Optimal timing and severity of rewards and punishments: Implications for parents.
Joseph Price
July 12, 2006
The degree to which parents should praise and/or punish their children has been
subject to much debate. On one extreme, some researchers believe that any form or
reward, be it gold stars, A’s, or words of praise, are damaging to the internal motivation
of children. Other researchers believe that praise is central to the healthy emotional
development of children. With regards to punishment, there are also divided camps, with
most researchers in agreement that parents should be consistent in their punishment,
which likely means that that probability of punishment should be 1 and the variance of
the severity should be zero.
One application of the optimal structure of punishment is the US penal system.
One of the major focuses has been the degree to which probability and severity of
punishments deter crime. Should judges give first offenders a second chance? Should
severity increase for repeat offenders?
Another application is the slot machine. Slot machine operators have control over
the frequency and size distribution of rewards. In this case, the question is how should we
structure the optimal dispersing of rewards in order to keep the person participating as
long as possible.
What does it teach us about an individual’s utility function?
I want to explore some of the laboratory experiments with children and their
response to rewards and/or punishments. One possibility would be a simple setting in
which the child can solve math problems. If they get it right, a reward is randomly
assigned (with a large mass point at zero). If they get it wrong, a punishment is randomly
assigned (possibly by taking away some of the rewards that they have already
accumulated).
What if we find out that consistent and equal punishments are best, but random
timing and random sizes of rewards is best?
Use this information to fit it to the type of utility function (risk averse, risk loving,
prospect theory) that would match the empirical results.
Later I can set up a model in which both punishing and rewarding is costly for the
parent. Based on these costs, what might be the optimal timing and severity of each.
I can link this to the labor literature on incentive mechanisms for increasing
productivity or monitoring behavior.
Goal of the paper:
1. Provide some guidance to parents on the optimal disbursement of punishments
and rewards. Should I always punish the child for a given act? Should I always
reward them or just some times?
2. Use these findings to teach us something about the utility functions of children.