The cumulative effects (CE) model explains free-operant choice by the
ratio of total numbers of responses and reinforcements, a probability-
like variable. Williams (1994) argues that the model is vulnerable to
experiments that disprove melioration, a local probability model. The
authors note critical differences between the nonlocal CE model and lo
cal probability models that allow the CE model to handle some data wit
h which they are incompatible. All models are simplifications of reali
ty; hence, a model's failures are as revealing as its successes. Willi
ams suggests that simple models may need to be abandoned in favor of a
''representational'' account. The authors point out that representati
ons must be both acquired and acted on. Acquisition requires processin
g of responses and reinforcers; action requires decision rules. Models
are simply testable suggestions for what these rules and processes mi
ght be.