For an industry founded on the bedrock principle that the efficient allocation of capital is king, IPO mechanics strike me as inefficient: Money on the table, expensive fixers, etc. Auctions seem like a superficially more efficient mechanism for pricing an IPO and distributing shares. How about this:

Solicit bids for shares. After bidding, sell all shares to the bidders for the highest price at which all shares are sold.

(I suspect that this would also work well for concert tickets.)