Six of one, half dozen of the other: Expanding and contracting numerical dimensions produces preference reversals

ABSTRACT-The scales used to describe the attributes of different choice options are usually open to alternative expressions, such as inches versus feet or minutes versus hours. More generally, a ratio scale can be multiplied by an arbitrary factor (e.g., 12) while preserving all of the information it conveys about different choice alternatives. We propose that expanded scales (e.g., price per year) lead decision makers to discriminate between choice options more than do contracted scales (e.g., price per month) because they exaggerate the difference between options on the expanded attribute. Two studies show that simply increasing the size of an attribute's scale systematically changes its weight in both multiattribute preferences and willingness to pay: Expanding scales for one attribute shifts preferences to alternatives favored on that attribute. In the cult classic This Is Spinal Tap, Nigel points out to the director that the dials on the band's amplifiers are numbered all the way to 11: ''You see, most blokes will be playing at 10. You're on 10, all the way up, all the way up. . . . Where can you go from there? Nowhere. What we do, is if we need that extra push over the cliff. . . . Eleven. One louder.'' The director asks, ''Why don't you just make 10 louder and make 10 be the top number, and make that a little louder?'' Nigel thinks for a bit and replies, ''These go to 11.'' This arbitrary use of scales is not limited to comedy. Consumer Reports rates cars along six attributes. Most attributes are described on 5-point scales, but the overall test score is expressed on a 100-point scale. Will this difference in scales affect which car consumers prefer? It should not. After all, a 5-point scale can easily be converted to a 100-point scale, and vice versa (a fact that Nigel misses). More generally, a scale with ratio properties can be converted from one scale to another by multiplying the original values by some constant factor without changing the information provided by the scale. Thus, a product that is superior to another by 20 points on a 100-point scale is still superior by the same proportion if the information is expressed as a 1-point difference on a 5-point scale. Nevertheless, this trivial transformation seems psychologically consequential. The expanded scale highlights the difference between the two choice options, making it potentially easier to discriminate between them. In contrast, the contracted scale minimizes the difference. Consider a recent demonstration of currency effects. Our argument parallels past findings on risk and ratio judgments. For example, Yamagishi (1997) has shown that people judge ratios expressed with large numerators and denominators (1,286/10,000) as riskier than larger ratios expressed with small numerators and denominators (24.14/100). Stone, Yates, and Parker (1997) were able to exaggerate such effects by putting the 1074 Volume 20-Number 9 Copyright r 2009 Association for Psychological Science information in graphs that made differences in numerators even more salient. Similarly, We believe that previous research on denominator neglect STUDY 1: PREFERENCES AND CHOICE In Study 1, we used a choice paradigm to test participants' preference for options that entail trade-offs across attributes. We predicted that participants would more strongly prefer the option that dominates on an attribute that is expanded. We created two choice sets. The first scenario presented cell-phone plans that varied in cost and number of dropped calls. This scenario contained a strong manipulation such that, when one attribute was expanded, the other was contracted. The second scenario presented movie-rental plans, in which we manipulated the expansion of one attribute (new movies per period of time) while leaving the other attribute (cost) untouched. We predicted that, in both scenarios, preference would increase for the option that was superior on an expanded attribute, causing preference reversal to arise between conditions. Method One hundred six University of Michigan undergraduates completed this study as part of a course requirement. The first scenario (cell-phone plans) asked participants to evaluate cellular phone plan options described in terms of number of dropped calls and cost. Number of dropped calls was either on an expanded scale (dropped calls per 1,000 calls) or a contracted scale (dropped calls per 100 calls). Price was also described either on an expanded scale (price per year) or a contracted scale (price per month). When one attribute was presented as expanded, the other was presented as contracted, thus creating two conditions (see The second scenario (movie rentals) tested discriminability by varying the expansion of only one attribute. Participants evaluated two movie-rental plans that were described in terms of new movie availability and price (see For both scenarios, participants indicated their preference for Plan A versus Plan B on a 7-point scale (1 5 strongly prefer plan A, 4 5 indifferent, 7 5 strongly prefer plan B). Note. Participants evaluated cell-phone plans described in terms of number of dropped calls and cost. Number of dropped calls was either on an expanded scale (dropped calls per 1,000 calls) or on a contracted scale (dropped calls per 100 calls). Price was also described either on an expanded scale (price per year) or on a contracted scale (price per month). In Condition 1, the number of dropped calls was presented on a contracted scale, and price was given on an expanded scale. In Condition 2, the number of dropped calls was presented on an expanded scale, and price was given on a contracted scale. Volume 20-Number 9 1075 Katherine A. Burson, Richard P. Larrick, and John G. Lynch, Jr. Results and Discussion An independent-samples t test showed a significant shift in plan preference based on attribute expansion for both scenarios. For the first scenario, preferences favored Plan B (the plan that was superior on price) when price was expanded and the number of dropped calls was contracted (M 5 4.45). However, preferences favored Plan A (the plan that was superior on the number of dropped calls) when the number of dropped calls was expanded and price was contracted (M 5 3.08), t(104) 5 À3.60, p < .001, d 5 0.706. We converted these data to choice proportions to test for preference reversals. Plan B was preferred when it was described as having a lower price per year but more dropped calls per 100 than Plan A (53% vs. 31%, respectively). 1 However, Plan A was preferred when it was described as having fewer dropped calls per 1,000 but a higher price per month than Plan B (69% vs. 23%, respectively); w 2 (1, N 5 106) 5 13.93, p < .001, j c 5 .363 for the linear contrast of the ordinal choice categories between conditions. For the second scenario, participants favored the superior plan for new movies (Plan B) more when new movies were expanded (M 5 4.33) than when they were contracted (M 5 3.38), t(104) 5 2.16, p 5 .033, d 5 0.424. A test of choice proportions showed that 56% of participants preferred Plan B when number of new movies was expanded to a yearly scale, compared to 38% who preferred Plan A. Contracting number of new movies to a weekly scale resulted in 33% preferring Plan B and 57% preferring Plan A, a significant reversal for the linear contrast of the ordinal choice categories, w The results of Study 1 show that attribute expansion increases preference for the alternative favored on an expanded attribute, despite the fact that the relative differences between alternatives remained the same. STUDY 2: PRICING In this experiment, we modified the second scenario of Study 1 to create a matching paradigm in order to determine participants' valuation of options that entail a trade-off across attributes (e.g., We manipulated both attribute expansion and product valence. Valence was manipulated by presenting the product as either better or worse than the average plan. We predicted that valence would interact with attribute expansion: The difference in willingness to pay for the above-average plan versus the below-average plan would be greater when framed as movies per year (expanded) rather than movies per week (contracted). Method Sixty-three University of Michigan students completed this 2 (attribute expansion: expanded vs. contracted) Â 2 (product valence: above vs. below average) design study in combination with other materials and were paid $8 for their participation. Participants were asked to evaluate two movie-rental plans, as in the second scenario in Study 1. One plan was labeled the average plan and the other was the target plan. Price was provided only for the average plan. Half of the participants evaluated the two movie-rental plans described in terms of new movies per week (i.e., the contracted attribute). The other participants evaluated the two plans described in terms of new movies per year (i.e., the expanded attribute). These plans are presented i

Underestimated Passive Volcanic Sulfur Degassing Implies Overestimated Anthropogenic Aerosol Forcing

The Arctic is warming at almost four times the global rate. An estimated sixty percent of greenhouse-gas-induced Arctic warming has been offset by anthropogenic aerosols, but the contribution of aerosols to radiative forcing (RF) represents the largest uncertainty in estimating total RF, largely due to unknown preindustrial aerosol abundance. Here, sulfur isotope measurements in a Greenland ice core show that passive volcanic degassing contributes up to 66 ± 10% of preindustrial ice core sulfate in years without major eruptions. A state-of-the-art model indicates passive volcanic sulfur emissions influencing the Arctic are underestimated by up to a factor of three, possibly because many volcanic inventories do not include hydrogen sulfide emissions. Higher preindustrial volcanic sulfur emissions reduce modeled anthropogenic Arctic aerosol cooling by up to a factor of two (+0.11 to +0.29 W m−2), suggesting that underestimating passive volcanic sulfur emissions has significant implications for anthropogenic-induced Arctic climate change

Complex exon-intron marking by histone modifications is not determined solely by nucleosome distribution

It has recently been shown that nucleosome distribution, histone modifications and RNA polymerase II (Pol II) occupancy show preferential association with exons (“exon-intron marking”), linking chromatin structure and function to co-transcriptional splicing in a variety of eukaryotes. Previous ChIP-sequencing studies suggested that these marking patterns reflect the nucleosomal landscape. By analyzing ChIP-chip datasets across the human genome in three cell types, we have found that this marking system is far more complex than previously observed. We show here that a range of histone modifications and Pol II are preferentially associated with exons. However, there is noticeable cell-type specificity in the degree of exon marking by histone modifications and, surprisingly, this is also reflected in some histone modifications patterns showing biases towards introns. Exon-intron marking is laid down in the absence of transcription on silent genes, with some marking biases changing or becoming reversed for genes expressed at different levels. Furthermore, the relationship of this marking system with splicing is not simple, with only some histone modifications reflecting exon usage/inclusion, while others mirror patterns of exon exclusion. By examining nucleosomal distributions in all three cell types, we demonstrate that these histone modification patterns cannot solely be accounted for by differences in nucleosome levels between exons and introns. In addition, because of inherent differences between ChIP-chip array and ChIP-sequencing approaches, these platforms report different nucleosome distribution patterns across the human genome. Our findings confound existing views and point to active cellular mechanisms which dynamically regulate histone modification levels and account for exon-intron marking. We believe that these histone modification patterns provide links between chromatin accessibility, Pol II movement and co-transcriptional splicing

Cellular and molecular regulation of tumor necrosis factor-alpha production by pentoxofylline

Tumor necrosis factor-alpha (TNF), a mononuclear phagocyte (MO)-derived peptide, is increasingly being recognized for its pleomorphic immunologic effects. A number of investigations have demonstrated that lipopolysaccharide (LPS) can induce TNF synthesis, yet mechanisms that regulate TNF expression at the cellular and molecular levels have not been fully elucidated. In this study, we present data demonstrating pentoxifylline, a methylxanthine, is efficacious in suppressing LPS-induced MO-derived TNF at the level of both TNF mRNA accumulation and TNF supernatant bioactivity. Pentoxifylline, at a dose of 1 x 10-5M, suppressed the production of both biologically active TNF and TNF mRNA expression by more than 50%. Furthermore, additional methylxanthines and dibutyryl cAMP have similar effects on TNF expression. These data support the mechanism for this suppressive effect is via the generation of intracellular cAMP.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27135/1/0000128.pd

Families’ roles in children’s literacy in the UK throughout the 20th century

This paper explores the changing roles of families in children’s developing literacy in the UK in the last century. It discusses how, during this time, understandings of reading and writing have evolved into the more nuanced notion of literacy. Further, in acknowledging changes in written communication practices, and shifting attitudes to reading and writ- ing, the paper sketches out how families have always played some part in the literacy of younger generations; though reading was frequently integral to the lives of many families throughout the past century, we consider in particular the more recent enhancement of children’s literacy through targeted family programmes. The paper considers policy implications for promoting young children’s literacy through work with families

Economic Games on the Internet: The Effect of $1 Stakes

Online labor markets such as Amazon Mechanical Turk (MTurk) offer an unprecedented opportunity to run economic game experiments quickly and inexpensively. Using Mturk, we recruited 756 subjects and examined their behavior in four canonical economic games, with two payoff conditions each: a stakes condition, in which subjects' earnings were based on the outcome of the game (maximum earnings of $1); and a no-stakes condition, in which subjects' earnings are unaffected by the outcome of the game. Our results demonstrate that economic game experiments run on MTurk are comparable to those run in laboratory settings, even when using very low stakes

Human Vav1 Expression in Hematopoietic and Cancer Cell Lines Is Regulated by c-Myb and by CpG Methylation

Vav1 is a signal transducer protein that functions as a guanine nucleotide exchange factor for the Rho/Rac GTPases in the hematopoietic system where it is exclusively expressed. Recently, Vav1 was shown to be involved in several human malignancies including neuroblastoma, lung cancer, and pancreatic ductal adenocarcinoma (PDA). Although some factors that affect vav1 expression are known, neither the physiological nor pathological regulation of vav1 expression is completely understood. We demonstrate herein that mutations in putative transcription factor binding sites at the vav1 promoter affect its transcription in cells of different histological origin. Among these sites is a consensus site for c-Myb, a hematopoietic-specific transcription factor that is also found in Vav1-expressing lung cancer cell lines. Depletion of c-Myb using siRNA led to a dramatic reduction in vav1 expression in these cells. Consistent with this, co-transfection of c-Myb activated transcription of a vav1 promoter-luciferase reporter gene construct in lung cancer cells devoid of Vav1 expression. Together, these results indicate that c-Myb is involved in vav1 expression in lung cancer cells. We also explored the methylation status of the vav1 promoter. Bisulfite sequencing revealed that the vav1 promoter was completely unmethylated in human lymphocytes, but methylated to various degrees in tissues that do not normally express vav1. The vav1 promoter does not contain CpG islands in proximity to the transcription start site; however, we demonstrated that methylation of a CpG dinucleotide at a consensus Sp1 binding site in the vav1 promoter interferes with protein binding in vitro. Our data identify two regulatory mechanisms for vav1 expression: binding of c-Myb and CpG methylation of 5′ regulatory sequences. Mutation of other putative transcription factor binding sites suggests that additional factors regulate vav1 expression as well

Golden Rule of Forecasting: Be Conservative

This article proposes a unifying theory, or the Golden Rule, or forecasting. The Golden Rule of Forecasting is to be conservative. A conservative forecast is consistent with cumulative knowledge about the present and the past. To be conservative, forecasters must seek out and use all knowledge relevant to the problem, including knowledge of methods validated for the situation. Twenty-eight guidelines are logically deduced from the Golden Rule. A review of evidence identified 105 papers with experimental comparisons; 102 support the guidelines. Ignoring a single guideline increased forecast error by more than two-fifths on average. Ignoring the Golden Rule is likely to harm accuracy most when the situation is uncertain and complex, and when bias is likely. Non-experts who use the Golden Rule can identify dubious forecasts quickly and inexpensively. To date, ignorance of research findings, bias, sophisticated statistical procedures, and the proliferation of big data, have led forecasters to violate the Golden Rule. As a result, despite major advances in evidence-based forecasting methods, forecasting practice in many fields has failed to improve over the past half-century

The Calculus of Committee Composition

Modern institutions face the recurring dilemma of designing accurate evaluation procedures in settings as diverse as academic selection committees, social policies, elections, and figure skating competitions. In particular, it is essential to determine both the number of evaluators and the method for combining their judgments. Previous work has focused on the latter issue, uncovering paradoxes that underscore the inherent difficulties. Yet the number of judges is an important consideration that is intimately connected with the methodology and the success of the evaluation. We address the question of the number of judges through a cost analysis that incorporates the accuracy of the evaluation method, the cost per judge, and the cost of an error in decision. We associate the optimal number of judges with the lowest cost and determine the optimal number of judges in several different scenarios. Through analytical and numerical studies, we show how the optimal number depends on the evaluation rule, the accuracy of the judges, the (cost per judge)/(cost per error) ratio. Paradoxically, we find that for a panel of judges of equal accuracy, the optimal panel size may be greater for judges with higher accuracy than for judges with lower accuracy. The development of any evaluation procedure requires knowledge about the accuracy of evaluation methods, the costs of judges, and the costs of errors. By determining the optimal number of judges, we highlight important connections between these quantities and uncover a paradox that we show to be a general feature of evaluation procedures. Ultimately, our work provides policy-makers with a simple and novel method to optimize evaluation procedures