What is the effect of a cancelled stock order on a stock and the market?

That article, like almost any article written by a non-expert and quoting only "research" from lobbying groups, hugely misses the point.

The vast majority of orders that end up being cancelled are cancelled as a standard part of exchanges' official market-maker programs.

Each exchange wants you and me to know that it has liquidity -- that when we go to buy or sell some stock, there will be someone waiting on the other side of the trade. So the exchange pays (via lowered fees or even rebates) hundreds of registered market makers to constantly have orders resting in each product's order book within a few ticks of the current NBBO or the last trade price. That way, if everyone else should suddenly disappear from the market, you and I will still be able to trade our shares for a price somewhat close to the last trade price.

But market makers who are simply acting in this "backstop" role don't actually want to have their orders filled, because those orders will almost always lose them money.

So as prices rise and fall (as much as tens of times per second), the market makers need to cancel their resting orders (so they don't get filled) and add new ones at new prices (so they meet their obligations to the exchange). And because the number of orders resting in any given product's order book is vastly larger than the number of actual trades that take place in any given time period, naturally the number of cancellations is also going to hugely outweigh the number of actual trades. As much as 97% to 3% (or even more).

But that's completely fine!

You and I don't have to care about any of that. We almost never need the market makers to be there to trade with us. They're only there as a backstop. There's almost always plenty of organic liquidity for us to trade against. Only in the rare case where liquidity completely dries up do we really care that the registered market makers are there. And in those cases (ideally) the market makers can't cancel their orders (depending on how well the exchange has set up its market maker program).

So, to answer your question, the effect of standard order cancellation on a stock is essentially none. If you were to visualize the resting orders in a product's book as prices moved up and down, you would essentially see a Gaussian distribution with mean at the last trade price, and it would move up and down with the price. That "movement" is accomplished by cancellations followed by new orders.

P.S. As always, keep in mind that your and my orders almost never actually make it to a real stock exchange anymore. Nowadays they are almost always sent to brokers' and big banks' internal dark pools. And in there you and I have no idea what shenanigans are going on. As just one example, dark pools allow their operators and (for a fee) other institutional participants access to a feature called last look that allows them to cancel their resting order as late as after your order has been matched against it! :(

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Regarding the question in your comment ...

If Alice is sending only bona fide orders (that is, only placing an order at time T if, given all the information she has at time T, she truly wants and intends for it to be filled) then her cancellation at a later time actually adds to the effectiveness of and public perception of the market as a tool for price discovery (which is its ultimate purpose).

[In the following example imagine that there are no such things as trading fees or commissions or taxes.]

Let's say Alice offers to buy AAPL at $99.99 when the rest of the market is trading it for $100.00. By doing so she is casting her vote that the "fair value" of a share of AAPL is between $99.99 and $100.00.

After all, if she thought the fair value of a share of AAPL was higher -- say, between $100.00 and $100.01 -- then she should be willing to pay $100.00 (because that's below fair value) and she should expect that other people in the market will not soon decide to sell to her at $99.99.

If some time later Alice does decide that the fair value of AAPL is between $100.00 and $100.01 then she should definitely cancel her order at $99.99, for exactly the reason discussed above. She probably won't get filled at $99.99, and by sitting there stubbornly she's missing out (potentially forever) on the possibility to make a profit.

Through the simple act of cancelling her $99.99 order, Alice is once again casting a vote that she no longer thinks that's AAPL's fair value. She is (very slightly) altering the collective opinion of the entire market as to what a share of AAPL is worth. And if her cancellation then frees her up to place another order closer to her perceived fair value (say, at $100.00), then that's another vote for her honest optinion about AAPL's price.

Since the whole goal of the market is to get a bunch of particpants to figure out the fair value of some financial instrument (or commodity, or smart phone, or advertising time, etc.), cancellations of honest votes from the past in order to replace them with new, better-informed honest votes in the present can only be a good thing for the market's effectiveness and perceived effectiveness.

It's only when participants start sending non-honest votes (non bona fide orders) that things start to go off the rails. That's what @DumbCoder was referring to in his comment on your original question.