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Bryson, J., & Leong, J. (2007). Primate errors in transitive inference: a two-tier learning model. Anim. Cogn., 10(1), 1–15.
Abstract: Abstract Transitive performance (TP) is a learning-based behaviour exhibited by a wide range of species, where if a subject has been taught to prefer A when presented with the pair AB but to prefer B when presented with the pair BC, then the subject will also prefer A when presented with the novel pair AC. Most explanations of TP assume that subjects recognize and learn an underlying sequence from observing the training pairs. However, data from squirrel monkeys (Saimiri sciureus) and young children contradict this, showing that when three different items (a triad) are drawn from the sequence, subjects`` performance degrades systematically (McGonigle and Chalmers, Nature 267:694-696, 1977; Chalmers and McGonigle, Journal of Experimental Child Psychology 37:355-377, 1984; Harris and McGonigle, The Quarterly Journal of Experimental Psychology 47B:319-348, 1994). We present here the two-tier model, the first learning model of TP which accounts for this systematic performance degradation. Our model assumes primate TP is based on a general-purpose task learning system rather than a special-purpose sequence-learning system. It supports the hypothesis of Heckers et al. (Hippocampus 14:153-162, 2004) that TP is an expression of two separate general learning elements: one for associating actions and contexts, another for prioritising associations when more than one context is present. The two-tier model also provides explanations for why phased training is important for helping subjects learn the initial training pairs and why some subjects fail to do so. It also supports the Harris and McGonigle (The Quarterly Journal of Experimental Psychology 47B:319-348, 1994) explanation of why, once the training pairs have been acquired, subjects perform transitive choice automatically on two-item diads, but not when exposed to triads from the same sequence.
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Hogue, M. - E., Beaugrand, J. P., & Lague, P. C. (1996). Coherent use of information by hens observing their former dominant defeating or being defeated by a stranger. Behav. Process., 38(3), 241–252.
Abstract: This study examines the role of observation during the formation of triads in female domestic hens. Results indicate that during hierarchy formation, a hen observing agonistic interactions and conflict settlement between its former dominant and a stranger uses this information when in turn confronted by the latter. Under a first condition (E, N = 15 triads), bystanders witnessed their prior dominant being defeated by a stranger before being introduced to them. In a second condition (C1, N = 16 triads), bystanders witnessed the victory of their prior dominant over a stranger. In a third condition (C2, N = 15 triads), bystanders witnessed two strangers establishing a dominance relationship before being introduced to their prior dominant and to a stranger the former had just defeated. The behavioural strategies of bystanders depended on the issue of the conflict they had witnessed. Bystanders of the E condition behaved as having no chance of defeating the stranger. They never initiated an attack against it, and upon being attacked, readily submitted in turn to the stranger. On the contrary, bystanders of the C1 condition behaved as having some chances against the stranger. They initiated attacks in 50% of cases, and won 50% of conflicts against the stranger. Under condition C2, bystanders first initiated contact with the strangers in only 27% of cases, which approximates the average of their chances for defeating the stranger. However, bystanders finally defeated the strangers in 40% of cases. These results suggest that bystanders of conditions E and C1 gained some information on the relationship existing between their prior dominant and the stranger and that they used it coherently, perhaps through transitive inference, thus contributing to the existence of transitive relationships within the triads. Alternate explanations are examined.
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Nakamaru, M., & Sasaki, A. (2003). Can transitive inference evolve in animals playing the hawk-dove game? J. Theor. Biol., 222(4), 461–470.
Abstract: What should an individual do if there are no reliable cues to the strength of a competitor when fighting with it for resources? We herein examine the evolutionarily stable strategy (ESS) in the hawk-dove game, if the opponent's resource-holding potential (RHP) can only indirectly be inferred from the outcome of past interactions in the population. The strategies we examined include the classical mixed strategy in which no information on past games is utilized, the `imprinting' strategy in which a player increases/decreases its aggressiveness if it wins/loses a game, the `immediate inference' strategy in which a player can infer the strength of those opponents it fought before, and the `transitive inference' strategy in which a player can infer the strength of a new opponent through a third party with which both players have fought before. Invasibility analysis for each pair of strategies revealed that (i) the transitive-inference strategy can always invade the mixed strategy and the imprinting strategy, and itself refuses invasion by these strategies; (ii) the largest advantage for transitive inference is achieved when the number of games played per individual in one generation is small and when the cost of losing an escalated game is large; (iii) the immediate inference, rather than the transitive inference, can be an ESS if the cost of fighting is small; (iv) a strong linear ranking is established in the population of transitive-inference strategists, though it does not perfectly correlate to the ranking by actual RHPs. We found that the advantage of the transitive inference is not in its ability to correct a misassessment (it is actually the worst in doing so), but in the ability of quickly lining up either incorrect or correct assessments to form a linear dominance hierarchy.
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