Appendix 1: Definitions and Theoretical Propositions
from the Universal Theory of Performance

1. P = Performance:
A class of behaviours (operants)
that satisfy a set of performance criteria.
 

 

 7. SEUP = 
Subjective Expected Utility of  P, which =   sum over all values of 
i = 1, to i = n, of the product [Pr(Oi/P)] times [SEUOi/P]. 
2. Ep  = Effort:
Effort to Perform P.		 8. UEP = Negative Utility:
Cost of Effort to Perform.
3. Oi = Outcomes:
One of the possible Outcomes following P.
 
 

 

 9. SEUEP =
Subjective Expected Utility
of  EP, which 
=   sum over all values of 
i = 1, to i = n, 
of the product [Pr(P/EP)] times (SEUP), minus cost of effort (UEP).
4. Pr(Oi/P)  = 
Probability of Oi
given occurrence of P.		 10. AP = Ability:
Ability to perform P.
5. Pr(P/Ep)  = 
Probability of P,
given occurrence of Ep.		 11. CP = Constraints:
Environmental Constraints on Performance.
6. SEUOi/P = 
Subjective Expected Utility (Value) 
of positive Outcomes,  Oi's, that are 
contingent on P.
 		 12. NP = Non-Performance:
Of all Non-Performance responses that interfere with or are incompatible with performance P, the one that has the most positive 
Subjective Expected Utility of Effort
(SEUENP) associated with it.*
* Non-Performance terms: All of the terms 1 through 11, which apply to P,
can also be written for NP, by replacing P by NP.

Performance Motivation and Probability of Performance

        With the use of the above quantities, the Universal Theory of Performance makes numerous predictions.
One primary prediction is that level of Motivation to Perform will be a direct function of SEUep, and an inverse function of SEUenp.

14. Mp = Performance Motivation = f[SEUep - SEUenp].

In words, what this formulation says is that a person's motivation to perform a task is high to the extent that it is believed that effort to perform is low, and will be followed reliably by that performance, and to the extent that it is believed that such performance will be reliably followed by a highly valued set of outcomes.  It also says that motivation to perform a task will be low to the extent that it is believed that effort required for the most preferable incompatible non-performance behaviour is low, and will be followed by that non-performance, and to the extent that it is believed that such non-performance will be reliably followed by a highly valued set of outcomes.

        Certainly, strength of the actual Performance, or Probability of Performance, Pr(P), will usually be related to Performance Motivation (Mp), but only to the extent that one possesses the requisite skill, knowledge, or ability (Ap) to translate effort into actual performance; and to the extent that environmental constraints (Cp) do not prevent actual performance from occurring.

15. Pr(P), Probability of Performance = f[(Mp) x (Ap - Cp)].

        Clearly, these detailed mathematical formulations of Appendix 1 may be incorrect in many of their assumptions, especially those involving combinations of effects, such as the influence of Ability and Constraint upon final Performance.  Whether these operate additively, as suggested, or interact in a multiplicative fashion, which might be characterized by dividing Ability by Constraints, or combine in some more complex manner, has yet to be determined.  Also, theorists disagree about the specific influence of alternative responses.  Some suggest that responses will be allotted to each alternative in proportion to their relative expected values and some basic research, in some species and for some problems, supports this ‘matching law' (Herrnstein 1974).  Other theorists suggest that outcome maximization occurs, meaning that the single response that yields the highest expected value will occur to the exclusion of all less profitable responses.  Thibaut and Kelley's (1959) Comparison Level for Alternatives says that one changes from one choice to another only when one anticipates higher levels of outcome (O) from the alternative response.  Downing (1975) suggests that behaviour approaches outcome maximization as one gains experience with and understanding of the outcomes and contingencies associated with various responses.  While the issue cannot be definitively decided, ‘Experiments have consistently shown that a response rises in rate either when its reward increases or when the reward for other concurrent responses decreases' (Brown and Herrnstein 1975; pp.83-84).

Directional Effects of Each Input Variable

        For purposes of CSB theory alone, we might be content with specifying the directional effects of each input variable independently, and in doing so we can argue with greater certainty about the validity of such effects.

        The list of those variables, and the directional effect of each individually on High Levels (Probabilities) of Performance, Pr(P), are as follows:

The first six all contribute to high levels of Performance, P.

 1. HIGH  Subjective Expected Utility of Outcomes believed to be contingent upon Performance:
    High SEUoi/p.

 2. HIGH  Perceived Probability (contingency) that Performance will lead to valued outcomes:
    High Pr(Oi/P).

 3. HIGH  Expectancy that Effort will result in Performance: High Pr(P/Ep).

 4. HIGH  Ability to convert Effort into Performance: High Ap.

 5. LOW  amount of Effort required for Performance: Low Ep.

 6. LOW  level of constraints on Performance:  Low Cp.

 The last six all relate to conditions surrounding the best alternative Non-Performance NP.

 7. LOW  Subjective Expected Utility of Outcomes believed to be contingent upon Non-Performance:
    Low SEUoi/np.

 8. LOW  Perceived Probability that the best Non-Performance will lead to valued outcomes:
    Low Pr(Oi/NP).

 9. LOW  Expectancy that Effort will result in Non-Performance: Low Pr(NP/Enp).

10. LOW  Ability to convert Effort into Non-Performance: Low Anp.

11. HIGH  amount of Effort required for Non-Performance: High Enp.

12. HIGH  level of Constraints on Non-Performance:  High Cnp.