by Scott Hoge
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Rplay = -1 + 0.899•0 + 0.1•5 + 0.001•200 = -1 + 0 + 0.5 + 0.2 = -0.3,
where 0.899 + 0.1 + 0.001 = 1 are the probabilities of losing, winning five, and winning the jackpot, respectively. On average, you'd lose nearly one-third of a quarter, or 7.5 cents, for every game played. We multiply the probabilities of the individual outcomes (in this case, 10% and 0.1%) by the reward or loss in each case to arrive at the final value of expected reward. Obviously, in saving money it is wiser not to play at all, as the expected reward of not playing is
Rno play = 0 > -0.3 = Rplay.
Now, what if someone told you to trust him that you would win the jackpot on the first game? In a gambling scenario, this would amount to treating two possibilities as impossible, resulting in an expected reward of 199 quarters:
Rtrust = -1 + 0•0 + 0•5 + 1•200 = 199.
The concept of reward expectation is important here because it gives us a mechanism for treating possibilities as impossible: by adjusting probability values in calculation of the preferred action. Crucially, we see that
Rno play = 0 < 199 = Rtrust.
What this means is that without adjusting actual probabilities, we have calculated a new preferred action. This, I argue, gives a second definition of 'trust': the adjustment of probability figures in the calculation of preferred actions.
Rno play < Rtrust
This is very consistent with the image of the Judeo-Christian God as a being who is meant to be feared: if you don't have faith that he exists, you are told, he will torture you. But 'faith' in God, created by threat of torture, doesn't mean that God exists.
Rno play < Rtrust
Someone less inclined to use tactics of behavioral reinforcement might find a more positive use of the word 'trust' as a social signal. A friend might say "Trust me" as a mark of honesty to build reputation associated with the remark, so that the next time he or she says "Trust me," the likelihood from your point of view that the trusted statement is true will rise accordingly. This gives us a fourth definition of 'trust,' and specifically of "Trust me": as a signal of honesty on built reputation.
The foundation of Christianity, and synonym for 'faith': What is 'trust'? To have faith that Christ rose from the dead, or that suffering will be followed by salvation: these require placement of trust. But 'trust' can be defined in many different ways.
When a friend tells you he'll be at the airport at 8 o'clock, and you say, "I trust you," what does that mean? It can mean that based on your acquaintance with your friend's past loyalty, you believe it highly likely that he will be there. Trust, in this case, is a probability judgment: you have sufficient reason to confide in your friend's statement.
But what does it mean when your friend tries to rush you into a night club wearing something revealing and says, "Trust me"? Is 'trust' a probability judgment in this case, or an act that you can perform? Or perhaps a social signal?
If trust (or faith) were really something that you could deliberately choose, then what kind of act would it be? It would amount to treating possibilities as if they were impossible, or at least less likely. The possibility that your friend is just trying to dominate you for a laugh: in trusting your friend, you'd put this possibility out of your mind, wouldn't you? But if it really is a possibility, at least from your point of view, then how do you treat it as impossible?
In probability theory, we use a concept called 'mathematical expectation' to predict the expected reward of certain actions. Suppose that, in playing a slot machine, every game costs a quarter, you have a 10% chance of winning five quarters, and a 0.1% chance of winning 200 quarters. Here, your expected reward for one game is given by the following formula:
In saying, "Trust me" -- if we interpret the word in this light -- the man is really just encouraging you to play. And the command to trust, in this case, is a command to perform certain actions as opposed to others.
This brings us quite naturally to a third definition of 'trust': as a social signal. Of course, you can adjust the probabilities, but the question is, why would you? A rational money-saver would choose not to play, so what could the command to trust possibly accomplish?
I will argue that the command to trust is used as a social signal, often in a position of dominance and with intent to manipulate, in which the rewards in the calculation of the preferred action are altered by threat of punishment in order to reinforce the action calculated by adjusting probabilities. Suppose, for instance, that after choosing not to play, the man who told you to trust him approaches you aggressively and shoves you against the machine. In doing so, he creates a feared association between the word 'trust' and the new preferred action, playing, and alters the reward expectation Rno play by force to match the inequality with Rtrust:
Rpunished < Rplay.
Similarly, trust may also be encouraged by deliberate reward for the trusted action, as when the man has lunch with you the next day simply for trusting him:
Rno play < Rrewarded.
Placement of trust ("I trust you") may be used as a signal to the trustee that the truster trusts, has good reason to trust, or wants the trustee to follow the desired course of action, as when giving money to someone who claims to be homeless.
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