For example, while other markets and the real world moves on, you gain info. So the later in the batch you can submit a trade, the greater your advantage.
Technical/practitioner notes:
1. Gaming is a bit of an overloaded term, and in this context, implies that agents are doing something wrong. Mechanism design assumes that agents will respond rationally and strategically to the mechanism they're presented with, so whatever happens is on the designer. Ideally, the mechanism chosen will result in an individual response that collectively optimize the designer's objective function, e.g., maximizing social welfare or the auctioneer revenues. Suppose the mechanism chosen isn't the "best" one for a specific set of agents & goods. In that case, agents might have individually rational behaviors that result in sub-optimal outcomes relative to what was achievable with another mechanism.
2. Prop 6 isn't entirely predicated on having a random call time (there will be competition over price as long as there are two "fast" types in the market). However, randomizing auction call times is still practically speaking useful.
Open and closing auctions are batch auctions.
To facilitate liquidity seeking, the major exchanges publish a periodic "imbalance" feeds in the minutes and seconds up to the auction. As you can imagine, its gamed in a multitude of ways, including special order types (D-Quotes on the NYSE anyone?) that only a select few market participants know about or have access to.
The point is, whatever mechanism you choose: over time that mechanism morphs and transforms. New options are provided under the guise of liquidity seeking but really serve to benefit the HFTs.
How does a priority queue work?
If the trades are priority queued, then you have just recreated the speed "arms race" that this idea hopes to eliminate.
Maybe it cancels out the advantage of being ‘first’? I am admittedly well outside my area of expertise.