Need a way to duplicate a vocal effect....

Yep....Double tracking. Based on a more thorough search of the web I found it began with the Beatles, continued by Paul with Wings and so forth. And yes, Madonna did use it along with many other artist. It was also known as ADT.

Understood. What I've read is that that is precisely why they came up with ADT. So as not to waste more studio time performing something that never comes out quite the same again. Some peoples pipes will give after constantly repeating trying to achieve a good performance, plus smokers will really contribute to wearing them down, (lot's of Mary Jane smoking back in those days).
 
So it's a matter of opinion if it's no substitute or a crude attempt. Or is it that you're stating that double-tracking was already being used before they came up with ADT? (I know that John and Paul in the Beatles recorded a lot of unison parts in "I wanna Hold Your Hand" and most of their earlier stuff prior to the Beatles flagrant use of ADT later). So that in a sense is true double-tracking, no?
 
I love listening to pop music, and my palette does not distinguish between either. Heck the sell numbers of those classic songs keeps going and going so I'm not alone in that opinion. Double tracking or ADT, I like em both so how are they achieved?

Being able to double-track your own vocal well is an acquired skill. Back in the day when there was no alternative, not everybody was proficient at it, and consequently it was sometimes very obvious and crude-sounding. Especially given that pop songs in the 60's were cranked out at an assembly-line pace, with two sides of a single finished in one day (or less) and an album in 3 or 4 days. Listeners just got used to that effect and accepted it. Lots of big hits featured very badly double-tracked vocals.
 
John Lennon was one singer who was marginally good at it, although that may speak more to McCartney's demands for perfection than Lennon's innate abilities. It was, in fact, the famously technology-ignorant Lennon who asked why they couldn't invent something to fake double-tracking, prompting an engineer at EMI to do just that, inventing ADT for him. 
 
Meanwhile, those who took the time to get double-tracking down were creating some astounding and very commercially successful records. The biggest of them all was Pink Floyd's Dark Side of the Moon, wherein almost every vocal and guitar solo was doubled the old-school way. You don't even notice it until it's pointed out, it's done so well. 
 
Perhaps the ultimate in double-tracked (actually, triple-tracked) juiciness is Queen's operatic masterpiece "Bohemian Rhapsody". In that case, the band's three singers sang together three times. That spectacular Wagnerian chorus is only 9 voices. Such is the power of double-tracking.
 
The same technique was used by Fleetwood Mac, a band that also featured three good singers who could seamlessly overdub themselves. One of my favorite tunes that shows off the technique is a song called "Little Lies". No plugin is ever going to duplicate that thick-cream chorus. You'll hear the same effect in some of the Carpenters' recordings, where they had the added benefit of blending siblings' voices for greater homogeneity. 
 
Bottom line is that no artificial process is really going to duplicate the real double-tracking effect. However, you can combine real double-tracking with digital fakery to thicken it up. One technique is to  apply the clone-and-nudge gimmick to a real overdub, so you end up with 3 tracks from 2.