Chapter 10 - Choice, Matching, and Self-Control

Concurrent Schedules

A complex schedule consisting of simultaneous presentation of two or more independent schedules, each leading to a reinforcer

-Organism allowed a choice between responding to one schedule or another

Ex; Pigeon given a choice between responding on a read key (associated with VR 20 schedule) or a green key (associated with VR 50 schedule)

-Pigeon comes to prefer the VR 20 alternative (more reinforcement per responses)

Matching Law

Principle that the proportion of responses emitted on a particular schedule matches the proportion of reinforcers obtained on that schedule

-Predicts that a pigeon will emit twice as many responses on a VI 30 schedule than a VI 60 schedule

-And predicts a pigeon emits 3 times as many responses on a VI 20 schedule than a VI 60 schedule (since the VI 20 schedule provides 3 times the rate of reinforcement)

-Therefore, it predicts a consistent relationship between proportion/percent of reinforcers obtained on an alternative and the proportion (percentage) of responses emitted

Matching Law Equation

RA / (RA + RB) = SRA / (SRA + SRB)

SR - number of reinforcers earned

RA/RB - number of responses emitted on a schedule A or B

SRA/SRB - Number of reinforcers earned on schedule A or B

Example of Matching Law Equation

Pigeon given a choice between responding on VI 20 second vs VI 60 second schedules

-Will earn three times as many reinforcers on VI 20 than on VI 60

-During a 60 minute session the pigeon earns all 180 reinforcers available on a VI 20 schedule and all of the 60 reinforcers available on a VI 60 schedule

SR(VI 20s) / (SR(VI 20s) + SR(VI 60s)) = 180 / (180+60) = 180/240 = 0.75

-75% of the reinforcers were from the VI 20 second, and 25% were from the VI 60 second

-This is then compared to actual response data emitted on each alternative to confirm if the pigeon matched the proportion of responses she emitted on each alternative to proportion of reinforcers obtained

Matching and Human Behaviour

In group situations, we choose between directing conversation to one person or another with each providing different rates of reinforcement (ex; someone providing more approval to us while speaking will have more of our attention)

Deviations from Matching

Three types of exceptions from matching:

1. Undermatching

2. Overmatching

3. Bias from Matching

Changeover Delay (COD)

Short period of time that must pass before any response can produce a reinforcer and results from switching from one schedule to another

Undermatching

Proportion of responses on the richer schedule verses the poorer schedule is less different that would be predicted by matching (“under” matching = “less” different)

-Occurs when little cost for switching from one schedule to another (lower changeover delay between schedules results in greater alternations creating undermatching)

-A slight cost for switching (greater changeover delay/COD) = more time spent on richer alternative

Example: Matching law predicts proportion of responses to be .75 on the richer VI 20 schedule and .25 on the poorer VI 60 schedule

-If we instead find proportions of 0.60 and 0.40 (respectively), undermatching occurred

Overmatching

Proportion of responses on the richer schedule versus the poorer schedule is more different than would be predicted by matching (“over” matching = “more” different)

-Occurs when cost of moving from one alternative to another is too high

Example: Matching law predicts proportion of responses should be .75 on the richer VI 20 schedule and .25 on the poorer VI 60 schedule

-Instead we observe proportions of .85 and .15 respectively, overmatching occurred

Bias from Matching

One response alternative attracts a higher proportion of responses than would be predicted by matching, regardless of whether the alternative contains the richer or poorer schedule

-Precise way to measure preference for certain types of outcomes and indicate degree of preference for different reinforcers

Example: Matching law predicts proportion of responses should be .75 on the richer VI 20 schedule and .25 on the poorer VI 60 schedule

-Instead, we observe proportions of .85 on VI 20 and .35 on VI 60 then bias has occurred

Explanations for the Matching Law

1. Maximization/Optimization Theory

2. Melioration Theory

Maximization (Optimization) Theory

Matching law occurs because it maximizes one’s overall level of reinforcement

Melioration Theory

Distribution of behaviour in a choice situation shifts towards those alternatives that have higher value regardless of the longer-term effect on overall amount of reinforcement, shifting will cease at the point where the two outcomes are approximately equal in cost/benefit

Example: When a pigeon is first confronted with a concurrent VI 30 and VI 60 schedule it emits an equal number of responses to both

-Response emitted on VI 30 will result in twice as many reinforcers, thus in terms of benefits the VI 30 will have a much higher value than the VI 60, making it more attractive and will shift its behaviour towards that reinforcer

-Shift will cease at the point of matching because that is the point the two alternatives have equal value

-Pigeon still earns twice as many reinforcers on VI 30, but doing so expends twice as many responses (cost of each alternative now matches the benefits)

Melioration vs Optimization Theory Example

Rat faced with a concurrent VR 60 and VI 80 will spend more time on the VI 80-sec than necessary to pick up all of the available reinforcers on the schedule

-Consistent with the melioration theory but contradicts the maximization/optimization theory

Problems with Melioration Theory

Tendency to move toward the higher valued alternative can result in a substantial reduction in total amount of reinforcement obtained, three ways this occurs:

1. Alternative might not require as much responding as one is distributing toward it to obtain all of the available reinforcers

• Example: Pigeon presented with concurrent VR 100 VI 30 sec schedule (VR = 100 responded on average for a reinforcer, while VI = first response after an average interval of 30 seconds will result in a reinforcer)

-Best strategy would be to spend most time on VR then briefly switch to VI every 30 seconds to pick up an additional reinforcer (maximize amount of reinforcement)

-In reality, pigeons match the amount of time spent on VI to number of reinforcers earned (more time on VI less time on VR than they should)

2. Overindulgence in a highly reinforcing alternative can often result in long-term habituation to that alternative, thus reducing its value as a reinforcer

3. Melioration is often the result of behaviour being too strongly governed by immediate consequences as opposed to delayed consequences (reinforcement)