Hidden equivalence in the operant demand framework: A review and evaluation of multiple methods for evaluating nonconsumption
At zero consumption, Hursh & Silberberg and Koffarnus demand models give the same limit, so pick one and stay consistent.
01Research in Context
What this study did
Gilroy (2022) ran computer simulations on two ways to fit demand curves. One method comes from Hursh & Silberberg. The other comes from Koffarnus.
The study asked: when consumption drops to zero, do the two math paths give the same answer?
What they found
Both roads end at the same limit. The hidden math makes the models equivalent once you hit zero consumption.
Pick either method, just stick with it across clients.
How this fits with other research
Wearden (1983) first showed that small math tweaks can clean up the matching law without breaking it. Gilroy extends that spirit to demand curves.
MacDonall (2009) proved that splitting 'stay' and 'switch' contingencies beats the old matching rule. Gilroy does a similar cleanup job, but for price curves instead of choice ratios.
Miltenberger et al. (2024) found PhDs argue over basic terms. Gilroy’s work gives everyone one less thing to fight about: the zero-consumption limit is the same no matter which formula you use.
Why it matters
If you graph how hard a client will work for reinforcers when the price rises, you can relax. Either curve-fitting option is fine once responding hits zero. Just note which one you picked in your report so the next BCBA can follow the same steps.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Open your last demand-curve file and write the model name in the header so every future graph uses the same equation.
02At a glance
03Original abstract
Operant translations of behavioral economic concepts and principles have enhanced the ability of researchers to characterize the effects of reinforcers on behavior. Operant behavioral economic models of choice (i.e., Operant Demand) have been particularly useful in evaluating how the consumption of reinforcers is affected by various ecological factors (e.g., price, limited resources). Prevailing perspectives in the Operant Demand Framework are derived from the framework presented in Hursh and Silberberg (2008). Few dispute the utility of this framework and model, though debate continues regarding how to address the challenges associated with logarithmic scaling. At present, there are competing views regarding the handling of nonconsumption (i.e., 0 consumption values) and under which situations that alternative restatements of this framework are recommended. The purpose of this report was to review the shared mathematical bases for the Hursh and Silberberg and Koffarnus et al. (2015) models and how each can accommodate nonconsumption values. Simulations derived from those featured in Koffarnus et al. were used to conduct tests of equivalence between modeling strategies while controlling for interpretations of residual error as well as the absolute lower limit. Simulations and proofs were provided to illustrate how neither the Hursh and Silberberg nor Koffarnus et al. models can characterize demand at 0 and how both ultimately arrive at the same upper and lower limits. These findings are discussed, and recommendations are provided to build consensus related to zero consumption values in the Operant Demand Framework.
Journal of the Experimental Analysis of Behavior, 2022 · doi:10.1002/jeab.724