awry when we deter from the independence of individual guesses.