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Unread 02-06-2011, 17:10
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Tristan Lall Tristan Lall is offline
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FRC #0188 (Woburn Robotics)
 
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Re: Please help Wave Robotics earn $1,000!!!

Let me lay out a straightforward comparison, in the hope of divorcing this somewhat from the rates of return and other complexities.

Pretend you're a worker in Wisconsin, making the minimum wage of $7.25/h. You're employed for 40 h/wk, and have the option of working up to 5 h/wk overtime at your normal wage. (Overtime beyond that requires supervisor's consent, and is paid at 1.5 times the normal wage.) You're paid weekly, and your work is tracked by a timeclock.

Consider two scenarios, A & B, for one particular week:
  1. You work 40 h in total. Every day, you spend a few minutes with the pig, totalling 1 h.
    • You are paid $7.25/h × 40 h = $290.00
    • Your employer gets 40 h of productivity from you ($productivity/h × 40 h).
    • You give up 1 h of leisure as a donation (so no loss to society).
    • Wave Robotics makes $1 000.00 if they win, $0.00 if they lose. (Expected value to Wave is $500.00.)
    • Society gets $1 000.00 + $productivity/h × 40 h either way.
  2. You work 41 h in total. You donate 1 h worth of wages ($7.25) to Wave.
    • You are paid $7.25/h × 41 h = $297.25
    • Your employer gets 41 h of productivity from you. (They are better off.)
    • You give up one hour of leisure (of your own accord, so no loss to society).
    • Wave gets some amount, based on the number of donors.
    • The benefit to society is variable, and can be represented as $donated + $productivity/h × 41 h.
Let's assume for simplicity that the extra productivity in B is small, and can be neglected.

So in A, Wave needs to mobilize enough supporter-deposits to win the contest. In B, Wave needs to attract enough donor-hours to match the expected value from A (69, if the odds are even that they will win or lose, so the expectation is $500), or enough donors to match the benefit to society (138, for $1 000).

At 50 coins/min, or 3 000 coins/h, the tipping point between a net benefit and a net loss to society is at 138 h × 3 000 coins/h = 414 000 coins. If you can win with fewer coins in play than that, it's a net plus to society, and you should play the game. If you can't, then an alternative was a better solution.

In terms of statistical equivalence, you only need to make more than the expected value for the team to come out ahead. So it's best for the team to put the tipping point at 69 h × 3 000 coins/h = 207 000 coins. That's why the right choice for the team isn't necessarily the right choice for society.

So, as it actually played out, you used something like 1.5 million coins to win (plus your opponent had a million and change, and those have to be accounted for too). At those wage rates, it would have been a net loss to society. Hopefully, that's a clear statement of what I'm trying to get across.

Now, to add in one more complexity: in case B, the benefit to society is variable. That means, if Wave fails to attract enough donors, they could actually ruin their entire effort and make society worse off than in A (where the payout is guaranteed). So I guess you could call case A a form of insurance against insufficient donors—you accept a lower (fixed) return in exchange for certainty.

But that's where the perversity of A comes in: since society always makes $1 000 from the grant, all you have to do is make sure your own actions don't harm society. Unfortunately, while every coin that you deposit helps Wave—at 414 000 total coins (the sum for Wave and the opponent), you start harming society. (That's why it's not crazy to say that "cheating" and getting kicked out could actually be better for society than playing the game.)

Last edited by Tristan Lall : 02-06-2011 at 17:13.
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