Entrepreneur: Start & Grow Your Business

An incentive compatible conjoint ranking mechanism.


by Lusk, Jayson L.^Fields, Deacue^Prevatt, Walt

Conjoint analysis is one of the most popular marketing research tools, used in hundreds if not thousands of academic and business research studies, e.g., see Green, Krieger, and Wind (2001) or Green and Srinivasan (1990) for reviews. Conjoint analysis typically involves people rating, ranking, or choosing among various options that differ by several attributes so as to elicit consumer preferences, estimate demand, and/or forecast market share. Until very recently, virtually all conjoint applications were hypothetical. That is, a person's ranking, rating, or choice had no immediate financial consequence. At worst, hypothetical valuation questions are open to strategic manipulation on the part of the participant, and at the least they do not provide incentives for people to put cognitive effort into their decisions. Over the past twenty years, a wealth of evidence has accumulated indicating that responses to hypothetical willingness to pay and purchase intention questions are not always consistent with decisions when real money is on the line. For example, see the Meta analyses in List and Gallet (2001) and Murphy et al. (2005).

Such findings have led researchers to investigate methods for making traditional conjoint methods incentive compatible (IC). (1) One solution, proposed by Alfnes et al. (2006), Carlsson and Martinsson (2001), Ding, Grewal, and Liechty (2005), and Lusk and Schroeder (2004) is to make use of traditional choice-based conjoint analysis methods, but to randomly select one of several repeated choices between competing product profiles as binding. The participant purchases the product indicated as most preferred in the randomly selected choice set. Although this approach represents a useful step forward, it is limited to choice-based applications. Choice-based conjoint analysis has many advantageous properties, but it is lacking on at least one front: it is informationally inefficient relative to ranking-based conjoint applications. In a choice-based conjoint application, all that is known is which one option is most preferred out of a set of options. By contrast, ranking-based conjoint applications provide information on the consumer's complete preference ordering. These facts coupled with the observation that ranking-based conjoint applications remain widespread, e.g., see Baker and Burnham (2001) or Sayadi, Roa, and Requena (2005) for recent examples, suggest it is prudent to identify methods for making ranking-based conjoint methods IC.

The objectives of this study are: (1) to introduce a mechanism for making conjoint rankings IC and (2) to empirically compare traditional, hypothetical conjoint ranking responses to those using the new IC conjoint mechanism. The new mechanism entails people ranking profiles as in traditional conjoint analysis. However, unlike traditional conjoint analysis, an individual actually purchases a product profile with a probability proportional to its assigned rank. We illustrate a simple and straightforward method to implement the IC conjoint ranking mechanism in an empirical application related to consumer preferences for beef attributes.

An Incentive Compatible Conjoint Ranking Mechanism

Consider a mechanism where individual i is asked to rank J products that differ in terms of a vector of attributes [X.sub.j]. The utility individual i derives from product j is

(1) [V.sub.ij] = [[beta].sub.i] [X.sub.j] - [[gamma].sub.i] [P.sub.j]

where [[beta].sub.i] is a vector of marginal utilities, [P.sub.j] is the price of alternative j, and [[gamma].sub.i] is the marginal utility of income. Index the products such that [V.sub.i1] > [V.sub.i2] > ... > [V.sub.i(J-1)] > [V.sub.iJ]. That is, product j = 1 is the most preferred product, j = 2 is the next most preferred product, and so on. The goal is to create a mechanism in which an individual has an economic incentive to truthfully reveal their preference ranking for the J goods. Stated differently, a mechanism is needed wherein an individual's expected utility is maximized when the products are ranked such that product j = 1 receives a rank of 1, product j = 2 receives a rank of 2, and so on.

Let [r.sub.j] represent the ranking of product j such that [r.sub.1] is the ranking of product 1, [r.sub.2] is the ranking of product 2, and so on. An IC mechanism can be constructed by requesting individuals to rank the J products where there is a J + 1 - [r.sub.j]/[[summation].sup.J.sub.j=1] x 100% chance of actually receiving product j and paying [P.sub.j]. The formula implies there is a higher chance that an individual receives a product with a lower rank than a product with a higher rank. For example, if there were five products to be considered, the mechanism would ensure that there would be a ((5 + 1 - 1)/15) x 100 = 33.3% chance of an individual actually receiving the product ranked first, a ((5 + 1 - 2)/15) x 100 = 26.7% chance the product ranked second would be received, and so on. The equation stated above also ensures that there is a 100% chance that one of the products will actually be purchased (although as will be shown in the empirical application, one of the ranked options can be a no-purchase option). (2)

An individual's expected utility from ranking J products is:

(2) E[U.sub.i] = [J.summation over (j=1)](J + 1 - [r.sub.j]/[[summation over].sup.J.sub.j=1] j) [V.sub.ij].

Equation (2) shows that the expected utility derived from ranking J goods is the sum of the probability of receiving product j times the utility received from purchasing product j. An individual's goal is to rank the products in a way so as to maximize expected utility given in equation (2). It should be clear that expected utility is maximized when an individual assigns the highest rank to product j = 1, the second highest rank to product j = 2, and so on. This result arises because product I was previously defined as the most preferred product, product 2 as the second most preferred product, and so on. Expected utility cannot be made higher by assigning a more preferred product a higher rank. This implies that the mechanism is IC; an individual's best strategy in terms of maximizing expected utility is to assign the most preferred product the lowest rank, the second most preferred product the second lowest rank, and so on. The mechanism is also IC under a variety of other nonexpected utility models. For example, under prospect theor.y (Kahneman and Tversky 1979), individuals mis-perceive probabilities such that probabilities, p, are weighted, w(p), in such a way that low probabilities are over-weighted and high probabilities events are under-weighted. However, so long as [partial derivative]w(p)/[partial derivative]p > 0, as is assumed in prospect theory, equation (2) is maximized by ranking the most preferred product first, the second most preferred product second, and so on.

Although this mechanism might, at first, seem a bit complicated to utilize in an empirical setting, it is actually quite easy to implement. In what follows, we briefly describe one such way the mechanism can be implemented. In many conjoint ranking applications, individuals are given a set of cards describing each product and are requested to sort them in terms of their preference ranking. One easy way to make such a task IC is to create a spinning wheel of the sort found in board games or seen on the Wheel of Fortune, where the wheel is divided into a number of "slices" that differ in size. To facilitate decision making, the slices can be ordered such that the largest slice appears adjacent to the second largest slice, which appears adjacent to the third largest slice, etc. Instead of simply requesting that individuals hypothetical sort the cards, as is typically done, the following steps can be taken: (1) the individual places each card on a slice on the wheel, where the number of slices exactly equals the number of cards; (2) after all cards are allocated, the wheel is spun; and (3) the individual purchases the product indicated by the fixed-pointer around which the wheel is spun. Of course, any number of other implementation methods could be used that would ensure a profile with a lower rank has a higher probability of being purchased. (3)

Empirical Application

In what follows, we describe an empirical application of the IC conjoint ranking mechanism and test whether results from such a mechanism are similar to results from traditional, hypothetical conjoint rankings. We also explore whether making the conjoint task IC interacts with two other treatment variables: information and product type.

Subjects

Participants were recruited near the meat counter in a suburban grocery store located in the southeastern United States Harrison and List (2004) discuss the advantages of carrying out value elicitation in a field setting such as a grocery store. Subjects were offered the chance to enter a drawing for $500 in free groceries in exchange for participation in the study and, as will be described in more detail, some subjects were offered free cuts of meat for participation. A total of 515 subjects took part in the study.

Procedures

Participants were requested to rank the relative desirability of several meat products that differed by the attributes of: (a) whether the animal was pasture-grazed, (b) whether the animal was administered growth hormones and antibiotics, (c) whether the meat was traceable back to the farm, (d) package size, and (e) price. These attributes are of interest for a number of reasons. On the policy front, there is ongoing action related to traceability and there have been recent legislative action to ban the use of some antibiotics in livestock production. Valuation estimates are needed to determine the welfare effects of such policies. On the marketing front, firms are increasingly interested in selling "natural" products without hormones and there is increasing interest in the value of "grass fed" beef. Although several previous studies have estimated consumers' values for these characteristics, e.g., Alfnes and Rickertsen (2003), Dickinson and Bailey (2002), Lusk, Fox, and Roosen (2003), Lusk, Feldkamp, and Schroeder (2004), Lusk, Norwood, and Pruitt (2006), McCluskey et al. (2005), Umberger et al. (2002), to our knowledge this is the first study to investigate preferences for pasture-raised beef relative to nonpasture-raised beef (based on perceptions and not on taste) and to study the effect of information about the healthfulness of such products. This latter issue has become increasingly important as evidenced by the USDA's recent solicitation of comments on a proposed standard for grass-fed and pasture-fed beef claims.

The IC conjoint task involves the exchange of real money and real food. There is some debate in the literature about the proper way to compensate people for participating in experiments so that elicited valuations are not unduly influenced by the compensation approach. A common approach is to give people money for participating and then request that participants purchase a product with the endowed money. However, several studies have shown that people's willingness-to-pay for a good in an experiment is significantly influenced by the amount of money given to them (e.g., Loureiro, Umberger, and Hine 2003; Rutstrom 1998). This led Loureiro, Umberger, and Hine (2003) to remark (p. 271), "[n]ew ways of compensating participants in experimental auctions should be investigated." A solution to this problem might be to provide participants no compensation at all. However, such an approach is likely to drastically reduce participation rates, which would increase sample selection bias and would significantly underestimate people's values for goods as there are often many cash constrained people in a store setting, e.g., many consumers come to a store planning to pay by credit card or check and do not have any cash to participate in a value elicitation experiment even though they might have a positive willingness-to-pay for the good in question.

Accordingly, we utilized a slightly different approach to compensate participants and to estimate the marginal utility of income. In particular, rather than asking people to pay a price for a particular meat option, people were offered various cash amounts with each option. In regard to this procedural choice, it is important to note three important facts. First, one might argue that loss-aversion would create a difference between the approach used here and one in which individuals ranked products that they wished to purchase. However, Novemsky and Kahneman (2005) argue that in money transactions, of the sort involved in this exchange, there should be no loss aversion. Second, empirical findings suggest this sort of compensation mechanism yields accurate predictions of people's shopping behavior. For example, Lusk, Pruitt, and Norwood (2006) found responses from an in-store experiment where people chose between various products coupled with cash offers (as in this study) accurately predicted actual retail sales in the grocery store several weeks later. Further, Ding (2007) utilized a related compensation mechanism where auction winners were paid an amount equal to the difference in price and a certain cash amount ($250 in one experiment and $320 in another). Ding (2007) found significantly better out-of-sample predictive performance with this compensation mechanism as compared to traditional hypothetical approaches where no compensation is given at all. Finally, the purpose of this study is to compare traditional, hypothetical conjoint response to a new IC conjoint mechanism. In both treatments (hypothetical and nonhypothetical) people ranked the products and cash offers in terms of which they would like to receive. Thus our approach permits an unconfounded test of the effect of moving from a traditional, hypothetical conjoint method to the new IC conjoint mechanism.

Table 1 lists the attributes and attribute levels investigated in this study. An orthogonal fractional factorial design consisting of 16 product profiles was created such that all main and two-way interaction effects were independently identifiable. These 16 profiles were blocked into sets of eight. Each subject was asked to rank the desirability of the eight profiles in addition to a "no meat" option that consisted simply of an offer of an amount of cash that was higher than any of the cash offers that included a meat offering. This latter option was included to account for people that participated in the study but did not want to take home any meat. If a "cash only" offer were not presented, it is likely that the price/cash effect would be overstated in the sense that nonmeat preferring individuals would simply choose meat profiles with higher cash offers. Our econometric model, which is explained momentarily, explicitly controls for the "no meat" option, providing an estimate of the disutility of "no meat" holding constant price/cash. (4) Individuals were given nine cards (eight containing a meat product description and one "no meat" option) and were asked to rank the cards according to their desirability.

Individuals were randomly assigned to one of the eight treatments (there are three treatment variables each varied at two levels each, [2.sup.3] = 8). Treatments varied according to whether: (1) the conjoint ranking was IC or whether the ranking was hypothetical, (2) the conjoint task related to beef steaks (ribeyes) or ground beef, and (3) whether information was provided about the health benefits of pasture grazed beef. The purpose for including two other treatment variables in addition to whether the conjoint ranking was real or hypothetical was to determine whether the IC property has an effect, not just on product attributes, but on the effect of other treatment variables. The study took place over a one-week time period and the treatment was alternated every hour. The fewest number of participants in any one treatment was 59 (the hypothetical, steak, no-info treatment) and the most participants in a treatment was 75 (the hypothetical, ground beef, no-info treatment).

The first treatment variable is the nature of the decision task: either hypothetical or nonhypothetical. Traditional conjoint analysis involves people hypothetically ranking a series of product descriptions according to their relative desirability. This is exactly what was done in our treatments where the conjoint task was hypothetical. Specifically, individuals in the hypothetical treatment were given the following instructions:

For participating in this survey, we would like you to consider the

desirability of several hypothetical gifts. Although you will not

actually be given any of these gifts, we ask that you please think

carefully about your answers.

You will be viewing a poster with 9 gift coupons, each of which

describes a hypothetical gift. Gifts vary in the type and amount of

meat that you can receive. Each gift option also indicates whether

the meat comes from cattle that were raised in a pasture, were

produced without antibiotics or added growth hormones, and/or

whether the meat is traceable back to the farm. All gift options

also vary by a cash amount that would be given to you in addition

to the meat.

Your task is to sort the 9 gift coupons you have been shown in

terms of their desirability to you.

Please write the letter of the gift option you find most desirable

in the space below next to the number 1, the letter of the gift

option you find second most desirable next to the number 2, and so

on. The option you find least desirable should be put next to the

ranking of 9.

Although it is typically assumed that individuals "do their best" and rank products according to their preferences, there is no monetary cost to individuals deviating from their true preferences or monetary reward for putting cognitive effort into the ranking task.

In the IC, nonhypothetical treatments, individuals were also given nine cards to rank, but in this case, they were asked to place the cards on a wheel that was divided into nine slices of varying size. Participants were asked to place the option they found most desirable in the largest slice on the wheel marked with a number one, the second most desirable option in the second largest slot marked two, and so on. Once all nine cards were allocated, the wheel was spun around a fixed pointer. Once the wheel stopped spinning, the pointer indicated the option that was actually received. Thus, in the nonhypothetical treatments, individuals were actually given the meat and/or the cash associated with the option that was selected by the wheel. More specifically, participants in this treatment were instructed as follows:

For participating in this survey, we would like to offer you a

gift. You will be given 9 cards, each of which describes a gift you

might receive. Gifts vary in the type and amount of meat that you

can receive. Each gift option also indicates whether the meat comes

from cattle that were raised in a pasture, were produced without

antibiotics or added growth hormones, and/or whether the meat is

traceable back to the farm. All gift options also vary by a cash

amount that will be given to you in addition to the meat.

Your task is to sort the nine cards you have been given in terms of

their desirability to you. You should see a wheel in front of you.

You should place the gift option you find most desirable next to

the largest slot marked 1, the second most desirable gift option

you next to the second largest slot marked 2, and so on. Put the

card describing the gift option you want the least next to the

number 9 on the wheel.

Once all 9 cards are set up next to the wheel, you will spin the

wheel. Where the pointer stops will indicate the gift option you

will actually receive. This is a real decision making exercise, we

will really give you the steak and/or the cash associated with the

gift option that is selected.

The second treatment variable is product type. Because individuals' cognitive processes may differ depending on the type of good and whether the product is of high or low quality, we utilized two types of meat: ground beef and ribeye steak. These two products represent the two ends of the spectrum in terms of beef product prices and quality; ground beef is one of the lowest price beef products, whereas ribeye steak is one of the highest price beef products.

The final treatment variable is information. In some treatments, participants were not given any information about the product attributes; a situation that reflects what would happen were a consumer to encounter a new product or brand in the marketplace where they would have to make a purchase decision based on whatever information they had at the time. However, firms might be interested in advertising or providing information on the benefits of certain attributes. To investigate this effect, some people were given the following information:

Some gift options indicate that the meat is from Cattle Grazed in

Pasture Only. Research has shown that cattle fed a diet of grass

from pastures have higher levels of Omega 3 fatty acid, Conjugated

Linoleic Acid, and Vitamin E than grain fed beef. Research has also

shown that human consumption of Omega 3 fatty acid, Conjugated

Linoleic Acid, and Vitamin E is associated with reduced risk of

heart disease, reduced body weight, and other health benefits that

result from consumption of antioxidants.

Econometric Model

Let the deterministic portion of the utility function for person i, alternative j, and meat type m (m = ground beef or steak) corresponding to the conceptual model in equation (1) be rewritten as:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where Pasture takes the value of 1 if meat option j was from cattle that were pasture fed only and 0 otherwise, Hormone takes the value of 1 for meat products from cattle that were not administered growth hormones or antibiotics, Trace takes the value of 1 for meat products that are traceable back to the farm and 0 otherwise, Size takes the value of 1 for package sizes of two pounds and 0 otherwise, Cash is the amount of money offered to the individual with option j, None takes the value of 1 for the option where no meat product was offered and 0 for all other options, Non-Hyp equals 1 for the IC, nonhypothetical ranking treatment and 0 for hypothetical rankings, and Info equals 1 for treatments that provided information about pasture fed beef and 0 otherwise. The parameters in (3) are specified to vary by meat type, m, because the value of product attributes and the effect of the IC mechanism may differ by meat type. Finally, let the random utility function be specified as [U.sub.ijm] = [V.sub.ijm] + [[epsilon].sub.ijm], where [[epsilon].sub.ijm] is an iid random error term included to indicate the fact that people's preferences cannot be ascertained with certainty.

Because of the ordinal nature of the dependent variable (the person's ranking), we estimated a rank-ordered logit model that assumes people choose the option they find most desirable and rank it first, then choose the option they find second most desirable out of the remaining options and rank it second, and so on. Assuming [[epsilon].sub.ijm] are distributed type I extreme value, Beggs, Cardell, and Hausman (1981) show that out of a set of J products, the probability that option 1 is preferred to option 2, option 2 is preferred to option 3, option 3 is preferred to option 4, and so on is given by

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

which is simply the product of J - 1 multinomial logit models. In equation (4), [[lambda].sub.ijm] is a scale parameter that is inversely related to the variance of the error term. Typically [[lambda].sub.ijm] is unidentifiable and is assumed equal to one. However, the relative scale associated with different data sets or experimental treatments can be estimated.

Estimating the relative scale parameter is important in this application for three reasons. First, in a discrete choice model such as this, preference/utility parameters are confounded with the scale (see Swait and Louviere 1993). Thus, to identify the effect of moving from IC to non-IC rankings, the relative variance of the treatments must be controlled prior to comparing utility parameters. Second, Haab, Huang, and Whitehead (1999) illustrated that responses to nonhypothetical choice tasks are often less "noisy" than responses to hypothetical choice tasks. They argue that with nonhypothetical decisions, there are higher opportunity costs to deviating from the rational response, which should result in a lower error variance for nonhypothetical responses as compared to hypothetical responses. Third, previous research has identified that error variance is increasing in ranks (Ben-Akiva, Morikawa, and Shiroishi 1992; Hausman and Ruud 1987). That is, there is less often "noise" in the initial ranks than there is in the later ranks. To accommodate these issues, the scale function is parameterized as follows:

(5) [[lambda].sub.ijm] = exp ([J-1.summation over (k=2)] [[mu].sub.km][[rank].sub.k] + [[rho].sub.1m]Non-Hyp + [[rho].sub.2m]Info)

where [rank.sub.k] takes the value of 1 for the kth rank ordered choice and 0 otherwise and where [[mu].sub.k] and [[rho].sub.k] are parameters to be estimated. Noting that exp(0) = 1, the scale function in equation (5) takes the value of one for those data associated with the most preferred, first rank (in which [[mu].sub.1] is implicitly set to 0) in the hypothetical, no information treatments. Recognizing that the scale function is inversely proportional to the error variance, we would expect, based on the aforementioned literature, for [[mu].sub.k] to fall as k increases and for [[rho].sub.1m] > 0. (5)

The parameters of the model are estimated by maximizing the natural logarithm of equation (4) summed across the N individuals in the sample. Given this model setup, the effect of moving from IC to non-IC treatment can have a complex effect on behavior. Making the ranking task IC might (a) increase or decrease the marginal utility of any of the product attributes, (b) exacerbate or dampen the effect of information, and/or (c) affect the model variance.

Results

Model estimates for ground beef and steak are presented in table 2. The first six rows of results correspond to the estimated preferences when treatment variables are zero, i.e., the treatment is hypothetical and no information is presented. Results are generally consistent with a priori expectations. Results indicate that individuals, on average, preferred pasture-grazed beef over beef that did not have such an attribute, beef from cattle that were not administered growth hormones or antibiotics over hormone and antibiotic treated cattle, beef that was traceable back to the farm versus nontraceable beef, two instead of one pound of beef (except for steak), more cash to less, and having a pound of beef to no beef at all.

Before moving forward, it is useful to compare these baseline empirical results relating to people's preferences for beef product attributes to that found in previous studies. The relative size of the coefficients suggests participants valued the hormone attribute more than the pasture or traceability attributes in the hypothetical no-information treatment. This qualitative result is consistent with the findings of Dickinson and Bailey (2002). Dickinson and Bailey (2002) further found, using experimental auctions, that average willingness-to-pay for traceability in roast beef sandwiches was $0.23. In our application, willingness-to-pay for a product attribute is calculated by taking the ratio of the attribute coefficient to the cash coefficient. Carrying out such a calculation reveals an average willingness-to-pay for traceability of about $1.40 per choice occasion for ground beef and $3.19 per choice occasion for steak in the base-line treatments. Thus, the values of traceability found here among consumers in the southeastern United States using a conjoint ranking mechanism are quite a bit higher than those found by Dickinson and Bailey (2002) among people working at Utah State University using experimental auctions.

Estimates in table 2 further reveal willingness-to-pay values for no-hormone use in the base-line treatment of $1.78 for ground beef and $3.34 for steak. These statistics are much lower than those found by Lusk, Roosen, and Fox (2003) who estimated the value of nonhormone use in beef steaks at $8.12/lb for U.S. consumers using a hypothetical choice experiment. However, the values are similar to those obtained by Lusk and Schroeder (2004) who found that people in a choice experiment were willing to pay between $1.36 and $3.75 (depending on the estimated model and whether the decision task was real or hypothetical) to have a "natural" steak rather than a "generic steak."

The next several rows of results relate to the primary hypotheses of interest: whether behavior in the new IC ranking mechanism differed from that in the traditional hypothetical ranking approach. For ground beef, moving from hypothetical to IC rankings had no significant impact on any of the utility coefficients or on the error variance. Interestingly, preferences for ground beef were also unaffected by information about pasture grazed beef. The lack of sensitivity to changes in both the information and elicitation mechanism could be a reflection of the fact that people often do not appear to behave rationally when dealing with low-valued goods. For example, List and Lucking-Reiley (2002) found people's behavior in auctions appeared significantly more rational when bidding on expensive sports cards as compared to sports cards that retailed for only $2. They argue such behavior arises because the opportunity costs of irrational behavior increases with the value of the good. As such, we would expect people to be more sensitive to treatment effects when ranking higher-valued steaks. As shown in table 2, this is exactly what we find.

In the steak model, moving from hypothetical to nonhypothetical rankings has a number of effects. In the no information treatments, moving from non-IC to the IC mechanism decreases the marginal utility of pasture-raised beef, decreases "price sensitivity," and increases the utility of "no meat." It is telling that the two parameters, Cash and None, were significantly affected by the hypothetical nature of the mechanism because it is these two parameters that people would attempt to manipulate if they desired to strategically respond to the survey. For example, Wertenbroch and Skiera (2002) argue, (p. 230), "[i]f subjects believe that their responses will be used to set long-term market prices, they have an incentive to under-state their [willingness-to-pay]. If they believe that their responses will determine the introduction of a desirable new product, they may perceive reasons to overstate their [willingness-to-pay]."

That people were less sensitive to changes in Cash when the steak decision task was nonhypothetical means, holding the magnitude of other parameters constant, that the computed amount of money required to make an individual indifferent between two options that differ in the level of an attribute (e.g., marginal willingness-to-pay) would be larger in the IC mechanism than the traditional hypothetical approach. This finding may initially seem counter-intuitive, as most studies find higher willingness-to-pay in hypothetical versus real treatments. Note, first, however, that whether price sensitivity should increase or decrease when a task is made IC is theoretically ambiguous. On one hand, people might be expected to become more price sensitive with an IC mechanism as they will actually receive the cash. On the other hand, making a decision task IC might force people to more carefully consider other product attributes when completing the ranking, since they will now be taking a meat product home, rather than simply picking the options with the highest cash offer. Second, it is important to note that the marginal utility of other attributes is not held constant when a decision task is made IC. In particular, the disutility associated with the "no meat" option significantly increases when the task is IC. This is the same as saying that the utility from having a steak significantly decreases when the task is IC. This latter result is exactly what studies such as Lusk and Schroeder (2004) found: the utility of having a steak falls when the task is real instead of hypothetical. That the marginal utilities of most of the other steak attributes (hormone, traceability, and size) are uninfluenced by whether the decision task is IC is also consistent with Carlsson and Martinsson (2001) and Lusk and Schroeder (2004), who found little difference in real and hypothetical marginal utilities for product attributes.

Results in table 2 also indicate that information significantly affected preference parameters. Providing information about pasture-grazed beef significantly increased the marginal utility of the pasture attribute as expected. Interestingly, the marginal effect of information interacted with the IC-treatment effect for the Size, Cash, and None attributes. To see this, note that the utility of None can be written as: -11.873 + 1.289 x Info + 8.082 x Non-Hyp - 5.698 x Info x Non-Hyp. This implies that when information was provided in the hypothetical mechanism, the value of having a steak decreased; however, providing information in the IC mechanism increased the utility of having a steak.

Turning to the scale function, results reveal that moving from hypothetical to nonhypothetical rankings increased the scale in the steak model, which implies that error variance decreased (the p-value from a two-tailed t-test is only 0.08, but the hypothesis that the scale factor is greater than zero is rejected at the p = 0.04 level according to a one-tailed test). This result is consistent with the findings of Haab, Huang, and Whitehead (1999) and suggests that, holding all else equal, predicted market shares will be more uniform using hypothetical responses as compared to IC responses. Providing information in the steak rankings was associated with an increased error variance. Finally, for both the steak and ground beef models, we find that the error variance significantly increased for choices associated with higher ranks. Apparently, people were more consistent in determining which options were among the few most desirable as compared to determining the relative ranking among options of medium to low desirability.

To further investigate the implications of the results, market share simulations were conducted. The estimates in table 2 were used to predict the market share that a new pasture-raised product would garner relative to a traditional beef product. To carry out the simulation, parameters in table 2 were substituted into the logit formula, assuming the only products in the choice set were a new pasture-raised product and a traditional nonpasture raised product. Table 3 reports results from the market share simulations assuming conventional and pasture-fed steak (ground beef) were available for sale at $8.00/lb ($2.25/lb) and $10.00/lb ($4.25/lb), respectively. The first column of results shows the predicted market share using estimates from the IC, nonhypothetical mechanism. Results indicate that the pasture-fed product would be expected to achieve about 52% market share in the steak market and 56% in the ground beef market. These results contrast sharply with the market share estimates from the hypothetical treatment, which predicts that pasture-fed beef would only achieve about 39% market share in the steak market and 42% market share in the ground beef market. The 95% confidence intervals suggest that this is a statistically significant difference in predicted market shares for pasture-raised steaks, but not for ground beef. Obviously, pasture-raised products do not currently enjoy market shares as high as those estimated in table 3, and it is important to recognize that table 3 reports estimates of demand at given prices and that a host of supply-side factors need be considered to project an equilibrium quantity sold.

Conclusions

Although conjoint analysis is one of the most popular marketing research tools, it suffers from a potentially serious shortcoming: the method is not incentive compatible. This paper introduces a conjoint ranking mechanism that overcomes this shortcoming. The mechanism requires people to rank a set of product profiles, where a profile that is assigned a lower rank is more likely to be purchased. The method of implementation used in this article involved subjects placing cards containing descriptions of the product profiles on various sized slices of a wheel, which was subsequently spun to determine the product that was ultimately received.

The new mechanism was investigated in an empirical application related to consumer preferences for beef attributes. Results reveal that the consumers' preferences for ground beef were statistically indistinguishable when ranking products with the new incentive compatible mechanism and ranking products in a traditional hypothetical format. The fact that no differences were observed may be attributable to the fact that ground beef is a low-valued good and the opportunity cost of deviating from rational behavior is relatively small. This line of reasoning is supported by the additional finding that providing people information about pasture raised beef did not affect preferences for that attribute when evaluating ground beef. In contrast to the low-valued ground beef products, the new, nonhypothetical mechanism significantly influenced rankings of steaks. In particular, people were less sensitive to price changes in the incentive compatible mechanism than they were in the hypothetical rankings. Further, people tended to overstate their utility of having a steak in the hypothetical rankings as compared to the incentive compatible approach. Results also reveal that the error variance of the random utility function was significantly lower when the decision task was nonhypothetical. Finally, we found that the forecasted market share of a new pasture-raised steak was significantly lower in the hypothetical ranking as compared to the forecast from the incentive compatible mechanism.

Although conjoint ranking methods have the potential to provide much more information about people's preferences than conjoint choice methods, our results reveal this information advantage is partially offset by the fact that less information is conveyed about people's preferences for less preferred, higher ranked options as compared to the more preferred, lower ranked options. The next step in our research program is to determine which implementation method (choices versus ranking) and mechanism (hypothetical or nonhypothetical) best predicts actual retail shopping behavior.

The authors would like to thank Bailey Norwood for his suggestion of the use of a spinning wheel to implement the incentive compatible ranking mechanism.

[Received September 2006; accepted September 2007.]

References

Alfnes, F., A.G. Guttormsen, G. Steine, and K. Kolstad. 2006. "Consumers' Willingness to Pay for the Color of Salmon: A Choice Experiment with Real Economic Incentives." American Journal of Agricultural Economics 88:1050-61.

Alfnes, F., and K. Rickertsen. 2003. "European Consumers' Willingness to Pay for U.S. Beef in Experimental Auction Markets." American Journal of Agricultural Economics 85:396-405.

Baker, G.A., and T.A. Burnham. 2001. "Consumer Response to Genetically Modified Foods: Market Segment Analysis and Implications for Producers and Policy Makers." Journal of Agricultural and Resource Economics 26:387-403.

Beggs, S., S. Cardell, and J. Hausman. 1981. "Assessing the Potential Demand for Electric Cars." Journal of Econometrics 17:1-19.

Ben-Avia, M., T. Morikawa, and F. Shiroishi. 1992. "Analysis of the Reliability of Preference Ranking Data." Journal of Business Research 24:149-64.

Carlsson, F., and P. Martinsson. 2001. "Do Hypothetical and Actual Marginal Willingness to Pay Differ in Choice Experiments?" Journal of Environmental Economics and Management 41:179-92.

Dickinson, D.L., and D. Bailey. 2002. "Meat Traceability: Are U.S. Consumers Willing to Pay for It?" Journal of Agricultural and Resource Economics 27:348-64.

Ding, M.R. 2007. "An Incentive-Aligned Mechanism for Conjoint Analysis." Journal of Marketing Research 44:214-23.

Ding, M., R. Grewal, and J. Liechty. 2005. "Incentive-Aligned Conjoint Analysis." Journal of Marketing Research 42:67-83.

Green, P.E., A.M. Krieger, and Y. Wind. 2001. "Thirty Years of Conjoint Analysis: Reflections and Prospects." Interfaces 31:S56-S73.

Green, P.E., and V. Srinivasan 1990. "Conjoint Analysis in Marketing: New Developments with Implications for Research and Practice." Journal of Marketing 54:3-19.

Haab, T.C., J. Huang, and J.C. Whitehead. 1999. "Are Hypothetical Referenda Incentive Compatible? A Comment." Journal of Political Economy 107:186-96.

Harrison, G., and J.A. List. 2004. "Field Experiments." Journal of Economics Literature 42:1009-55.

Hausman, J.A., and P.A. Ruud. 1987. "Specifying and Testing Econometric Models for Rank-Ordered Data." Journal of Econometrics 34:83-104.

Kahneman, D., and A. Tversky. 1979. "Prospect Theory: An Analysis of Decision under Risk." Econometrica 47:263-91.

List, J.A., and C. Gallet. 2001. "What Experimental Protocol Influence Disparities between Actual and Hypothetical Stated Values? Evidence from a Meta-Analysis." Environmental and Resource Economics 20:241-54.

List, J.A., and D. Lucking-Reiley. 2002. "Bidding Behavior and Decision Costs in Field Experiments." Economic Inquiry 40:611-9.

Loureiro, M.L., W.J. Umberger, and S. Hine. 2003. "Testing the Initial Endowment Effect in Experimental Auctions." Applied Economics Letters 10:271-5.

Lusk, J.L., T. Feldkamp, and T.C. Schroeder. 2004. "Experimental Auction Procedure: Impact on Valuation of Quality Differentiated Goods." American Journal of Agricultural Economics 86:389-405.

Lusk, J.L., F.B. Norwood, and R. Pruitt. 2006. "Consumer Demand for a Ban on Subtherapeutic Antibiotic Use in Pork Production." American Journal of Agricultural Economics 88:101533.

Lusk, J.L., J.R. Pruitt, and F.B. Norwood. 2006. "External Validity of a Field Experiment." Economics Letters 93:285-90.

Lusk, J.L., J. Roosen, and J.A. Fox. 2003. "Demand for Beef from Cattle Administered Growth Hormones or Fed Genetically Modified Corn: A Comparison of Consumers in France, Germany, the United Kingdom, and the United States." American Journal of Agricultural Economics 85:16-29.

Lusk, J.L., and T.C. Schroeder. 2004. "Are Choice Experiments Incentive Compatible? A Test with Quality Differentiated Beef Steaks." American Journal of Agricultural Economics 86:467-82.

Lusk, J.L., and J. Shogren. 2007. Experimental Auctions: Methods and Applications in Economic and Marketing Research. Cambridge, UK: Cambridge University Press.

McCluskey, J.J., T.I. Wahl, Q. Li, and P.R. Wandschneider. 2005. "U.S. Grass-Fed Beef: Marketing Health Benefits." Journal of Food Distribution Research 36:1-8.

Murphy, J.J., G.P. Allen, T. Stevens, and D.A. Weatherhead. 2005. "A Meta-Analysis of Hypothetical Bias in Stated Preference Valuation." Environmental and Resource Economics 30:313-25.

Novemsky, N., and D. Kahneman. 2005. "The Boundaries of Loss Aversion." Journal of Marketing Research 42:119-28.

Rutstrom, E.E. 1998. "Home-grown Values and Incentive Compatible Auction Design." International Journal of Game Theory 27:427-41.

Sayadi, S., M.C.G. Roa, and J.C. Requena. 2005. "Ranking versus Scale Rating in Conjoint Analysis: Evaluating Landscapes in Mountainous Regions in Southeastern Spain." Ecological Economics 55:539-50.

Swait, J., and J. Louviere. 1993. "The Role of the Scale Parameter in the Estimation and Comparison of Multinomial Logit Models." Journal of Marketing Research 30:305-14.

Umberger, W.J., D.M. Feuz, C.R. Calkins, and K. Killinger-Mann. 2002. "U.S. Consumer Preference and Willingness-to-Pay for Domestic Corn-Fed Beef versus International Grass-Fed Beef Measured Through an Experimental Auction." Agribusiness: An International Journal 18:491-504.

Wertenbroch, K., and B. Skiera. 2002. "Measuring Consumers' Willingness to Pay at the Point of Purchase." Journal of Marketing Research 39:228-41.

(1) To date, most applications of IC preference elicitation methods have involved experimental auctions. Lusk and Shogren (2007) show that more than 100 academic studies have been conducted using IC auctions to value new goods and services; however, to date such auction methods have not gained the widespread popularity among marketing academics and professionals as has conjoint analysis.

(1) To date, most applications of IC preference elicitation methods have involved experimental auctions. Lusk and Shogren (2007) show that more than 100 academic studies have been conducted using IC auctions to value new goods and services; however, to date such auction methods have not gained the widespread popularity among marketing academics and professionals as has conjoint analysis.

(2) In principle, any function in which the probability of receiving a product is monotonic in the assigned rank would be suitable; the function presented here is a particularly easy to implement.

(3) If it is desirable to let respondents express indifference between product profiles, the mechanism described in this section can be easily modified simply by letting people assign two products the same rank and re-scaling the probabilities to sum to one. In practice, this is easily handled by leaving one of the slices on the wheel blank and re-spinning the wheel if it happens to land on the blank slice.

(4) If people only cared about receiving additional money and not about the meat products, this would be reflected in our econometric results by finding the estimated utility derived from the amount of cash provided with the "no meat" option outweighing the disutility of having no meat; as we show later in our results, this is not the case.

(5) We also investigated whether [[rho].sub.1m] was rank dependent--i.e., whether the error-variance effect resulting from moving from non-IC rankings to IC rankings depended on the rank. We could not reject they hypothesis that the IC treatment effect in the scale equation was the same for initial ranks as it was for the latter ranks according to a likelihood ratio test (p-values were 0.17 for the steak model and 0.47 for the ground beef model).

Jayson Lusk is professor and Willard Sparks Endowed Chair, Department of Agricultural Economics, Oklahoma State University, and Deacue Fields and Walt Prevatt are associate professor and professor, respectively, both in the Department of Agricultural Economics, Auburn University. Table 1. Meat Attributes and Attribute Levels Used in Conjoint Study Attributes Attribute Levels Pasture feed Cattle grazed in pasture only

(nothing mentioned about how

animal was fed) Antibiotic and Cattle raised without antibiotics,

hormone use no growth hormones added

(nothing mentioned about

growth hormones or antibiotics) Traceability Cattle traceable back to farm

(nothing mentioned about

traceability) Size 1 1-lb steak (or 1-lb ground beef)

21-lb steaks (or 2-lbs ground

beef) Cash offered $3 (or $1 if ground beef)

$5 (or $2 if ground beef)

$7 (or $3 if ground beef)

$9 (or $4 if ground beef) Table 2. Rank-Ordered Logit Estimates

Ground Beef

Parameter Std. Error Variable

Pasture 1.071 *** (a) 0.167

Hormone 1.237 *** 0.254

Trace 0.972 *** 0.196

Size 0.616 *** 0.240

Cash 0.696 *** 0.144

None -6.763 *** 0.882

Info * Pasture 0.257 1.013

Info * Hormone 0.341 1.235

Info * Trace -0.407 0.513

Info * Size -0.643 ** 0.321

Info * Cash