I totally believe you. I just think it is a very strange and remarkable coincidence that the sayings aren’t related. In other words, if the ‘carrot and stick’ approach meant to lure with an award that one is never going to actually get, and it is also used to mean ‘punish and reward’ then it is amazing that ‘punish and reward’ also happens to use a *carrot and a stick *in its example. That seems to me like it must be related…that maybe the reward/punishment morphed from the original meaning. And that is completely ok.
I heard this a lot in Canada. I asked people about it, and they insisted it was “John Henry”. I guess John Hancock doesn’t mean much to them, heh.
There’s nothing wrong with that usage as long as you understand you are making your own phrase and not using the idiom. The original term is vicious circle. You could say “unfortunate trend for events to repeat and reinforce themselves” too and be correct.
However, a lot of people aren’t riffing creatively on the idiom, they’re just sort of approximating English usage and hoping nobody cares.
I’ve never heard of a “carrot and stick” approach; only a “carrot on a stick” approach. After looking it up, I conclude that these are two separate idioms, the first of which sounds stupid.
Forte also means strong. Those aren’t two homophones, though- they’re the same word. In Italy, I guess you could say, there’s no such thing as a loud or soft sound. There are just strong and weak sounds. So it’s more like people using the Italian pronunciation for the Italian meaning.
I was driving through Atlanta once in the mid-90s and a song by the Squirrel Nut Zippers came on. This was back when the big-band sound had made a comeback. The DJ – a tiny little college “alternative” radio station – back-announced the song, which I’d never heard before that particular road trip. He said, and I quote,
“That was the Scroll Nut Zippers.”
I spent the next 50 miles trying to figure out what the fuck a Scroll Nut Zipper might be. I finally figured it out when I reached a town wherein the DJs could properly pronounce the word, “squirrel.”
/hijack
A vicious circle isn’t an idiom though.
Since other single-word mispronunciations have made it into this thread, I must say I can’t stand hearing mischievous mispronounced. There is no “i” after the “v”, so why do people say it like there is one? Check any dictionary- I’ll wait.
Others commonly mispronounced here in South Georgia are salmon, plantain, and et cetera (that one’s not just in the south).
I had a friend who once went to a Rolling Stones concert. She later told me that they played “Symphony For The Devil”.
Maybe she first heard the song in the Blood, Sweat & Tears version, which is called Symphony for the Devil.
My BF’s pet peeve is when people say “I could care less” when they actually mean “I couldn’t care less”.
The first time I heard it was at a Chirstmas party in IA and when I corrected it the whole dang houseful of in-laws told me I was wrong. No surprise there, as I discovered it was their mission in life.
And of course everyone who says it to you correctly, Mr. Meacham, says, “John Hancock.” What I’m sayin’. 
“As a part of our prioritization effort, we want to be sure that all of our projects have the proper precedents.”
“We plan to pole the audience.” (I found an excuse to miss that meeting.)
Huh? At least in US English “vicious circle” *is *the idiom. “Vicious cycle” is a recent bastardization, probably the result of some mis-heard illiteracy.
Or at least that’s how it seems to me.
Ouch! I bet you did.
You are correct.
I support the position that vicious circle is the parent expression and that vicious cycle is the more recent ripoff/misreading, but I will acknowledge what this recent poll demonstrates:
“A vicious ________”
In My Humble Opinion
08-11-2010, 10:04 AM
Not everyone is as convinced as I. 
I love “It’s a doggy dog world”. Reduces me to fits of giggles!
It oddly arouses me.
An idiom is a phrase that has meaning beyond what the words literally mean. For example, take something like “He’s a rotten apple”. Obviously when people say that they don’t mean he is a piece of fruit that has gone bad. The phrase has taken on a meaning beyond the literal meaning of its words. So if you say “He’s a spoiled banana” it’s nonsense because those words don’t have a common figurative meaning attached to them.
On the other hand, a “vicious cycle/circle” has no real meaning beyond the literal definition of the words. We can have terrible circles, awesome circles, deadly circles, and so forth. Replacing circle with cycle doesn’t change the meaning of the phrase, so there is nothing wrong with doing it. You can’t say, “I think you meant vicious circle” because vicious circle and vicious cycle have the exact same meaning.
There is a certain major university with one of the largest alumni associations in the world who are particularly supportive of their football program. The sports development office sent out a fundraising bulletin to hundreds of thousands of people that contained a note at the end saying that they needed extra money as they were behind in a few areas and making payments, “In the rear.”
They said it twice.