I'll add another issue: iterative markets can be highly manipulable, far more so than normal prediction markets.
Let's say I build up a large stake in one of the markets (e.g. T0) by making "bad" trades - buying YES at 50% for example even though I know the "fair" probability is 49%. Then just before T0 resolves, I manipulate the price of T1 up - perhaps to 60%. If I do this right, I might take a small loss on T1, but make a big gain on T0, for a large net profit.
This has been demonstrated in practice - for example, https://manifold.markets/harfe/will-white-win-in-manifold-plays-ch was a game that used iterative markets where the final market predicts the winner of the game, and there's a market for each move N that predicts the price of market N+1 (simplifying some details). And this exact type of manipulation worked profitably - even though the market design already included some attempted countermeasures.
In a normal prediction market, this sort of thing is far far less likely to work profitably. If you attempt to manipulate the price for profit, as in a pump-and-dump scheme, you need to convince someone else to buy from you, otherwise ultimately you lose when the market resolves. This is possible but much more limited than the sort of manipulation I described.
In general, whenever the resolution of a market depends on a metric which can be cheaply manipulated, that creates much more incentive for exploits like this. In most derivative prediction markets, the main/underlying market is much bigger than the derivative market, so manipulation is usually expensive and therefore not profitable. In iterative markets, all of the markets are both underlying and derivative and are about the same size, making them very exploitable.
Iterative predictions in a non-market context (e.g. Metaculus) are much less susceptible to manipulation problems, but there's also much less benefit to using iterative predictions because they don't suffer from discount rate distortions nearly as much as markets do.
What are the tradeoffs on making the rounding more/less fine-grained?
I'll add another issue: iterative markets can be highly manipulable, far more so than normal prediction markets.
Let's say I build up a large stake in one of the markets (e.g. T0) by making "bad" trades - buying YES at 50% for example even though I know the "fair" probability is 49%. Then just before T0 resolves, I manipulate the price of T1 up - perhaps to 60%. If I do this right, I might take a small loss on T1, but make a big gain on T0, for a large net profit.
This has been demonstrated in practice - for example, https://manifold.markets/harfe/will-white-win-in-manifold-plays-ch was a game that used iterative markets where the final market predicts the winner of the game, and there's a market for each move N that predicts the price of market N+1 (simplifying some details). And this exact type of manipulation worked profitably - even though the market design already included some attempted countermeasures.
In a normal prediction market, this sort of thing is far far less likely to work profitably. If you attempt to manipulate the price for profit, as in a pump-and-dump scheme, you need to convince someone else to buy from you, otherwise ultimately you lose when the market resolves. This is possible but much more limited than the sort of manipulation I described.
In general, whenever the resolution of a market depends on a metric which can be cheaply manipulated, that creates much more incentive for exploits like this. In most derivative prediction markets, the main/underlying market is much bigger than the derivative market, so manipulation is usually expensive and therefore not profitable. In iterative markets, all of the markets are both underlying and derivative and are about the same size, making them very exploitable.
Iterative predictions in a non-market context (e.g. Metaculus) are much less susceptible to manipulation problems, but there's also much less benefit to using iterative predictions because they don't suffer from discount rate distortions nearly as much as markets do.