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Would this not be more fair towards traders who don't trade at high frequency?

And would it not be possible to distribute this fixed frequency to other exchanges, modulo relativity?

The reason I'm asking is because I recently learned that high-frequency traders are beating inter-market sweep orders.

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    $\begingroup$ The problem could still persist, because if all trades are executed at 1s intervals and a market cannot fulfill the orders a HFT you could still make the same order at the next stock exchange. This order would not beat the original intermarket sweep order but it would be executed at the same time. Unless you have a smart tiebraking rule this still puts the HFT at and advantage. $\endgroup$ – Giskard Nov 25 '15 at 15:59
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    $\begingroup$ Fairness is not a relevant concept when it comes to trading, it is not a sport. $\endgroup$ – Pepin_the_sleepy Nov 25 '15 at 21:54
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    $\begingroup$ Fairness may be the concern of a policymaker, however. $\endgroup$ – HRSE Nov 26 '15 at 3:15
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    $\begingroup$ Efficiency may be another concern of the policymaker and this problem disincentivizes non HFT traders from trading. Even without a policy intervention a Stock Exchange might launch such a policy to become popular. $\endgroup$ – Giskard Nov 26 '15 at 8:46
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    $\begingroup$ The French bourse (Euronext Paris) uses an auction mechanism, once or twice each dayfor the trading of certain shares. 11:30am and 4.30pm for Euronext firms, and 3pm for Alternext firms. Since this is the primary trading time for these shares this may be an example of your proposed policy. $\endgroup$ – BKay Apr 15 '16 at 9:25
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As long as trading faster is not explicitly forbidden, there will be people who want to trade faster if they can take advantage of it.

If you are able to trade fast enough, you can take advantage of arbitrage situations. For instance, if you can detect a fall in the price of soy on the New-York exchange, buy soy on the New-York Exchange, and sell it on the Chicago exchange before the price in Chicago adapts, you will profit from it.

So, on the positive side, the answer to your question in the title "Why do stock exchanges not operate at a fixed frequency?" seems to be "because it's not impossible/forbidden to operate faster and people benefit from it".

Now, on the normative side, there are certainly a fair amount of people who believe that stock exchanges would perform ``better" if they operated at a fixed frequency.

Roughly, increasing the frequency of trades is good if it allows prices to adapt faster to new economic information. Some people argue, however, that past a certain threshold, increasing the speed of trade cannot foster more effective price adjustments. The argument is that relevant economic information only arrives every so often, and there is no point in trading faster than the fastest stream of relevant information. Past this threshold -- so the argument goes, increasing the speed of trade only allows for increased high-frequency speculation in which traders benefits from arbitrage situations that are unrelated with ``actual" economic fundamentals.

I don't think they are the first to propose it, but Budish, Crampton and John have a recent pair of papers in which they advocate for a cap on the speed of transactions for similar reasons : The High-Frequency Trading Arms Race: Frequent Batch Auctions as a Market Design Response, and Implementation Details for Frequent Batch Auctions: Slowing Down Markets to the Blink of an Eye.

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    $\begingroup$ A study by the SEC in 2014 stated that very high trading frequency is "unnecessary" (below 0.2s), but failed to identify clear downsides or damages to the markets. papers.ssrn.com/sol3/papers.cfm?abstract_id=236311 $\endgroup$ – Hector Apr 15 '16 at 9:50
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    $\begingroup$ @Hector: That link is broken and I can't seem to find it based on what you wrote. Could you revise your comment and provide some more information and, if possible, a fresh link? Thanks! :) $\endgroup$ – Simon Shine Apr 19 '16 at 9:38
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    $\begingroup$ @SimonShine Indeed, the link is dead. The article is "Too Fast or Too Slow? Determining the Optimal Speed of Financial Markets", by Daniel Fricke and Austin Gerig sec.gov/dera/staff-papers/working-papers/… (seems to be 2015, rather than 2014 as I indicated in my earlier comment) $\endgroup$ – Hector Apr 19 '16 at 9:55

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