According to Wikipedia, "Illusion of control is the tendency for human beings to believe they can control, or at least influence, outcomes that they demonstrably have no influence over." As I'm sure you know already, this bias and the stock market are not that separate from each other.
Outside of Benjamin Graham's "Mr. Market," allegories for the stock market tend to emphasize our weakness with respect to it. "The market god" is an old favourite, although some prefer to conjoin "goddess" with a bad word in front.
These symbolizations are designed to make us shed our illusion-of-control biases when investing or speculating. Some people get scared, and some get scarred through not listening. Speculators, particularly momentum traders and pure chart junkies, are the group most reputed to suffer from this bias.
Unfortunately, there's an insidious variant that gets into the skull of a naive value investor - the kind that you'd believe is inoculated against this bias. The value-variant of the illusion-of-control bias can kick in when a value guy's found a real bargain...a real dollar selling at only fifty cents. The kind that makes a real value investor exclaim, "If this goes down, I'll be sure to buy more of it!"
That question - "if the stock you like goes down, would you buy more of it?" - marks the turf where the illusion of control bias lurks. What if you snap up the dollar at fifty cents, only to find it selling a week later at forty-five cents? Would you buy more?
If so, would you buy in further if that dollar sinks down to forty cents? Provided that the fundamentals are as sound as they were, would you "double-dog down" on the stock?
What, then, if it falls to thirty? Then what?
In many cases when this bias runs rampant in the excited value investor's brain, the dollar is genuine - and the averaging down does pan out eventually. The trouble is, as the averaging down continues, portfolio balance gets out of whack. So, if the dollar winds up falling to twenty-five cents, and it takes its sweet time getting up to a dollar, the excited investor has to sit on the benches waiting for it to turn out...while having months of losses to sweat over while being haunted by imaginary flaws.
In addition: tying up the portfolio in that way means that other opportunities have to be let go, even if they're more compelling than the first - unless said investor bites the bullet and takes a large loss. Since patience to fruition is a silver rule in value investing, this step is a very difficult one for value investors to implement. If part of the position has to be liquidated because of immediate money needs...
It would be nice to believe that the illusion-of-control bias can be rendered harmless by sound analysis and valuation self-discipline. It can, but only under three conditions: one, you're absolutely sure you can hold on to your position forever; two, you don't care about an interim loss even if it persists for some time; three, no-one else involved cares either. If all of these conditions don't obtain, then self-discipline in portfolio management has to be the immunizing agent.
That third condition can obtain for an individual investor, but often doesn't for an institutional investor. These people not only face market pressures, in the form of liquidations if they stick to their guns, but also legal pressures. Given the current legal climate, it isn't very far-fetched to imagine that a Ben Graham value manager might be sued for holding on to too many "value traps" ...only to see them spurt up after an adverse judgment's been handed down. It's that kind of a world sometimes.