A Short Word on Predictions

Prediction markets are a modern extension of a process called :wisdom of the crowds - the aggregated predictions of a large group of people can be more accurate than the average prediction of an informed individual or expert. Prediction markets allow traders to predict certain outcomes by buying shares. The market price will indicate what traders think the probability of a given outcome will be.

I’m curious about how well prediction markets will be at predicting city/state events in Oregon. Standard polling methods that require telephone interviews or online questionaires can be demographically skewed, have large error bars, and are static. Prediction markets offer a :lower barrier to entry to participants, incentives honesty, and :can follow real-time updates of public sentiment. I’m interested in seeing if, given enough participants, prediction markets can be more accurate than alternative polling methods at the city/state level.

:x Lowbar

At time of writing, the official US Census population counter says the US has a population of 335,911,620 people, Oregon has a population of 4,237,256, and Portland has a population of 652,503. We could ask each and every one of them about their opinion on all matters of state and culture, but that would take forever. :Statistically, Once we know how many people we need to poll to derive the national zeitgeist, it’s just a matter of getting in contact with them, right? Except that every contact method comes with baked in assumptions that will skew the results. Problematic polling pushes pollsters to phone a pool of people. Actually, almost every polling method has drawbacks. Let’s walk through them.

In-person interviews - not everyone wants to be interviewed, energy intensive, expensive, people may lie to interviewer

Landline Phone interviews - not everyone has a landline, people may lie to interviewer

Cell Phone interviews - not everyone has a cell phone, people may lie to interviewer

Online Surveys - not everyone has internet access, on the internet no one knows if you’re a dog, people may lie on survey

Mail Surveys - not everyone has a mailbox, people may lie on survey

:x Updates

Polls and Prediction Markets approach the problem of “what do people think” in fundamentally different ways. Polls are a snapshot in time. Pollsters can take several shapshots to extrapolate a trend, but the results will always lag real-time. Prediction Markets are updated real-time as information becomes available to the trading public. Press releases and news reports represent delta to be traded on.

:x Sample

Short answer: This formula - $ n = \frac{Z^2 \times p \times (1 - p)}{E^2} $

:x Galton

Source: GALTON, F. Vox Populi . Nature 75, 450–451 (1907).

Wikipedia says that Aristotle was the first to recoginize the “wisdom of the crowds”. But Francis Galton is used as the classic example. :Source

In 1907, polymath Francis Galton attended a weight-judging competetion at the West of England Fat Stock and Poulty Exhibition at Plymouth. 800 contestants were asked to estimate what a fat ox would weigh after it had been slaughtered and dressed. Being the absolute nerd that he was, Galton took the opportunity to examine the tickets after the contest. He found that the :median of the estimates (1207 lbs) was within 0.8% of the actual weight (1198 lbs). However, when he charted the distribution of estimates he discovered that 1/4 of the estimates deviated 3.7% (45lbs) above the median and 1/4 of the estimates deviated 2.4% (29lbs) below the median. Combine those two groups together and that collective represents the “average” estimate. And since we know the limits of the average we can say that the “average error” is $ \frac{1}{2} (45\, \text{lbs} + 29\, \text{lbs}) = 37\, \text{lbs} = 3.1\% $ . Since the average error is 3.1% but the median error was 0.8%, we can conclude that the aggregated predictions of a large crowd is more accurate than the average prediction.

Of course, Francis Galton was using this experiment to prove a political point, making the case that democratic judgement of the voters should be considered trustworthy. Vox populi, the title of the article, is a Latin phrase that literally translates voice of the people.

:x Median

Middle number in a set of numbers. In this case, the median number was the person who was closest to the actual weight of the dressed ox.

:x Wiki-Ari

Aristotle is credited as the first person to write about the “wisdom of the crowd” in his work Politics. According to Aristotle, “it is possible that the many, though not individually good men, yet when they come together may be better, not individually but collectively, than those who are so, just as public dinners to which many contribute are better than those supplied at one man’s cost”.

Wisdom of the crowd. (2023). Retrieved December 15, 2023, from https://en.wikipedia.org/wiki/Wisdom_of_the_crowd#Classic_examples