Hmm. So let's say we assign every trader a unique ID and randomly (or not) prioritize the IDs every tick. (I'm assuming you're shuffling the IDs and not the individual orders; otherwise, as jsnell points out, it averages out to the pro rata case.) The main problem I can see is that if someone can get their hands on multiple IDs, they can duplicate their orders across all their IDs and we're back to the pro rata system.

Even if you make sure to assign just one ID per trading firm, firms could coordinate to share their IDs. For example, if you're not using your ID this tick, you might place an order on my behalf for a small fee. And I'll also have sent some of my orders through an independent broker to take advantage of their ID. (Of course, if that broker places many such orders, and only some of those fill, they'll need some policy for which of their customers get the trades... maybe they could use time priority?)

It's conceivable (if unlikely) that the SEC could enact and enforce a ban on such collusion. Even then I think there would be other perverse incentives, but I'll need to think more about it.

A random ordering will create an incentive to split orders into smaller pieces. Which at the limit is going to devolve to the the proportional fulfillment case once everyone submits only orders of the minimum size.

Weight the orders by size.

That's exactly what pro rata does.

I was gonna post a comment saying what they meant was obvious, but then I just went "ohhhh." * That's actually quite an annoying little problem there.

One work-around might be to add rules to the exchange forbidding the placing of multiple bids by the same entity at the same price, and then allocating randomly.

This is also reminding me of the Talmud's descriptions of how to pay off debtors when there isn't enough money to go around: http://mindyourdecisions.com/blog/2008/06/10/how-game-theory... Such a system could work for exchanges too, although it still encourages over-bidding.

Surely also over-bidding has its own risk/reward curve so it would be reasonable to allocate pro-rata and let people work out how much to over-allocate.

* And realised what the implications were.

What you see as "an annoying little problem", I see as a sign that the system is consistent and robust. It's a good thing that the system doesn't distinguish between a hundred one-share orders and a single hundred-share order; such a distinction would be totally arbitrary. (By contrast, ranking orders by time is not arbitrary. All else being equal, it's better for things to get resolved faster; the only question is whether we're giving too much of a reward for too little of an improvement.)

Elsewhere in this thread (http://news.ycombinator.com/item?id=3856015) I argue against treating orders differently based on the "entity" that placed them.

In general, we want traders to spend their time thinking about asset prices and risk, not market structure and game theory. The price-time priority system is a very simple one that rewards traders for deciding what they want and then announcing it right away. All the modifications that have been proposed in this thread encourage traders to play games, second-guess one another, or otherwise work around the system.

There are definitely tradeoffs, but personally I think it's better to use the cleaner system and accept the latency arms race than to add a layer of artificial incentives -- and for what it's worth, it appears that nearly every major electronic market has come to the same conclusion.

Finally, thanks for the link to the Talmud article: it was a very cool application of game theory to history. (Of course, I don't see any indication in the article that the Talmudic system would be an improvement over pro rata.)

Just referring back to this from the comments on the second part, and just wanted to mention I meant "annoying little problem" in the sense that it seems a shame there can't be other solutions, like how Arrow's Impossibility Theorem prevents achieving a perfect voting system (http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem). I definitely see what you mean about this being the most optimal solution from the point of view of actual pricing and risk. The downside though is there is profit to be made in slicing time every quicker which can't be prevented without breaking something else, but the money spent on this time-slicing is broadly wasted because it is just an arms race.

So I don't think the current solution is necessarily wrong; just annoying we can't get all the benefits and also avoid the arms race.

No problem, I very much like the Talmud article and how simple the explanation works out to being.