Ch. 10 Flashcards
concurrent schedule of reinforcement
consists of the simultaneous presentation of two or more independent schedules, each leading to a reinforcer.
The organism is thus allowed a choice between responding on one schedule versus the other.
Choice between concurrent VR schedules is easy because an exclusive preference for the richer alternative clearly provides the better payoff.
concurrent VI schedules —> It is so systematic, in fact, that it led to the formulation of what is known as the matching law.
matching law
holds that the proportion of responses emitted on a particular schedule will match the proportion of reinforcers obtained on that schedule (note that it is proportion of responses and reinforcers and not number of responses and reinforcers).
The matching law therefore predicts a consistent relationship between the proportion (or percentage) of reinforcers obtained on a certain alternative and the proportion (or percentage) of responses emitted on that alternative.
Matching appears to be a basic principle of choice behavior, applicable to a variety of situations and species.
principle of matching may underlie various aspects of human social interaction.
matching law expressed as a formula
RA / RA + RB = SRA / SRA + SRB
Or
RA / (RA + RB) = SRA / (SRA + SRB)
- R represents the number of responses emitted
- SR is the number of
reinforcers earned - the subscripts A and B refer to the two schedules of reinforcement.
- Thus, RA is the number of responses emitted on schedule A,
- RB is the number of responses emitted on schedule B,
- SRA is the number of reinforcers earned on schedule A,
- SRB is the number of reinforcers earned on schedule B.
RA / (RA + RB)
Therefore, the term to the left of the equal sign:
indicates the proportion of responses emitted on schedule A. It is the number of responses emitted on schedule A divided by the total number emitted on both schedules.
SRA / (SRA + SRB)
The term to the right of the equal sign:
indicates the proportion of reinforcers earned on schedule A. It is the number of reinforcers earned on schedule A divided by the total number earned on both schedules.
Cher ami matching example
given a choice between responding on a VI 20-sec versus a VI 60-sec schedule of reinforcement.
1st assumption one should make is that she will go back and forth between the two alternatives in order to pick up all or almost all of the available reinforcers on each schedule which is in fact what hungry pigeons readily learn to do.
She will earn about 3 times as many reinforcers on the VI 20-sec schedule (which provides an average of three reinforcers per minute) as on the VI 60-sec (which provides an average of one reinforcer per minute).
Imagine that during a 60-minute session, this is precisely what she does: she earns all of the 180 reinforcers that became available on the VI 20-sec schedule during that one hour session and all of the 60 reinforcers that became available on the VI 60-sec schedule.
insert these values into the right-hand (reinforcer) side of the equation:
SR V1 20s/ (SR V1 20s + SR V1 60s) = 180/ (180 + 60) = 180/240 = .75
This means that the proportion of reinforcers that Cher Ami obtained from the VI 20-sec schedule during that session was .75.
In other words, 75% (or three-fourths) of the reinforcers that she earned were obtained from the VI 20-sec schedule, which also means that the remaining 25% (or one-fourth) of the reinforcers were obtained from the VI 60-sec schedule
Therefore, as expected, Cher Ami obtained three times as many reinforcers from the VI 20-sec schedule as from the VI 60-sec schedule (75% vs. 25%).
Cher Ami example part 2
The question now is, did Cher Ami match the proportion of responses she emitted on each alternative to the proportion of reinforcers she obtained from each alternative?
To answer this question, we have to look at the actual number of responses she emitted on each alternative.
Suppose, for example, that during that one-hour session, she emitted 2,240 responses on the VI 20-sec schedule and 775 responses on the VI 60-sec schedule.
She clearly emitted more responses on the richer schedule, but did she closely match proportion of responses to proportion of reinforcers obtained?
To determine this, we need to insert those response numbers into the left-hand (response) side of the equation.
R VI 20s:/(R VI 20s + R VI 60s) = 2,240/(2,240 + 775) = 2,240/3015= .74
This shows that Cher Ami emitted .74 (or 74%) of her responses on the VI 20-sec schedule, which closely matches the proportion of reinforcers, 75 (or 75%), that she obtained on the VI 20-sec schedule.
Thus, as predicted by the matching law, the proportion of responses that Cher Ami emitted on the VI 20-sec schedule closely matches the proportion of reinforcers that she obtained on that schedule.
Note that she did not have to distribute her responses in this way in order to pick up all of the available reinforcers. For example, she could just as easily have obtained all of them by distributing her responses equally between the two alternatives. But she didn’t do that; instead, in keeping with the matching law, she closely matched the proportion of responses she emitted on an alternative to the proportion of reinforcers she obtained on that alternative.
If asked to calculate what the matching law predicts concerning the expected proportion of responses emitted on two concurrent VI schedules of reinforcement, you should:
(1) assume that the pigeon (or rat or person) will earn all of the available reinforcers on each schedule during the session, and
(2) insert the expected number of reinforcers earned on each schedule into the right hand (reinforcer) side of the matching equation.
This will give you the expected proportion of reinforcers that will be earned on each schedule.
According to the matching law, this proportion will also be the predicted proportion of responses emitted on each schedule.
- Note that you do not need to bother with the left-hand (response) side of the equation in making this prediction.
You use that side of the equation only if you have already run such a session and have actual response numbers to work with.
— this will then enable you to confirm whether the pigeon did in fact match the proportion of responses emitted to the proportion of reinforcers earned on each alternative.
undermatching
the proportion of responses on the richer schedule versus the poorer schedule is less different than would be predicted by matching (to remember this, think of undermatching as less different).
Undermatching can occur when there is little cost for switching from one schedule to another.
changeover delay or COD.
In experimental studies of matching, the act of switching from one schedule to another results in a changeover delay
a short period of time that must pass before any response can produce a reinforcer.
It is as though when the pigeon switches from one key to another, the first peck on the new key is simply a statement of intent that says, “I now want to try this key.” Then there is a two-second delay before any peck can actually earn a reinforcer.
Without a COD, a pigeon will eventually learn to alternate pecks back and forth on each key, catching each reinforcer as soon as it becomes available. Only when a slight cost for switching is added to the situation does the pigeon spend more time on the richer alternative.
foraging situation is analogous to?
COD
This experimental procedure seems analogous to foraging situations in which an animal has to travel a certain distance from one food patch to another.
overmatching,
the proportion of responses on the richer schedule versus the poorer schedule is more different than would be predicted by matching (to remember this, think of overmatching as more different).
Overmatching can occur when the cost of moving from one alternative to another is very high.
Bias from matching
Occurs when one response alternative attracts a higher proportion of responses than would be predicted by matching, regardless of whether that alternative contains the richer or poorer schedule of reinforcement.
Bias in matching can, therefore, be used to indicate degree of preference for different reinforcers.
For example, suppose that our two schedules are VI 20-sec and VI 60-sec, and that we alternate which schedule is associated with a red key versus green key.
The matching law predicts that the proportion of responses on the red key should be .75 when the richer VI 20-sec schedule is presented on it, and .25 when the poorer VI 60-sec schedule is presented on it.
But if the proportions instead turned out to be .85 when the VI 20-sec schedule is presented on it and .35 when the VI 60-sec schedule is presented on it, then bias has occurred.
The pigeon is emitting 10% more responses on the red key than predicted by matching, both when it is the richer alternative and when it is the poorer alternative. (Of course, this also means that the pigeon is emitting 10% fewer responses on the green key.)
As with the phenomenon of behavioral contrast
the matching law reminds us that operant behavior should often be viewed in context.
The amount of behavior directed toward an alternative is a function of the amount of reinforcement available on that alternative as well as the amount of reinforcement available on other alternatives.
This notion has important implications for everyday behavior.
melioration theory
the distribution of behavior in a choice situation shifts toward those alternatives that have higher value regardless of the long-term effect on the overall amount of reinforcement.
This shifting will cease at the point where the two outcomes are approximately equal in terms of costs versus benefits.