I have not red Michael Lewis's new book (I am a fan of his,
and have used some of his older books as texts in my courses before).
However, I have read the recent articles in the press about the book.
I do not find any logical arguments there specifically against high frequency trading. On the other hand I do see valid arguments against a whole host of nefarious practices on Wall Street such as front-running, preferential access (at a fee) to flow of orders, investment banks running their own private exchanges (dark pools), adding extra decimal places to pricing, etc. I also see a bunch of bogus arguments such as investments in high tech (use of private networks with very low latencies), superior algorithms, etc. They are bogus because the alternative is to use ancient technologies that can not support the trading volume on the market and can not facilitate liquidity, the main reason for the very existence of markets.
As long as the economy follows the power law distribution for everything there will always be some using high-powered computers and some, at the opposite end of the spectrum, using the abacus. The solution is not to slow down the adoption of newer technologies but to provide the incentive to adopt such technologies. The SEC has not been doing its homework well when it comes to market technologies. SEC should look at everything in terms of ensuring equitable access (not necessarily equal) to order data and an impartial market clearing system.
High frequency trading is a red herring. The culprit is some one else.
In
the US, until recently, the stock trading was concentrated in a handful
of exchanges, but the market was not fragmented in that VERY few
companies listed themselves on more than one US stock exchange
(exceptions include HP, and Charles Schwab). With the development of the
dark pools, the market got fragmented. There is nothing wrong with such
fragmentation per se because it does provide some benefits: increased
competition, and innovations in trading. However, it does have certain
problems: lack of transparency, greater search costs, etc. as long as
there is no single national market information system.