Judgment and Decision Making, vol. 6, no. 4, June 2011, pp. 333-342
Nudge to nobesity II: Menu positions influence food orders
Eran Dayan* Maya Bar-Hillel#
“Very small but cumulated decreases in food intake may be sufficient to have significant effects, even erasing obesity over a period of years” (Rozin et al., 2011). In two studies, one a lab study and the other a real-world study, we examine the effect of manipulating the position of different foods on a restaurant menu. Items placed at the beginning or the end of the list of their category options were up to twice as popular as when they were placed in the center of the list. Given this effect, placing healthier menu items at the top or bottom of item lists and less healthy ones in their center (e.g., sugared drinks vs. calorie-free drinks) should result in some increase in favor of healthier food choices.
Keywords: choice architecture, menu, middle bias, edge bias, nudge, obesity, position effects.
Obesity is a growing problem throughout the world. Fighting it via dieting is apparently ineffective (e.g., Mann et al., 2007; Garner & Wooley, 1991). In a companion paper, Rozin et al. (2011) present arguments and facts to substantiate these two claims, which we shall not repeat here. They then suggest that the war on obesity could benefit from nudges (Thaler & Sunstein, 2008), not only from heavy efforts and investments in resources. Nudges are small, cheap, easily implementable and often hardly noticed changes in the choice architecture (i.e., the manner or setting in which the choice set is presented) that do not affect the choice set itself, yet affect the appeal of different options in it. Rozin et al.’s nudge to nobesity is very simple: if you want to increase or decrease the popularity of a food item, make it easier or harder to access, respectively. In the same spirit, the present paper explores another possible nudge to nobesity. We show that placing a food item on a menu at the beginning or the end of its category increases its popularity compared to placing it in the middle.
Restaurants present customers with lists of their offerings. When the menu is displayed in writing, items are presented simultaneously. When a waiter recites the day’s specials, items are presented sequentially. Our study involved only printed menus. Menu items may be organized in various ways, such as by type (e.g., Soups; Salads; etc.), or according to main ingredients (Fish dishes; Vegetarian dishes; etc.). Within each category they are typically listed in vertical ordering. When designing menus, does this order matter?
One may seek answers from two kinds of sources—the “how to” literature on menu design, and the psychological literature on position effects. Familiar position effects such as primacy and recency refer to stimuli presented sequentially, and their dependent variable is not usually choice. But the effect called “edge avoidance” (Rubinstein, Tversky & Heller, 1986), “centrality preferences” (Shaw et al., 2000), “middle bias” (e.g., Attali & Bar-Hillel, 2003), or “center-stage effect” (Valenzuela & Raghubir, 2009) refers to choice from among simultaneously presented options—and the various names indicate the typical findings: “People choosing from an array of identical options reliably prefer the middle ones” (Christenfeld, 1995). When items are not identical, the effect’s manifestation is that when options are presented in the middle of an array they are chosen more often than when they are presented on its edges.
Baseline menu: A1, A2, A3, A4 E1, E2, E3, E4, E5, E6, E7, E8, E9, E10 S1, S2, S3, S4, S5, S6 D1, D2, D3, D4, D5, D6, D7, D8 Mirror menu: A4, A3, A2, A1 E10, E9, E8, E7, E6, E5, E4, E3, E2, E1 S6, S5, S4, S3, S2, S1 D8, D7, D6, D5, D4, D3, D2, D1 Inside-Out base: A2, A1, A4, A3 E5, E4, E3, E2, E1, E10, E9, E8, E7, E6 S3, S2, S1, S6, S5, S4 D4, D3, D2, D1, D8, D7, D6, D5 Inside-Out mirror: A3, A4, A1, A2 E6, E7, E8, E9, E10, E1, E2, E3, E4, E5 S4, S5, S6, S1, S2, S3 D5, D6, D7, D8, D1, D2, D3, D4
These studies do not, of course, apply to options for which position may be inherently important, such as theater or airplane seats, skyscraper floors, restaurant tables, or place in queues. Rather they use options for which it is hard to imagine why position would matter, such as: i. in which of 4 opaque boxes people choose to hide, or seek, a “treasure” (Rubinstein, Tversky & Heller, 1986); ii. similarly, in what position people place, or guess, answers in multiple-choice tests (Attali & Bar-Hillel, 2003); iii. which good they choose from a set of identical (Christenfeld, 1995; Shaw et al., 2000) or non-identical (Valenzuela & Raghubir, 2009) goods offered; iv. what stall they head for in a public bathroom (Christenfeld, 1995); etc. All these studies found that placing an item in the middle, rather than the edges, of the choice set enhanced its popularity.
We are aware of only three exceptions in which there seems to be an advantage to being first or last in a simultaneously presented choice set rather than in its middle. Nisbett and Wilson (1977) asked their subjects to consider a linear array of 4 identical pairs of stockings (a fact of which their subjects were not aware), and serendipitously found a “pronounced left-to-right position effect, such that the right-most object in the array [which was also the last perused] was heavily over-chosen” (p. 243)—namely, “last-is-best”. In contrast, Koppell and Steen (2004) analyzed real ballot-voting data that was almost like a controlled study, inasmuch as “the order of candidates’ names was rotated by precinct” (p. 267), and found that “candidates received a greater proportion of the vote when listed first than when listed in any other position” (p. 267)—namely, “first-is-best”. Finally, Christenfeld (1995) asked respondents to choose a route between two points, either on hypothetical maps or for real. The destination point could not be reached by walking a straight line, but the paths to be chosen from had the same total length and number of turns. Respondents showed a preference for the path reached by making the first turn as late as possible. The paths cannot be classified into first, last, or middle, but the possible points of taking the first turn can, and in that sense, respondents preferred the last.
In contrast to all the above-mentioned findings, the restaurant trade publications on menus advocate both edges (namely, the first and last) as the positions where one should place the items whose popularity one wants to enhance (e.g., “A menu item’s position within a list can also affect sales. People tend to remember the top two items on a list and the bottom item…”, Panitz, 2000, p. 82; “People do not read menus, they scan them … As a result, the most frequently selected items are those in the first and last position in the category list…” Main, 1998, p. 80). These recommendations, however, were never backed by research, and none, to the best of our knowledge, exists (Panitz’s claim is certainly valid, but it is not clear why one needs to rely much on memory when choosing from a menu). Moreover, when Kincaid and Corsun (2003) attempted to put other accepted truths regarding “the impact of menu layout on item sales” to an empirical test, their title question, “Are consultants blowing smoke?” (p. 226), was answered in the affirmative. However, since they did not study “edge bias” specifically, we have no direct menu results to either contrast with or add to the “edge avoidance” we reported above.
In the present study, therefore, we did not hypothesize a bias either in favor of or against middle positioned items, but rather checked whether one exists, using 2-tailed significance testing.
Participants. 240 Hebrew University students, ages 19–35, 52% female, were recruited individually around the campus. Participants were assigned at random to the 4 conditions, in equal numbers.
Design, stimuli and procedure. Four menu versions were prepared, differing only in order of item presentation within category. The menu offered 4 appetizers (A), 10 entrées (E), 6 soft drinks (S) and 8 desserts (D), in that order. The names of the items and their descriptions were copied from that of an Israeli pizzeria chain. No prices were displayed. The four menus (in Hebrew) appeared in four different orders, shown schematically in Table 1. Call one the Baseline (arbitrarily designated). Then the other three were: Mirror (that reversed the Baseline order completely within each category); Inside-Out Base (that reversed the Baseline order within the top half and within the bottom half of each category, but not the top and bottom halves themselves, thereby turning middle items into extreme items and vice versa); Inside-Out Mirror. Each participant received a single menu, and was asked to choose a single item from each category. They were promised that one participant would be chosen by lottery, the winner to be rewarded with a real meal at the pizzeria, consisting of his or her exact questionnaire choices. The reward was sufficiently motivating that participants volunteered the few minutes needed to make their menu selections.
Number of orders as a function of item position Item name N 1st 2nd M++ M+ M- M-- PU Last A1 Ensalada Verde 55 14 - 1 - 11 10 - - 20 A2 Caprese 101 29 - - 22 23 - - 27 A3 Empanada 50 16 - - 10 12 - - 12 A4 Colorada 34 7 - - 7 8 - - 12 Appetizer total 240 66 - - 50 53 - - 71 E1 Cumbia 8 2 - - 3 2 - - 1 E2 Milonga 9 - 3 2 - - 2 2 - E3 Lambada 47 - - 12,13 2 - - 10, 12 - - E4 Tango 15 - 4 5 - - 3 3 - E5 Candombe 14 4 - - 3 1 - - 6 E6 Friconne 63 17 - - 16 15 - - 15 E7 Samba 24 - 5 8 - - 4 7 - E8 Salsa 2 - - 0, 1 - - 0,1 - - E9 Meringue 28 - 10 6 - - 6 6 - E10 Rumba 30 9 - - 6 7 - - 8 Entrée total 191 22,27 32 22 21 12,14 28 25 15 10,13 18 30 D1 Cookies ice-cream 21 4 - - 6 4 - - 7 D2 Choc-chip ice-cream 24 - 7 5 - - 6 6 - D3 Strawberry ice-cream 26 - 7 3 - - 9 7 - D4 Cappuccino ice-cream 16 4 - - 3 4 - - 5 D5 Carmela 30 6 - - 8 9 - - 7 D6 Nicoletta 69 - 22 11 - - 16 20 - D7 Chaja 33 - 8 5 - - 7 13 - D8 Dulce de Leche ice-cream 21 7 - - 5 4 - - 5 Desserts total 240 21 44 24 22 21 38 46 24 S1 Orange Juice 50 18 - - 12 11 - - 9 S2 Sprite 5 - 1,1 - - - - 2,1 - S3 Coca Cola 75 21 - - 16 14 - - 24 S4 Fanta 3 0 - - 1 1 - - 1 S5 Soda water 2 - 0,0 - - - - 1,1 - S6 Lemonade 105 34 - - 24 23 - - 24 Soft drinks total 233 4,3 73 - 1,1 - 53 49 - - 3,2 58 Grand total 904 26,30 192 66
45 13,14 153 148 53 10,13 64
183 1 Here (and in the other tables), - occurs in a cell that was not represented by a position. 2 Double entries in a cell occur when the item appeared in the same position in two different menu orders.
Item position Item name 1st 2nd M++ M+ M- M-- PU Last % extreme D7 Chakha - 24 15 - - 21 39 - 64 A1 Ensalada Verde 25 - - 20 18 - - 36 621 D6 Nicoletta - 32 16 - - 23 29 - 61 S3 Coca Cola 28 - - 21 19 - - 32 60 E9 Meringue - 36 21 - - 21 21 - 57 E10 Rumba 30 - - 20 23 - - 27 57 A3 Empanada 32 - - 20 24 - - 24 562 A4 Colorada 21 - - 21 24 - - 35 562 A2 Caprese 29 - - 22 23 - - 27 55 S6 Lemonade 32 - - 23 22 - - 23 55 D2 Choc-chip ice-cream - 29 21 - - 25 25 - 54 S1 Orange Juice 36 - - 24 22 - - 18 54 D3 Strawberry ice-cream - 27 12 - - 35 27 - 54 E6 Friconne 27 - - 25 24 - - 24 51 E7 Samba - 21 33 - - 17 29 - 50 D5 Carmela 20 - - 27 30 - - 23 43 Appetizer total 28 - - 21 22 - - 30 57* Entrée total 17 12 11 15 13 7.9 9.4 16 53 Desserts total 8.8 18 10 9.2 8.8 16 19 10 56 Soft drinks total 31 - - 23 21 - - 25 56 Grand total 21 7.3 5 17 16 5.9 7.1 20 56* 1 Here and elsewhere, irregularities in sums (e.g., 25+36=61, but table shows 62) are due merely to rounding errors. 2 Here, and elsewhere, apparent ties (e.g., between A3 and A4) were broken by the next digit, not shown. * indicates significance at the .05 level or better, 2-tailed.
Table 2 shows the popularity of the items (namely, the number of orders they received) as a function of their within-category position. Since we used only four different orders, not all items appeared in all possible positions (excepting the Appetizers). All items did, however, appear both in the top half and in the bottom half of their category offers (this was assured by the Mirror reversals). Additionally, items that were either first or last in their category (A1, A4; E1, E10; S1, S6; D1, D8) always exchanged positions with items in its middle (e.g., A2, A3; E5, E6; S3, S4; D4, D5, respectively). Because all categories had an even number of offerings, this “middle” consisted of 2 items. Among the items that were neither at the extremes nor in the middle, some nonetheless moved closer to, or further from, the middle (as when E2, E9 and D2, D7 exchanged positions with E4, E7 and D3, D6, respectively), but some retained their position vis-à-vis the middle or the extremes in all 4 menu orders (this was the case for E3, E8, S2, and S5). The latter could not provide data for our hypothesis, so although their data are reported in Table 2, they were ignored in the position analyses.
In Table 2, M+ and M- designate the middle positions, where M+ is atop M-; M++ and M-- designate positions just above or just below the middle ones, respectively; PU is the penultimate position.
Since Table 2 gives the data in full, all questions can be answered from it directly. Nonetheless, for reader ease, we prepared another table derived from it. Table 3 omits the hypothesis-irrelevant menu items (E3, E8, S2 and S5). It also omits menu items which were chosen by fewer than 24 (i.e., 10%) of the participants (E1, E2, E4, E5, E6, S4, D1 and D4). This removed 107 observations from the table, which are nonetheless included in all analyses at the category level. Table 3 also converts frequencies to percents, to facilitate between-item comparisons. Finally, item order is rearranged, from the item showing the greatest benefit for an extreme position, D7, to that showing the least benefit for an extreme position, D5 (which, in fact, was the only item that showed a deficit for the extreme position). This is shown in the rightmost column (which sums the percent of choices of the top and bottom items).
All but one item (D5 Carmela) of the 16 individual items in Table 3 (and all but 4 items of the 28 items in Table 2) show that an individual item, no matter how popular or unpopular, benefits from being placed at the beginning or end of its category list rather than at its middle (2-tailed sign test, p=0.0005 and p=0.0002, respectively). Although the individual items show that advantage to range up to 64%, none was significant. At the category level, the advantage ranged up to 57%, with the Grand Total being a significant 56% overall (p<.001 by 2-tailed sign-test). Even in the category of “unpopular items” (namely those ordered so infrequently that they were left out of Table 3), the advantage was 54%.
The category results are visually displayed in Figure 1.
Although this paper is concerned exclusively with middle-vs.-edges
position effects, the data afford an opportunity to check for primacy
and recency effects as well. None, however, was found: 50.5% of the
choices were for the items at the top half of their category vs.
49.5% for the bottom half. Moreover, the Total percents show a
striking symmetry around the middle (see the bottom line of Table 3).
Item popularity as a function of distance from the middle was
21%–20% (first vs. last); 7%–7% (second vs. penultimate);
5%–6% (M++ vs.
M--); 17%–16% (M+ vs. M-).
These data also show, somewhat surprisingly, that the edge advantage was not larger for first/last position vs. middle than for second/penultimate position vs. near-middle (notice how items of the former and the latter kind interleave throughout the table, which is ordered by the magnitude of the effect). The enhanced popularity of the first/last positions was 55% (out of 674 observations), and that of the second/penultimate positions was 57% (out of 228 observations; the difference is not significant).
Base Menu Freq I/O menu Freq A1 Frangelico Quarto 2 A2 8 A2 Kahlua / Grappa Quarto 3 A1 2 A3 Frangelico Espresso 4 A4 17 A4 Irish Cream 17 A3 5 Alcoholic coffee total 26 - 32 S1 Mineral water 51 S3 78 S2 San Pelegrino 85 S2 87 S3 Coke / Diet Coke 50 S1 45 S4 Sprite / Diet Sprite 41 S6 5 S5 Nut drink 5 S5 8 S6 Passionfruit drink 6 S4 46 Soft drinks total 238 - 269 D1 Croissant 18 D5 35 D2 Brownie 16 D4 24 D3 Coffee cake 29 D3 35 D4 Banana bread 28 D2 11 D5 ried fruit cake 29 D1 9 D6 Cookie platter 20 D10 8 D7 Carrot cake 39 D9 2 D8 Tiramisu 2 D8 4 D9 Chocolate souffle 2 D7 42 D10 Fruit salad 7 D6 26 Desserts total 190 - 196
Clear and unambiguous as the results of Study 1 are, they are nonetheless hypothetical choices, made—for better or for worse—under controlled, but artificial, conditions. In contrast, Study 2 was run on the real choices of real customers in a Tel Aviv café. The menu, naturally, listed prices (in New Israeli Shekels; see Appendix). The management cooperated with the study manipulations in two respects. First, they agreed, for the study period, to alternate (across days) the usual menu with one identical to it in every respect except for the order of some menu items. Second, they recorded customer orders for our benefit, as detailed below.
The café is a small town-center coffee-shop, open 7 days a week, from 8am till one or two hours after midnight, and catering primarily to students and young professionals. It consists of seven tables and a counter, and offers a wide selection of hot or cold drinks based on coffee, tea, or ice-cream, and served with or without alcohol, as well as a selection of sodas and fresh juices. It also serves desserts such as cakes and ice-cream. There were altogether about 60 listings on the menu, some of which stand for multiple possibilities (e.g., “coffee” can be had in a caffeinated and decaffeinated version; “ice-cream” comes in many flavors; some canned drinks can be had in a diet version; etc.). The study focused on only 3 categories (which appear as such on the menu): Coffee with alcohol—4 items; Soft drinks—6 items; Desserts—10 items. An exact replica of the menu, translated into English, appears in the Appendix.
During the period of the study, all orders made from these categories were recorded, separately and discreetly, by the waiters. Orders placed without resort to the menu (e.g., by some regular customers) were not recorded.
The study took place in summer, though not on a daily basis. Each form was given on 15 days, alternating, with exactly the same distribution over the days of the week (thus controlling for possible systematic variations in days of the week). The Baseline menu is the café’s standard menu. The Inside-Out version changed only the positions of the items in the study’s 3 target categories, exchanging items on the two ends of the category with items from the middle of the category, as shown in Table 4.
Participants. Participants were the self-selected clientele who ordered from the three target categories during the period when observations were collected. We cannot say exactly how many customers were involved, only how many orders were involved (459 from the Base menu, and 492 from the I/O [Inside-Out] menu). Some customers may have ordered more than one item during a single visit, and some may have been repeat customers, but no records were made of these possibilities.
Design, stimuli and procedure. There were two versions of the menu, in which 20 items out of the 60 in the menu differed only in their order within their category (see Table 4). Data were collected with no particular protocol. We are aware that asking the café’s waiters (who necessarily were not blind to the manipulation, but were blind to the hypothesis) to record the data is a possible source of noise, adding to the naturally occurring noise from having no control over the customers and their choices. However, it is hard to imagine how any biases, including those that are time sensitive (e.g., more sloppiness at the end of the day, due to waiter fatigue, or less sloppiness at the end of the day, due to waiter “warm up”), might interact with our variable of interest.
Popularity in percents as a function of item Item N 1st 2nd M++ M+ M- M-- PU Last % extreme D1 27 67 - - 33 - - - - 67 S3 128 61 - - 39 - - - - 61 * D2 27 - 59 41 - - - - - 59 D6 46 - - - - 43 - - 57 57 D5 64 - - - - 45 - - 55 55 S4 87 - - - - 48 - - 53 53 S1 96 53 - - 47 - - - - 53 D7 81 - - - - - 48 52 - 52 A4 34 - - - - 50 - - 50 50 D4 52 - 46 54 - - - - - 46 A total 58 17 - - 8.6 36 - - 38 55 S total 322 40 - - 30 14 - - 16 56 * D total 316 17 13 12 12 9 13 14 10 54 Grand total 696 28 5.7 5.6 20 14 5.9 6.3 15 55 * * indicates significance at the .05 level or better, two-tailed.
Table 4 lists the categories and item names that were manipulated in Study 2. It shows the two orderings of the menu side-by-side, and the number of times each item was requested during the study period.
Table 5 was derived from Table 4 in the same manner as Table 3 was derived from Table 2. Thus, it does not show the hypothesis-irrelevant items (S2, S5, D3, D8), and it does not show items whose total number of orders over the study period fell under 24 (A1, A2, A3, S6, D9, D10—a total of 56 orders). The latter were nonetheless included in the category-level percents, shown at the bottom of the table, and in all analyses. Frequency of customer orders was replaced by percent of all orders from that category, and items are listed in the table from that showing the most benefit for an extreme location (D1 Croissant), to that showing the least benefit (D4 Banana bread).
Only one item of the 10 items in Table 5 (D4; A4 is tied), and only 2 of the 18 items in Table 4 (D4 and D10; A1, A4 and D8 are tied), show an advantage to a middle position (2-tailed sign test: p=.04; p<.007, respectively). At the category level, this advantage ranges up to 56%, with a grand mean of 55%—just a tad lower than the advantage found in Study 1 (56%). At the category level, only Soft drinks was significant. All in all, Study 2 showed much the same advantage to being placed at the beginning or end of a menu category as was shown in Study 1.
In this study, there was a larger gain when an item moved from the exact middle to the extreme end (55%), than when it moved from the near-middle to the near-end (51%; n.s.). Table 5 also seems to show an advantage to being listed in the top half of a category (59% of the choices; p<0.0001, 2-tailed sign test). However, we did not use a Mirror ordering here, so the effect of side is confounded with the nature of the items themselves, and thus cannot be attributed to position. Therefore, there is no point in checking for symmetry in Table 5 as we did in Table 3.
The category results are visually displayed in Figure 2.
Menu consultants may be wrong in some of their recommendations (Kincaid & Corsun, 2003; Reynolds, Merritt & Pinckney, 2005), but apparently they are not wrong on the particular one studied here. In two studies, one eliciting hypothetical choices and one observing real choices, we found that placing menu items at the beginning or end of their category increases their popularity by about 20% (namely the gain from 45% of the time when an item appeared in the middle of its category, to 55% of the time when it appeared at one of the ends of its category). This effect depended neither on the kind of foods in the category, nor on its size (4 items, 6 items, 8 items or 10 items—albeit the two were somewhat confounded).
We cannot offer a satisfying explanation for why menu choices would differ from the many other contexts in which different, usually even opposite, biases were found, surveyed in our introduction. Indeed, we found not one single study that showed an advantage to being both first and last over being in the middle. We are dismissing, of course, the vast literature on the serial position effect, because “position” there is temporal, not spatial, and the dependent variables are related to memory, not to choice. We must also dismiss the results in our companion paper, although Rozin et al. (2011) also found an edge advantage—placing food items at either side row of a three-row food display, rather than in its middle row, enhanced their popularity. But Rozin et al. had a convincing physical explanation for their results: the items in the middle were physically harder to access, requiring a longer reach under a plastic shield (“Sneeze Guard”). Alas, their account cannot be applied to choice from a menu.
From the other studies of position effects in simultaneous choice, we shall also put aside those that involve hide-and seek strategies (e.g., Rubinstein, Tversky & Heller, 1986; Attali & Bar-Hillel, 2003), because a menu is certainly not a set of options hiding one “correct” option for the chooser to discover, but rather a display inviting the chooser to suit him- or her-self only. Finally, we shall put aside those where all options are the same but for their position, which is not the case for menus. Of the remaining studies, perhaps the closest is the ballot voting study (Koppell & Steen, 2004), and the two consumer-choice studies (Nisbett & Wilson, 1977; Valenzuela & Raghubir, 2009). Alas, these did not find consistent position effects (the effects found, respectively, were primacy, recency, and “center stage”), and correspondingly, did not offer consistent accounts. Moreover, they also found the literature inconsistent, and offered their accounts speculatively (e.g., Koppell & Steen: “the literature is contradictory, with no clear pattern in the findings across studies”, p. 268; Nisbett & Wilson: “Precisely why the position effect occurs is not obvious. It is possible that subjects [were] “shopping around”, holding off on choice of early-seen garments on the left in favor of later-seen garments on the right”, p. 244; Valenzuela & Raghubir: “prior research examining the effect of physical position of products in an array has found inconsistent effects ([reference list follows]), and is divided as to why position effects occur. … evidence [for offered accounts] … is lacking …”, p. 185).
At this time, the topic of position effects in simultaneous choice is far from being well understood (see Bar-Hillel, 2011), and additional research is clearly called for.
Although our results may presently lack an explanation, we believe they are robust enough to warrant confidence, especially with an eye to real-world application rather than theory. We believe that we have presented enough evidence to recommend a nudge: Put the food you want to encourage at the extremes of the menu listings. This recommendation applies to the listings within category; we have not studied whether it is similarly possible to nudge people across category boundaries. If anyone who wishes to adopt this nudge to nobesity remains skeptical—it is ridiculously easy and cheap to test it in their specific context: change menu positions, and see.
Nudges can be used not only to promote healthier food choices, but any other agenda as well (higher earnings; faster turnover for more perishable foods; etc.). It is up to us to nudge to nobesity. Rozin et al. (2011) show in quantitative detail how even negligibly small effects can accumulate over time till they are significant. They also address the various caveats that can be raised against attempts to affect food intake by a single nudge. Their analysis applies to our nudge as well. And, like theirs, it can all be done dirt cheap and with minimal effort.
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