Second-order schedules of token reinforcement with pigeons: effects of fixed- and variable-ratio exchange schedules.
Variable-ratio token exchange keeps response rates high and pauses short, especially when the trade-in cost increases.
01Research in Context
What this study did
Cullinan et al. (2001) worked with pigeons on a two-step token system. Birds had to peck 50 times to earn a token. Then they had to trade tokens for food under either a fixed-ratio or variable-ratio exchange rule.
The team slowly raised the number of tokens needed for food. They watched how fast the birds pecked and how long they paused after each trade.
What they found
Response rates dropped more when the exchange rule was fixed-ratio than when it was variable-ratio. Birds took longer breaks before starting again under fixed-ratio.
Variable-ratio exchange kept the birds pecking faster and pausing less, even when the token cost went up.
How this fits with other research
Catania (1973) first showed the same pause pattern: second-order fixed-ratio schedules create long pre-ratio pauses, while variable-ratio schedules do not. Cullinan et al. (2001) confirm this with tokens instead of brief lights.
Argueta et al. (2019) extend the finding to a child with autism. In their classroom, fixed-ratio and variable-ratio exchange produced equal response rates, but the child chose the variable-ratio option every time. The bird data say variable-ratio boosts rate; the child data say it feels better even when rates match.
The two studies look opposite until you check the method. Pigeons faced rising token costs; the child did not. The pause problem only shows up when the exchange requirement grows.
Why it matters
When you run a token economy, think about how learners trade in their tokens. If the trade-in rule is fixed and the cost climbs, expect long waits and slower work. Switching to a variable-ratio trade-in schedule, or letting the learner choose, can keep momentum high and reduce frustration. Start small, then probe for pauses; if you see them, shuffle the exchange rule before the task stalls.
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Join Free →Count how many tokens a learner needs to trade in; if the number is rising and pauses are growing, switch the trade-in rule from fixed to variable ratio for one session and track response speed.
02At a glance
03Original abstract
Pigeons' key pecks produced food under second-order schedules of token reinforcement, with light-emitting diodes serving as token reinforcers. In Experiment 1, tokens were earned according to a fixed-ratio 50 schedule and were exchanged for food according to either fixed-ratio or variable-ratio exchange schedules, with schedule type varied across conditions. In Experiment 2, schedule type was varied within sessions using a multiple schedule. In one component, tokens were earned according to a fixed-ratio 50 schedule and exchanged according to a variable-ratio schedule. In the other component, tokens were earned according to a variable-ratio 50 schedule and exchanged according to a fixed-ratio schedule. In both experiments, the number of responses per exchange was varied parametrically across conditions, ranging from 50 to 400 responses. Response rates decreased systematically with increases in the fixed-ratio exchange schedules, but were much less affected by changes in the variable-ratio exchange schedules. Response rates were consistently higher under variable-ratio exchange schedules than tinder comparable fixed-ratio exchange schedules, especially at higher exchange ratios. These response-rate differences were due both to greater pre-ratio pausing and to lower local rates tinder the fixed-ratio exchange schedules. Local response rates increased with proximity to food under the higher fixed-ratio exchange schedules, indicative of discriminative control by the tokens.
Journal of the experimental analysis of behavior, 2001 · doi:10.1901/jeab.2001.76-159