Representations Underlying Transitive Choice in Humans and Other Primates

There is strong evidence for at least three different representations underlying transitive performance in various species of animals. We focus on understanding one of the most neglected, the production-rule-stack model (Harris & McGonigle, 1994), which to date best accounts for the performance of squirrel monkeys (Saimiri sciureus) and human children under 7 trained on the transitive inference (TI) task (e.g. given A > B and B > C, then A > C) when presented with three items from the training set. We present a version of this representation, the two-tier model, which explains how this sort transitive performance is learned. The two-tier model perfectly replicates the positive results of the production-rule-stack model and also accounts for additional data, particularly subjects’ failures to learn the TI task. We discuss the relation between models of transitive inference, and characterize the correspondence between TI performance and underlying representations. Of the three representations discussed, we find that the two-tier model is the most relevant for understanding general-purpose primate task learning. Transitive inference (TI) is the process of reasoning whereby one determines that if, for some quality, A > B and B > C, then A > C. In some domains, such as integers or heights, this property will hold for any A, B or C. For other domains, such as sporting competitions and primate dominance hierarchies, the property does not necessarily hold (Wright, 2001). Piaget first described TI as an example of concrete operational thought (Piaget, 1954). That is, children become capable of TI when they become capable of mentally performing the physical manipulations they would otherwise use to determine the correct answer. For TI, this manipulation involves ordering the objects into a sequence using the rules A > B and B > C, and then observing the relation between A and C. Yet Piaget was also aware of an ‘automatic’ transitive performance (TP), distinguished from true TI by the subject’s ability to explain their performance (Piaget, 1928; Wright, 2001). Since the 1970s, TI has been demonstrated in young children (Bryant & TRANSITIVE CHOICE IN PRIMATES 2 Trabasso, 1971) and a variety of animals — monkeys (McGonigle & Chalmers, 1977), rats (Dusek & Eichenbaum, 1997) and even pigeons (Fersen, Wynne, Delius, & Staddon, 1991) — not normally ascribed with concrete operational abilities. Further, Siemann and Delius (1993) have shown that for human adults who learned to choose between pairs of doors during an exploration-type computer game, there was no performance difference between individuals who formed explicit comparison models and those who did not (N = 8 vs. 7 respectively). These results cast doubt upon the belief that all transitive performance (TP), choosing A over C given the knowledge that A > B and B > C, is dependent on logical inference. Explaining transitive performance requires describing exactly what information is learned and how that information is used. This description is formally called its representation. For example, consider a subject learning that, given two containers A and B, they should choose A. One possible representation would be images sufficient for recognising A and B together coupled with an instruction to choose A. The shortcoming of such a representation is its specificity — the subject could not generalize this representation to apply to new visual stimuli (e.g. A coupled with C)1. Understanding the representation underlying transitive performance is critical to understanding the performance itself. For example, if the representation is sequential, we have to ask how the animal identifies that it should use a sequential representation when it is presented with apparently unrelated events involving only two items. On the other hand, if the representation is not sequential, then we need to explain how the animal appears to perform TI. Accounting for behavioral data from different species in different experimental training regimes, at least three different representations have been proposed to underlie pre/non-operational transitive performance (See Figure 1). These are: • a simple associative: a reinforcement weight paired with each individual stimulus; when more than one stimuli is present, the most reinforced one is selected. This representation is discriminated from others listed here in that items in the middle of the series may have no significant difference in weight (Frank, Rudy, & OReilly, 2003). This representation is most closely associated with the value-transfer model (von Fersen, Wynne, Delius, & Staddon, 1991; Zentall & Sherburne, 1994) • b innately sequential: an ordinal index in a series or an indexical value selected from a gradient; two items are compared by using their indexical values. This representation can be discriminated by generalizations (or mistakes) across series, e.g. the 3rd item of one series may be inserted as the 3rd item of another series. This behavior has to date only been shown in primates (Stromer, Mackay, Cohen, & Stoddard, 1993; Brannon & Terrace, 2000; Treichler, Raghanti, & Tilburg, 2003). This representation has been convincingly modelled in a related literature on human series learning (Henson & Burgess, 1997; Henson, 1998). • c ordered action associative: an ordered set of paired associations between stimuli and actions; each stimuli is associated with an action (e.g. select the stimuli). If there are actions associated with more than one present stimuli, whichever stimulus has the highest priority takes the agent’s attention and determines its behaviour. This representation can be discriminated from the others by the fact that it fails to give consistently correct answers This sort of error is referred to in the learning literature as over fitting — learning the exemplars perfectly but learning no general principles that might be applied in new contexts (Mitchell, 1997). TRANSITIVE CHOICE IN PRIMATES 3