Communication, Distortion, and Randomness in Metric Voting

In distortion-based analysis of social choice rules over metric spaces, voters and candidates are jointly embedded in a metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving only this ordinal (comparison) information, must select a candidate approximately minimizing the sum of distances from all voters to the chosen candidate. It is known that while the Copeland rule and related rules guarantee distortion at most 5, the distortion of many other standard voting rules, such as Plurality, Veto, or k-approval, grows unboundedly in the number n of candidates.An advantage of Plurality, Veto, or k-approval with small k is that they require less communication from the voters; all deterministic social choice rules known to achieve constant distortion require voters to transmit their complete rankings of all candidates. This motivates our study of the tradeoff between the distortion and the amount of communication in deterministic social choice rules.We show that any one-round deterministic voting mechanism in which each voter communicates only the candidates she ranks in a given set of k positions must have distortion at least 2n-k/k; we give a mechanism achieving an upper bound of O(n/k), which matches the lower bound up to a constant. For more general communication-bounded voting mechanisms, in which each voter communicates b bits of information about her ranking, we show a slightly weaker lower bound of Ω(n/b) on the distortion.For randomized mechanisms, Random Dictatorship achieves expected distortion strictly smaller than 3, almost matching a lower bound of 3 − 2/n for any randomized mechanism that only receives each voter's top choice. We close this gap, by giving a simple randomized social choice rule which only uses each voter's first choice, and achieves expected distortion 3 − 2/n.

Discriminative Fear Learners are Resilient to Temporal Distortions during Threat Anticipation

Discriminative fear conditioning requires learning to dissociate between safety cues and cues that predict negative outcomes yet little is known about what processes contribute to discriminative fear learning. According to attentional models of time perception, processes that distract from timing result in temporal underestimation. If discriminative fear learning only requires learning what cues predict what outcomes, and threatening stimuli distract attention from timing, then better discriminative fear learning should predict greater temporal distortion on threat trials. Alternatively, if discriminative fear learning also reflects a more accurate perceptual experience of time in threatening contexts, discriminative fear learning scores would predict less temporal distortion on threat trials, as time is perceived more veridically. Healthy young adults completed discriminative fear conditioning in which they learned to associate one stimulus (CS+) with aversive electrical stimulation and another stimulus (CS−) with non-aversive tactile stimulation and then an ordinal-comparison timing task during which CSs were presented as task-irrelevant distractors. Consistent with predictions, we found an overall temporal underestimation bias on CS+ relative to CS− trials. Differential skin conductance responses to the CS+ versus the CS− during conditioning served as a physiological index of discriminative fear conditioning and this measure predicted the magnitude of the underestimation bias, such that individuals exhibiting greater discriminative fear conditioning showed less underestimation on CS+ versus CS− trials. These results are discussed with respect to the nature of discriminative fear learning and the relationship between temporal distortions and maladaptive threat processing in anxiety.

Groove Filling Characteristics and Strength of Form-Fit Joints Produced by Die-Less Hydroforming

The manufacturing of modern lightweight structures and the implementation of multi material concepts, for example in automotive engineering, entails appropriate joining technologies. The absence of additional connection elements or filling materials as well as the possibility to join dissimilar metals are basic requirements in this field of application to reach the aspired weight reduction. In case of tubular joints the die-less hydroforming process meets these demands and thus makes it an interesting alternative to conventional welding and riveting processes. The present work focuses on form fit joints produced by die-less hydroforming. It provides a verification of a previously presented analytical approach that allows the calculation of the working fluid pressure required to bulge the tube material into the groove of the outer joining partner. For that purpose, the groove filling characteristics of joined specimens with different groove geometries are analyzed. Here both joining partners were made of the aluminum alloy EN AW-6060. Additionally the connection strength of the joined specimens are determined using tensile tests. The results prove that the groove angle is the main influencing factor on the connection strength and that it can be used for an ordinal comparison of different groove geometries.

Shared System for Ordering Small and Large Numbers in Monkeys and Humans

There is increasing evidence that animals share with adult humans and perhaps human infants a system for representing objective number as psychological magnitudes that are an analogue of the quantities they represent. Here we show that rhesus monkeys can extend a numerical rule learned with the values 1 through 9 to the values 10, 15, 20, and 30, which suggests that there is no upper limit on a monkey's numerical capacity. Instead, throughout the numerical range tested, both accuracy and latency in ordering two numerical values were systematically controlled by the ratio of the values compared. In a second experiment, we directly compared humans' and monkeys' performance in the same ordinal comparison task. The qualitative and quantitative similarity in their performance provides the strongest evidence to date of a single nonverbal, evolutionarily primitive mechanism for representing and comparing numerical values.