According to normative theories, reward-maximizing agents should have consistent preferences. Thus, when faced with alternatives A, B, and C, an individual preferring A to B and B to C should prefer A to C. However, it has been widely argued that humans can incur losses by violating this axiom of transitivity, despite strong evolutionary pressure for reward-maximizing choices. Here, adopting a biologically plausible computational framework, we show that intransitive (and thus economically irrational) choices paradoxically improve accuracy (and subsequent economic rewards) when decision formation is corrupted by internal neural noise. Over three experiments, we show that humans accumulate evidence over time using a "selective integration" policy that discards information about alternatives with momentarily lower value. This policy predicts violations of the axiom of transitivity when three equally valued alternatives differ circularly in their number of winning samples. We confirm this prediction in a fourth experiment reporting significant violations of weak stochastic transitivity in human observers. Crucially, we show that relying on selective integration protects choices against "late" noise that otherwise corrupts decision formation beyond the sensory stage. Indeed, we report that individuals with higher late noise relied more strongly on selective integration. These findings suggest that violations of rational choice theory reflect adaptive computations that have evolved in response to irreducible noise during neural information processing.decision making | irrationality | choice optimality | selective integration | evidence accumulation D aily decisions, such as choosing a holiday destination or accepting a job offer, involve comparing alternatives that are characterized by different attributes (1, 2). Understanding how the brain combines information from different attributes into unitary decision values is a key challenge in psychology and the neurosciences (3, 4). From a normative perspective, the value of an alternative should be independent of factors, such as the attractiveness of competing alternatives or the context in which preferences are elicited (5). Thus, the preference relationship between two alternatives ought to remain stable, regardless of changes to the choice set, incurred for example by the addition or removal of other choice alternatives (6).However, human preferences are often driven by irrelevant factors (7,8). For instance, an initial preference for one holiday destination (e.g., Bali) over another (e.g., Berlin) can reverse when an inferior alternative (e.g., Dresden) is added to the choice set, even if this "decoy" alternative is never chosen (9, 10). Similarly, an individual preferring a holiday in Bali to Berlin, and Berlin to Boston, will sometimes show a systematic "intransitive" (or inconsistent) preference for Boston over Bali (11). A canonical argument states that such violations of decision theory (hereafter "economic" or "choice irrationality") disclose fundamental limita...

Voluntary attention is at the core of a wide variety of cognitive functions. Attention can be oriented to and sustained at a location or reoriented in space to allow processing at other locations-critical in an everchanging environment. Numerous studies have investigated attentional orienting in time and space, but little is known about the spatiotemporal dynamics of attentional reorienting. Here we explicitly manipulated attentional reorienting using a cuing procedure in a twoalternative forced-choice orientation-discrimination task. We interrogated attentional distribution by flashing two probe stimuli with various delays between the precue and target stimuli. Then we used the probabilities that both probes and neither probe were correctly reported to solve a second-degree equation, which estimates the report probability at each probe location. We demonstrated that attention reorients periodically at ;4 Hz (theta) between the two stimulus locations. We further characterized the processing dynamics at each stimulus location, and demonstrated that attention samples each location periodically at ;11 Hz (alpha). Finally, simulations support our findings and show that this method is sufficiently powered, making it a valuable tool for studying the spatiotemporal dynamics of attention.

185/200 words)Voluntary attention is at the core of a wide variety of cognitive functions. Attention can be oriented to and sustained at a location, or reoriented in space to allow processing at other locations -critical in an ever-changing environment. Numerous studies have investigated attentional orienting in time and space but little is known about the spatio-temporal dynamics of attentional reorienting. Here, we explicitly manipulated attentional reorienting using a cueing procedure in a 2-AFC orientation discrimination task. We interrogated attentional distribution by flashing two probe stimuli with various delays between the pre-cue and target stimuli. Then, we used the probabilities of both probes and none of the probes being correctly reported to solve a second-degree equation, which estimates the report probability at each probe location. We demonstrated that attention reorients periodically at ~4 Hz (theta) between the two stimulus locations. We further characterized the processing dynamics at each stimulus location, and demonstrated that attention samples each location periodically at ~11 Hz (alpha). Finally, simulations support our findings and show that this method is sufficiently powered, making it a valuable tool for studying the spatio-temporal dynamics of attention.

needs to be no more than 250 words (currently 250)Significance section needs to be no more than 100 words (currently 69) AbstractSet-size effects in change detection is often used to investigate the capacity limits of dividing attention. Such capacity limits have been attributed to a variety of processes including perception, memory encoding, memory storage, memory retrieval, comparison and decision.In this study, we investigated the locus of the effect of increasing set size from 1 to 2. To measure purely attentional effects and not other phenomena such as crowding, a precue was used to manipulate relevant set size and keep the display constant across conditions. The task was to detect a change in the orientation of 1 or 2 Gabor patterns. The locus of the capacity limits was determined by varying when observers were cued to the only stimulus that was relevant. We began by measuring the baseline set-size effect in an initial experiment. In the next experiment, a 100% valid postcue was added to test for an effect of decision. This postcue did not change the set-size effects. In the critical experiments, a 100% valid cue was provided during the retention interval between displays, or only one stimulus was presented in the second display (local recognition). For both of these conditions, there was little or no set-size effect. This pattern of results was found for both hard-to-discriminate stimuli typical of perception experiments and easy-to-discriminate stimuli typical of memory experiments.These results are consistent with capacity limits in memory retrieval, and/or comparison. For these set sizes, the results are not consistent with capacity limits in perception, memory encoding or memory storage. Set-Size Effects in Change Detection3 Significance SectionThe change detection paradigm is often used to demonstrate effects of divided attention. But it is not clear whether these effects are due to perception, memory, or judgment and decision. In this article, we present new evidence that the divided attention effect in change detection is due to limits in memory retrieval or comparison processes. These results are not consistent with limits in perception, memory encoding or memory storage.