Put Your Money Where Your Mouth Is

A lot of companies have employee referral programs. Typically the employee is paid some sort of bonus if the candidate is hired. From the employee's perspective, there's much to be gained by referring lots of people, even if some are long shots. This makes it hard for the employer to sort out the candidates that are really good.

I propose a system that forces the employee to put their money where the mouth is. To make a referral, you must wager an amount B. If the candidate is hired, you are paid $B. If they are rejected, you must pay the employer $B^2. That's right, you lose money on bad referrals. It turns out that the employee's income is maximized (and positive) when they wager exactly one half the odds that the candidate is hired.* So if you think a candidate has 2 to 1 odds of being hired, bet $1. If you think they have 10 to 1 odds, bet $5.

This has the nice property of forcing employees to reveal the true strength of a candidate. In practice, of course, this would probably reduce referrals. Real people (myself included!) are usually adverse to risk and don't always try to maximize expected returns. But you could imagine playing the game with play money and giving a quarterly award to the employee with the most winnings.

This technique has many other applications--anytime you want a good estimate of a probability from a single person. Anybody know if this is an original idea? Probably not, but I don't know where to start looking.

* Proof: let p be the probability that the candidate is hired. The referral's expected return is E=pB - (1-p)B^2. To maximize, we differentiate with respect to B, yielding E'=p - 2(1-p)B. Setting this to zero we find that E is maximized when B = 0.5 p / (1-p), or 0.5 the odds of the candidate being hired.