Measuring the free fall of antihydrogen

After the first production of cold antihydrogen by the ATHENA and ATRAP experiments ten years ago, new second-generation experiments are aimed at measuring the fundamental properties of this anti-atom. The goal of AEGIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) is to test the weak equivalence principle by studying the gravitational interaction between matter and antimatter with a pulsed, cold antihydrogen beam. The experiment is currently being assembled at CERN's Antiproton Decelerator. In AEGIS, antihydrogen will be produced by charge exchange of cold antiprotons with positronium excited to a high Rydberg state (n > 20). An antihydrogen beam will be produced by controlled acceleration in an electric-field gradient (Stark acceleration). The deflection of the horizontal beam due to its free fall in the gravitational field of the earth will be measured with a moire deflectometer. Initially, the gravitational acceleration will be determined to a precision of 1%, requiring the detection of about 105 antihydrogen atoms. In this paper, after a general description, the present status of the experiment will be reviewed

The ambiguity triangle: uncovering fundamental patterns of behavior under uncertainty

The probability triangle (also called the Marschak-Machina triangle) allows for compact and intuitive depictions of risk preferences. Here, we develop an analogous tool for choice under uncertainty - the ambiguity triangle - and show that indifference curves in this triangle capture preferences for unknown probabilities. In particular, the ambiguity triangle allows us to examine whether subjects adhere to the generalized axiom of revealed preference (GARP) and satisfy a non-parametric test for constant ambiguity attitudes. We find that more than 95% of subjects adhere to GARP and that about 60% satisfy our test for a constant ambiguity attitude. Yet, among these 60% of subjects there is substantial preference heterogeneity. We characterize this heterogeneity with finite-mixture estimates of a one-parameter extension of Expected Utility Theory wherein 48% of subjects are ambiguity averse, 22% are ambiguity seeking, and 30% are close to ambiguity neutral. The ambiguity triangle also highlights how variable ambiguity attitudes arise mainly because indifference curves are 'fanning-in' across the triangle. This fanning-in property implies that aversion to ambiguity increases as the likelihood of receiving a good outcome increases. We capture this behavior with a simple parametric model that also allows for finite mixture characterizations of preference heterogeneity for these subjects. We show that for a substantial share of these subjects (43%) their fanning-in is so strong that, although they are initially ambiguity seeking, they become strongly ambiguity averse as the likelihood of receiving a good outcome increases

The uncertainty triangle – uncovering heterogeneity in attitudes towards uncertainty

This paper develops a graphical tool – the uncertainty triangle – that allows for testing whether choices under uncertainty obey the generalized axiom of revealed preferences (GARP).We find that more than 95% of subjects made choices that can be rationalized by the maximization of a well-behaved utility function. The uncertainty triangle also makes it straightforward to characterize heterogeneity in attitudes towards uncertainty. To accomplish this we propose a oneparameter extension of Expected Utility in which uncertainty attitude is everywhere constant in the triangle. Experimental data indicate that about 60% of participants made choices consistent with the model and, within this group, 48% were uncertainty averse, 22% uncertainty seeking, and 30% uncertainty neutral. The remaining 40% of participants appear to hold variable uncertainty attitudes. A model that can accommodate this variability is proposed and calibrated

The two faces of independence: betweenness and homotheticity

Many studies document failures of expected utility’s key assumption, the independence axiom. Here, we show that independence can be decomposed into two distinct axioms – betweenness and homotheticity – and that these two axioms are necessary and sufficient for independence. Thus, independence can fail because homotheticity, betweenness, or both are violated. Most research has focused on models that assume subjects will violate both axioms or models that assume subjects will satisfy betweenness but violate homotheticity. Our decomposition of independence into betweenness and homotheticity allows us to show, however, that a significant share of subjects obey homotheticity but violate betweenness. Using data from a revealed preference experiment, and without making any parametric assumptions, we show that 1/3 of participants belong in the neglected class of preferences that violate independence but satisfy homotheticity, indicating that betweenness is violated. Another 1/3 of participants satisfy independence. The remaining 1/3 fail both independence and homotheticity and may also fail betweenness. Our results provide useful constraints on future modeling attempts by highlighting, in a non-parametric way, an empirically relevant class of preferences

An expected utility maximizer walks into a bar...

We conducted field experiments at a bar to test whether blood alcohol concentration (BAC) correlates with violations of the generalized axiom of revealed preference (GARP) and the independence axiom. We found that individuals with BACs well above the legal limit for driving adhere to GARP and independence at rates similar to those who are sober. This finding led to the fielding of a third experiment to explore how risk preferences might vary as a function of BAC. We found gender-specific effects: Men did not exhibit variations in risk preferences across BACs. In contrast, women were more risk averse than men at low BACs but exhibited increasing tolerance towards risks as BAC increased. Based on our estimates, men and women's risk preferences are predicted to be identical at BACs nearly twice the legal limit for driving. We discuss the implications for policy-maker

The Impact of Menstrual Cycle Phase on Economic Choice and Rationality

<div><p>It is well known that hormones affect both brain and behavior, but less is known about the extent to which hormones affect economic decision-making. Numerous studies demonstrate gender differences in attitudes to risk and loss in financial decision-making, often finding that women are more loss and risk averse than men. It is unclear what drives these effects and whether cyclically varying hormonal differences between men and women contribute to differences in economic preferences. We focus here on how economic rationality and preferences change as a function of menstrual cycle phase in women. We tested adherence to the Generalized Axiom of Revealed Preference (GARP), the standard test of economic rationality. If choices satisfy GARP then there exists a well-behaved utility function that the subject’s decisions maximize. We also examined whether risk attitudes and loss aversion change as a function of cycle phase. We found that, despite large fluctuations in hormone levels, women are as technically rational in their choice behavior as their male counterparts at <i>all</i> phases of the menstrual cycle. However, women are more likely to choose risky options that can lead to potential losses while ovulating; during ovulation women are less loss averse than men and therefore more economically rational than men in this regard. These findings may have market-level implications: ovulating women more effectively maximize expected value than do other groups.</p></div

Session order effects.

<p><b>(A)</b> Session order effects on loss aversion. Loss aversion increased from the first to second session, but remained stable for all subsequent sessions. Note that session order was randomized with regard to cycle phase. (<b>B)</b> Session order effects on risk aversion. Risk aversion increased from the first to second session, but remained stable for subsequent sessions.</p

Results from the GARP experiment.

<p><b>(A)</b> Budget sets used in the GARP experiment. Each line represents one budget set and circles on the line represent the bundles (or options) amongst which the subject can make a selection. (<b>B)</b> Rationality across the menstrual cycle. Measures of the Afriat’s Efficiency Index are plotted for subjects in each menstrual cycle phase and for an age-matched male control population (both n = 36 subjects). Measures for all phases were above 0.95, the common threshold for rationality, and not significantly differently across phases or compared to males (all p>0.3). Error bars represent standard errors. The dotted lines represent the AEI measurements for a random chooser (green) second grader (pink) and undergraduate (cyan) from Harbaugh et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144080#pone.0144080.ref022" target="_blank">22</a>].</p

Results from the gambling experiment for loss aversion.

<p><b>(A)</b> Effect of menstrual cycle phase on the number of times the safe certain option ($0) was chosen over the <i>mixed gamble</i> (ANOVA, p<0.01). <b>(B)</b> Histogram of the number of safe options chosen by each individual subject, computed as the difference for each subject between the number of safe options in each cycle phase and the average number of safe options chosen across cycle phases. Fig 6A is superimposed on the histogram to display group average and s.e.m. <b>(C)</b> Effect of menstrual cycle phase on loss aversion. Parameter fits are estimated simultaneously for all phases with the single best noise parameter (0.94 ± 0.04) controlling for session order effects. Parameter estimates for an age-matched male population are also plotted. Subjects are less loss averse during ovulation than other phases (all p<0.001). Loss aversion in menses, mid-follicular and luteal phases did not differ significantly from each other (all p>0.3).</p