The mathematics of scamming

Tuesday, 03 May, Year 8 d.Tr. | Author: Mircea Popescu

Suppose for the sake of this Gedankenexperiment that the cost of creating a new WoT identity is 0i, the EPDii is 1%, the SELDiii is ε, the DGFiv is 1.5 and the MDGIv is 10.

So then :

  1. new fellow comes in, creates his WoT ID,
  2. new fellow engages in 10 deals worth ε each, for a profit of 0.1ε total.
  3. new fellow is no longer new ; bumped to trading 1.5ε at a time, .
  4. no longer new fellow does 10 more deals, profit of 0.15ε
  5. and 10 more, 2.25ε ea ; profit of 0.225ε
  6. and 10 more, 3.375ε ea; profit of 0.3375ε and on it goes.

This makes rather obvious the fundamental disincentive against scamming a properly implemented WoT provides : as far as the agent is rational, his greatest incentive to scam is during that first dealvi, where the discounted value of future trades is lowest, and the difference between what he is worthvii and what the goods in his hands are worth is highest (=ε).

As time goes by, and the ID's worth (=SoD) increases, the present value of future trades and their respective profits also increase, but much faster than the SoD. To elucidate this point, consider the points of inflection : at C, the ID is worth 1ε total, (of which 0.1ε in cash and 0.9ε in goodwill). The ID can burn the 0.9ε in goodwill for a profit of 0.5εviii, but this -0.4ε EV trade is not actually rational. At E he is worth 1.5ε total (of which 0.25ε in cash and 1.25ε in goodwill), which he could burn for a .75ε profit, but this -0.5ε EV trade is even less rational than before! And at F he is worth 2.25ε (of which 0.475ε in cash and 1.775ε in goodwill), which he idem could burn for a payoff of 1.125ε, but thereby making a loss of 0.65ε, the worst to date.

It's true that the value of goodwill could in principle be discounted to the degree that trading 3 bucks in the bush for 2 bucks in the hand seems like a very reasonable move. It's also true that as far as incentive alignment goes, the WoT ID system beats the utter hell out of anything else ever devised.

Obviously, the various parameters we set in the first paragraph have a major impact on how this system plays outix. For instance, a higher EPD massively increases the incentive for honest behaviour, through significantly increasing the present value of future profitsx ; whereas outsized ε will bleed the system dry before it has a chance to get off the groundxi. All these parametric considerations aside - the WoT is here to stay, because it solves a fundamental problem in the best possible way.

Much like capitalism, and very much unlike democracy.

———
  1. This can trivially be increased. As an arbitrary example, if you require supplicant give you a blowjob before you'll acknowledge their identity, the cost of creating a new WoT identity in your context is equal to the market value of one blowjob. []
  2. Expected Profit per Deal. Known as gross margin in retail for instance. []
  3. Size of Entry Level Deal. How large an amount a new identity may trade. []
  4. Deal Growth Factor. A value under 1 means deal sizes contract over time ; and is a measure of recession. []
  5. Mean Deal Growth Interval. The mean number of trades between successive increases in deal size. []
  6. And note that scamming is not something one need to engage in voluntarity. One's intentions matter not one whit in the world of cold equations. Yes that poses a major problem for the young, and for the inept, and for the outsider. Tough, in a word. []
  7. A big fat 0, as per the assumption in note 1. If the cost of making a new identity is 0, then the value - not of a new identity, but of the actual physical real world person behind it! - is, you've guessed it, zero. ZERRRRRO.

    This creates a trap for those people without a WoT ID who mistakenly and unwarrantedly believe their value to be superior to 0. The difference between whatever hallucinated value they ascribe themselves and the actual 0 they are factually worth creates a trap for them, keeping them captive much in the way the gas trap under your toilet keeps mauvaises aires away from your bathroom. To confront the nulity of nonpersonhood requires too much internal energy for them, more than they can summon. As time goes by, their internal energy may increase, but the difference to surmount increases also, and so it's perfectly possible they'll never be able to bite the 144" shell that used to be a BB round they couldn't bite back in the day. []

  8. He only gets the 0.5ε ; as he could have ran off with the remainder 1ε back at step A. []
  9. As per an ancient Al Schwartz ditty, "kinetics proposes, thermodynamics disposes". We're here discussing thermodynamics, no more. []
  10. This is seen without exception in human society - where periods of abundance drive "law abiding" citizenry to parrot nonsense as if they believed it, yet with the first cooling in the economic engines suddenly "the people themselves" discover that "they had to do it", leaving the state to wonder in their wake. Which wake is also its wake. []
  11. For which reason Personal responsiblity and the Ponzi scam. []
Category: Bitcoin
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2 Responses

  1. Great article!

  2. Mircea Popescu`s avatar
    2
    Mircea Popescu 
    Friday, 20 May 2016

    Cheers.

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