Imagine a prediction market had an entry for whether or not someone would streak across the field during a Super Bowl. Someone might see this, buy into the market, and then go streak across the field to force the outcome to favor their position.

It’s not even theoretical. This actually happened (or rather was attempted with traditional betting markets, not prediction markets): https://www.insider.com/super-bowl-streaker-bet-on-himself-p...

Prediction markets give financial incentive to force specific outcomes. They aren’t just observations: They become incentives to influence the outcome. The bigger the market, the bigger the incentive.

I feel like this is left as an exercise to the reader and no proof is needed. Bettors in a prediction market are not divine speculators causally divorced from the real world. They are embedded, and when there are a lot of them and their financial incentives are towards a particular outcome, they might act in ways that aggregate to a greater likelihood of the event transpiring than in the counterfactual setting where they are pure observers of the simulations waging in a vacuum. It seems to me there are multiple ways to formalize and prove this and this contributes to my perception the original comment seems self-evident. If that is not the case then something is wrong in my intuition.

Numerous scandals in european soccer. an endemic problem in any big popular sport, really.

https://en.wikipedia.org/wiki/French_football_bribery_scanda...

https://www.dw.com/en/police-expose-european-soccer-bribery-...

etc etc etc

You can find many simple but observed real world examples of unintended consequences from indexing on observation by searching for examples of Goodhart's Law (which, as commonly generalized, should actually be called Strathern's Law):

"When a measure becomes a target, it ceases to be a good measure."

See Wikipedia to get started, then google search for examples: https://en.m.wikipedia.org/wiki/Goodhart%27s_law

There was a prediction market on the number of times celebrities tweet a week. Someone found one of the celebrities live streaming and kept paying them to delete their tweets.

Years ago there was a libertarian proposing this as "assassination politics": simply create a system that allows people to bet that "politician X will be assassinated before time T". People who want X assassinated take the other side of that bet. Eventually there may be enough money in the pot that someone considers it worth making the hit and collecting the bet, and the people on one side have paid for it without directly paying for it.

Markets are not based on fixed principles but are basically a game of psychology mixed with a few principles. So expectations play a big role in market outcomes.

If I had 500M to manage, I may just buy a lot of real estate in a specific place to drive up the prices in that area. I want prices to increase and with money I can create circumstances that would favor my preferred outcome.