So A) there are lots of markets that do pro-rata matching (larger orders get priority). B) there is a very reasonable bias against non-repeatable matching algorithms in current markets.

If you did randomized matching and 1 market participant seemed to have very good "luck", how could you convince the other market participants that the fix wasn't in? You have to understand that modern markets assume the worst case when it comes to collusion, insider trading, etc. Randomized fills is the worst case scenario given those assumptions.

>there is a very reasonable bias against non-repeatable matching algorithms in current markets.

What about psuedo-random that uses the trades themselves as a source of entropy?

Perhaps publicise the random numbers used at the same time as the order is executed, together with the identifier for the particular trades in the queue.

Publishing the number would not in any way, alleviate the concern that the system was not fair. You are thinking about this problem from a mathematics stand point when the issue is a social one.

I plead guilty to approaching from a mathematics PoV. My sole intent is to overcome the tyranny of distance and exploitation of the time difference. The only people I hope to convince are other, mathematically sophisticated traders. By social do you mean the public-at-large's suspicion?

1, 1, 1, 1, 1... Can you verify if this sequence is random or not?

OK, I'm lets stipulate that I am not particularly mathematically sophisticated.

However, I thought that you had a list of numbers at least as large as the number of trades expected in the 5 minute period, then you could order the trades by shuffling the numbers. I think it would not be too taxing to determine whether the sequence over time is random enough.

That said, I'm starting to see whether that it would impossible to know whether any particular 5 minute (or maybe day's worth) of trading is random enough. Perhaps crypto can come to the rescue here. Publish lists of random numbers in advance pgp signed.

Anyway, enough of my ramblings :-)

Or add a few hundred milliseconds of random jitter to the transaction time. This would remove any advantage to low-latency traders.