I think its clear that the first is the way to go. It isn't as bad for traders as it might seem (check out this: https://www.youtube.com/watch?v=ry3Fra9rHvA
[advanced mode at 2:30] which uses LMSR).
Can you think of a way for a market to be deep and liquid, without everyone having their clients open or storing more data in the blockchain? Then, do people issue shares which are themselves traded p2p? The way I have it now, one is just holding different accounts.
One difference would be that I'm not sure how difficult it is to deterministically calculate the log-math and force different computers to get exactly the same answer (same precisions, etc), but I assume we can always round up to the nearest 8th decimal or something.
I don't agree with Inkling's decision to avoid using trading terminology (for example "submit your prediction"), I think it should all be 110% Wall St. style finance (none of this "explain your reasoning" nonsense, either). I don't get why they dont have the historical price chart right there, either. These are front end decisions.