Law of Effect

1
Law of Effect

• Law of effect (Thorndike, 1911) behavior that is
  followed by a satisfying state of affairs is more
  likely to occur again and vice versa
• With each trial, latency response decreases (up
  to some point)
• With each trial, rate of responding increases (up
  to some point)
• Note that animals improve on performance
  optimize, not just repeat same behavior but make
  it better and more efficient
• Adaptation to the environment via learning
• Herrnstein considers this behavior
  change/adaptation a question, and not an answer
  (e.g., what are adapting to how are adapting
  how know to adapt, etc)

2
Violations of Law of Effect and adaptation

• Ferster and Skinner change in response rate
  between VR and VI schedules why if just stamping
  in of behavior? Why do this?
• Behavior on conjunctive schedules
• conjunctive schedule reinforces first response
  after certain number of responses AND first
  response after set amount of time
• double criteria
• CONJ FI(t) FR(n1)
• note for FI schedule rapid responding is
  penalized
• ratio schedules rapid responding more reward
• CONJ schedule combines rate of Sr is directly
  proportional to rate of responding only for rates
  of responding on FI schedule, not for FR
  schedule.

3
Herrnstein and Morse (1958)

• Used a CONJ FI 15 FR (0 to 240) with pigeons
• Found Rate of responding decreased with
  increases in FR value (which reduced rate of
  reward)
• Why is the animal doing this? cant be
  stamping in of response or wouldnt get
  fluctuations
• May have to do with response strength- how?

4
Reinforcement as strength

• Sr ? making a stronger link between responding
  and reward
• Relative frequency measure of strength
• response rate function of reinforcer rate
• How fast respond function of how fast get
  reinforced.
• Plot proportion of responses as function of
  proportion of reward
• Note This is a continuous measure, and not
  discrete trial animal has more choice
• Discrete trial trial by trial
• Free operant animal controls how many responses
  it makes

5
Reinforcement as strength

• Reinforcers come on interval, not ratio schedules
• if use FR or VR should get exclusive choice
• Why? faster respond more reinforcers
• VI schedules allow examination of changes in
  response rate as a function of predetermined rate
  of reinforcer
• With VI schedules, can use reinforcer rate as the
  independent variable!
• No proportionality between number of responses
  and number of reinforcers- all time based
• This becomes basis of matching law
• P1/P1 Po R1/R1 Ro
• Herrnstein explains why this true..
• animal matches ratio of responding to ratio of
  reward!

6
Explain the Use of COD

• COD change over delay
• Delay until the reinforcement schedule begins
  again
• Pecking left, switch to right..schedule is on
  hold for several seconds, then starts again
• In a sense, a time out for switching
• Use of a COD affects Response strength and
  choice
• Shull and Pliskoff (1967) used COD and no COD
  and ICS as reward
• Used Findley procedure (remember what this was?)
• matching occurred as long as used COD
• why important
• COD not controlling factor, controlling factor
  response ratio
• COD increases discriminability between the two
  reinforcer schedules
• Increased discriminability better matching
• Why?

7
Herrnsteins Matching Equation

• Single reinforcer and single response
• P1 kR1
• ------------
• R1Ro
• P1 rate of responding to alternative 1
• R1 rate of reinforcement for alternative 1
• Ro rate of unaccounted sources of reinforcement
• k asymptote of response rate

8
Can derive a more general two-choice equation

• P1 kR1
• ------------
• R1 R2 Ro
• ---------------------------------------------
• P2 kR2
• ------------
• R1 R2 Ro

9
Cancelling out

• P1 kR1
• -------------------------
• R1 R2 Ro P1 R1
• ---------------------------------------------
  ? ------ ------
• 
  P2 R2
• P2 kR2
• --------------------------
• R1 R2 Ro

10
Two-Parameter Matching Equation

• P1 R1
• ---- ----
• P2 R2
• Must assume that Ro is equal for both P1 and P2
• What are some possible Ros in our study?
• Note that are everything is measurable!

11
Objections to matching

• Several alternative models that suggest that
  matching is a special case
• Probability models or probability learning
• Use Melioration models and VR schedules
• But note here matching would be exclusive choice
• Can show mathematically can produce matching from
  probability learning
• Discrete trials procedures do not result in
  matching Why is this not surprising?
• Note, however
• getting some deviations from matching under
  certain circumstances-
• need to address these circumstances from the
  matching law model or else matching law becomes
  too limited-
• Baum will do this next week!

12

• Now.lets see how we can use this equation

13
Choice as Behavior and Behavior as Choice

• Know that relative rate of responding varies with
  relative rate of reinforcement must affect
  absolute rate of responding as well.
• P1 kR1/R1 Ro
• makes a hyperbole function
• some maximum rate of responding

14
How plot?

• Plot reinforcement rate (responses per minute) as
  a function of reinforcer rate (reinforcers per
  minute)
• Reinforcement rate on X axis
• Response rate on Y axis
• Makes a hyperbola
• Decelerating ascending curve
• Why decelerating- why reach asymptote?
• Note is a STEADY STATE theory, not an acquisition
  model
• Assumes complete knowledge
• Use after many, many sessions so no issue of
  whether animals knows schedule ratio

15
Example

• Plot response rate as a function of reinforcer
  rate

16
Now look at Herrnsteins figures

• figures on pages 255-256

17
Now you try Which rat(s) follows the equation?
Use P1/P2 R1/R2
Use P1 P1/R1Ro
18
Factors affecting the hyperbola

• Absolute rates affected by Sr rates
• Higher the reinforcement rate the higher the rate
  of responding
• True up to some point (asymptote)- why?
• Can also plot for P1/R2 R1/R2 and get same
  general trend

19
Enough!

• next section explains multiple schedule and how
  the model fits this, we will skip that for now
• Questions for our study
• Why are we using the four different schedules
• 60-15 15-60 30-15 15-30
• How will we plot our data? We dont have
  responses so we must use ____________.