(Having seen your edited and clarified comment, I think we basically agree.)

> the version where the market influences the decision is the much less effective way to do things.

Okay, so two possible scenarios: "market influences decision" and "decision influences market."

1. Polymarket offers a contract called something like: "Will the US launch any lethal boat strikes in the Caribbean on April 30, 2026?" A commander of a drone unit for the US military bets $500 on "yes". At 11:51pm on April 30, he's trying to decide whether or not to issue an order to fire on a boat, or to wait 15 minutes for better visual identification of the target. As a result of his bet on Polymarket, he's strongly incentivized to issue the order right now.

2. It's 11:51pm on April 30. A commander of a drone unit for the US military is reviewing images of a potential target boat. He idly opens a browser tab to Polymarket. Lo and behold, he sees that the odds of "Will the US launch any lethal boat strikes in the Caribbean on April 30, 2026?" are at only 0.3%. He's strongly incentivized to issue an order to strike right now and to quickly buy that Polymarket contract before news of the strike breaks.

Does it matter which of these two scenarios might actually be taking place? I don't think so.