تحلیل ریاضی: چرا پلن شرکتهای بازاریابی چند سطحی جواب نمی دهد؟ (مقاله انگلیسی)

* دانشمندان زیادی در امریکا به مقابله با شرکتهای بازاریابی شبکه ای می پردازند. در ادامه یکی از این مقالات ارائه میگردد. (منبع)

The mathematics: why MLM pyramid schemes cannot work!

In the classic "pyramid" scheme, participants attempt to make money solely by recruiting new participants into the program. The hallmark of these schemes is the promise of sky-high returns in a short period of time for doing nothing other than handing over your money and getting others to do the same.

The fraudsters behind a pyramid scheme may go to great lengths to make the program look like a legitimate version of a multi-level marketing program. But despite their claims to have legitimate products or services to sell, these fraudsters simply use money coming in from new recruits to pay off early stage investors. But eventually the pyramid will collapse. At some point the schemes get too big, the promoter cannot raise enough money from new investors to pay earlier investors, and many people lose their money. The chart below shows how pyramid schemes can become impossible to sustain:

This table shows how many new paying members must be recruited at each level for programs (schemes) that require each new member to recruit 4, 5, 6, 7, or 8 new members.

Level	Number of new members each level must recruit to be profitable. (columns indicate the numbers for requirements of recruiting 4, 5, 6, 7, or 8 new members)
	4	5	6	7	8
1	4	5	6	7	64
2	16	25	36	49	512
3	64	125	216	343	4096
4	256	625	1,296	2401	32,768
5	1,024	3125	7,776	16,807	262,144
6	4,096	15,625	46,656	117,649	2,097,152
7	16,384	78,125	279,936	823,543	16,777,216
8	65,536	390,625	1,679,616	5,764,801	134,217,728
9	262,144	1,953,125	10,077,696	40,353,607	1,073,741,824
10	1,048,576	9,765,625	60,466,176	282,475,249	8,589,934,592
11	4,194,304	48,828,125	362,797,056	1,977,326,743	68,719,476,736
12	16,777,216	244,140,625	2,176,782,336	13,841,287,201
13	67,108,864	1,220,703,125	13,060,694,016

You will notice that the reddish colored cells signify levels that are unachievable because there aren't that many people on earth (approximately 6 billion people)! The orange colored cells signify levels that are practically unachievable: there are no existing companies on earth with this many employees or members.  The yellow colored cells indicate levels that are mathematically possible, but would mean that the company would be huge by most standards (7,000 to 1 million employees) and this is VERY unlikely. The uncolored cells are levels that are possible and maybe even practically achievable - by really good con men! This does NOT mean that we are recommending  them!!!!

You can see that for most "programs", you'd better have no more than 3 levels of members "distributors", etc.) above you!

For the sake of this example, let's assume that the scheme depends on each participant recruiting 6 new members into the scheme. The figure below shows how many people will need to have joined the scheme at each level, in order for those above to be paid. Since the current total population of the world is approximately 6 billion people, after only 13 levels there are not enough people on the planet to keep the scheme going!  this means if there are 11 or 12 levels of "distributors" or "representatives" (or whatever they call the participants) above you, you can not possibly make a profit!

If a plan offers to pay commissions for recruiting new distributors, watch out! Most states outlaw this practice, which is known as "pyramiding." State laws against pyramiding say that a multilevel marketing plan should only pay commissions for retail sales of goods or services, not for recruiting new distributors.

Why is pyramiding prohibited? Because plans that pay commissions for recruiting new distributors inevitably collapse when no new distributors can be recruited. And when a plan collapses, most people -- except perhaps those at the very top of the pyramid -- lose their money.

Nothing irritates a die-hard MLM'er more than the preceding argument. If you point out the absurdity, for example, that if "the pitch" at an Amway meeting were even moderately accurate, in something like 18 months Amway's income would be larger than the Gross National Product of the entire United States.  If you point this out, they will shift their premise and say  "Well, that is absurd, of course. Not everyone will succeed, and so the market will never saturate."

Well, which is it? Are we recruiting "winners" to build a real business, or planning by design to profit off of "losers" who buy into our "confidence"?

During the initial pitch, they will emphasize that anyone can make it work, even if you have no previous experience selling.  "The product sells itself!  Just give them the trial kit!" (oh yes, you must purchase the trial kits, by the way!).  "It's the opportunity of a lifetime.", they'll tell you.