It's All in How You Slice It - Characterizations of Outcome Distributions in Models of Perceived Risk: a Review and a Proposed Model

John W. Vann, University of Missouri-Columbia
ABSTRACT - Perceived outcome distributions have been sliced up in many different ways in an effort to extract information that is relevant to perceived risk. Some models of perceived risk have characterized perceived outcome distributions by their inherent uncertainty, by variance-related measures, and/or by measures of central tendency. Others have utilized threshold values and have then characterized the resultant subportions of the distributions by their relative probabilities or by related semivariance measures. This paper will examine the advantages and disadvantages of each of these approaches and will propose a model which seems to incorporate the strengths of each.
[ to cite ]:
John W. Vann (1985) ,"It's All in How You Slice It - Characterizations of Outcome Distributions in Models of Perceived Risk: a Review and a Proposed Model", in NA - Advances in Consumer Research Volume 12, eds. Elizabeth C. Hirschman and Moris B. Holbrook, Provo, UT : Association for Consumer Research, Pages: 183-188.

Advances in Consumer Research Volume 12, 1985      Pages 183-188


John W. Vann, University of Missouri-Columbia

[This research was partially supported by a University of Missouri-Columbia, College of Business and Public Administration Summer Research Fellowship.]


Perceived outcome distributions have been sliced up in many different ways in an effort to extract information that is relevant to perceived risk. Some models of perceived risk have characterized perceived outcome distributions by their inherent uncertainty, by variance-related measures, and/or by measures of central tendency. Others have utilized threshold values and have then characterized the resultant subportions of the distributions by their relative probabilities or by related semivariance measures. This paper will examine the advantages and disadvantages of each of these approaches and will propose a model which seems to incorporate the strengths of each.


No brand is perfectly consistent in its performance. This inconsistency leads to a consumer's associating each brand with a range of possible performance levels rather than with just one level. Consumers anticipate that some performance levels are more likely than others. In fact, consumers are able to assign (subjective) probabilities to the various performance levels which they consider to be possible (Woodruff 1972). Collectively, the performance levels and associated subjective probabilities (i.e., expected frequencies) which a consumer associates with a brand comprise a perceived outcome distribution for that brand. Perceived outcome distributions may be conceptualized across different dimensions of consequences (e.g., financial, performance, psychological, physical, etc. (Peter and Tarpey 1975)) and for schemata representing different levels of abstraction (e.g., attribute level, brand level, product class level (Vann 1984)). Outcome distributions have been characterized in many different ways to incorporate information regarding their shape and/or location into models of perceived risk. Some of the characterizations only yield information regarding the location (valuation aspect), some only consider the shape (frequentistic aspect), and some incorporate information regarding both the shape and location of the outcome distribution

The risk associated with an outcome distribution has been variously characterized as related to the distribution's uncertainty, variance, standard deviation, semistantard deviation, some measure of central tendency, probability, and semivariance. In addition, some approaches (i.e., threshold models) use a target outcome value(s) to assess the risk inherent in an outcome distribution. The purpose of this paper is to review and conceptually examine the many ways in which outcome distributions have been characterized to reflect their shape and/or location and how this information has been incorporated into models of perceived risk. Finally, a model of perceived risk will be presented which captures more distributional information than earlier models while avoiding their conceptual inconsistencies.

The general criteria which will be applied to the various approaches have been garnered from various sources. First, perceived risk should increase with increasing perceived likelihood and extremity of bat outcomes associated with an alternative (Bauer 1960, Fishburn 1984). Second, perceived risk should decrease with increasing perceived likelihood and extremity of Root outcomes associated with an alternative (Fishburn 1982). Third, models of perceived risk should capture the situational and individual nature of risk by providing for differing minimum acceptable performance thresholds (Sarel 1982a). Finally, models of perceived risk should provide for individual differences in risk-seeking/risk-avoidance tendencies (Pras and Summers 1978).


If a consumer perceives an outcome distribution associated with an alternative which has more than one possible value, then that consumer will be uncertain regarding the outcome level which s/he should expect on the next occasion. Uncertainty has long been considered to be an essential element of perceived risk, and has often been used synonymously with risk (e.g., Arrow 1951, p. 405; Taylor 1974; Humphreys and Kenderdine 1979; see Fishburn (1984) for a dissenting view). Within the marketing/consumer behavior tradition, the call to action for research on perceived risk by Bauer (1960) as well as the collected works of his contemporaries at Harvard (Cox 1967a) stressed the link of uncertainty with perceived risk: ". . . risks -- that is a combination of uncertainty plus seriousness of outcome involved.. . (Bauer 1960, p. 391); "In short, risk is a function of two elements, uncertainty and consequences' (Cox 1967b, p. 6).

What, exactly, is uncertainty? Researchers and others have used many different terms in an effort to express what is meant by (the inverse of) uncertainty: "confidence" (Bauer 1960; Brody and Cunningham 1968; Barach 1968,1969; Wyer 1974; Bennett and Harrell 1975; Kahneman and Tversky 1982); "reliability" (Bauer 1960); "dependability" Deering and Jacoby (1972); "trust" (Kaul 1981). Kaul's explanation of trustworthiness seems to capture what many consumers probably mean when they discuss situations which are low in perceived risk:

Personally, the American institution I trust the most is McDonald's hamburgers. Not that I like them, particularly -- I think they taste like cardboard with everything on it -- but when you buy a McDonald's you know exactly what you're getting. And it doesn't matter whether you get it in Des Moines, Toledo or New York, it is the same hamburger. That's trustworthiness (Kaul 1981).

That's also low uncertainty. But, when discussing consumer uncertainty, it is important to consider about what the consumer is uncertain.

Sources of Uncertainty

Uncertainty may have different sources. It may arise from the consumer's lack of knowledge regarding the relevant outcome distribution(s) (i.e., internal uncertainty), or from the stochastic nature of the system(s) generating the outcome distribution(s) (i.e., external uncertainty) (Kahneman and Tversky 1982).

Consumers may experience uncertainty regarding the predictive ability (Cox 1967c) or the relative importance (Pras and Summers 1978) of a brand's attributes. Uncertainty may also arise from the consumer's perceived own inability to accurately judge outcome levels that s/he has experienced (Barach 1968, 1969; Copley and Callom 1971; Deering and Jacoby 1972; and Bennett and Harrell 1975). In delineating his "sorting rule," Cox hypothesized that a cue's "confidence value,. . . a measure of how confident they [consumers] were of categorizing a cue as being, say, 'good' or 'bad'" would determine whether they would use that cue to infer the quality of a product ". . . regardless of its predictive value" (1967c,p. 624). Even if consumers think that they can accurately predict and evaluate outcomes, another source of uncertainty is the potential disparity between the anticipated and the actual experience of the outcomes (Kahneman and Tversky 1984). Not only to preferences change over time, but the situation within which a product will be experienced may be different than anticipated. As March (1978) puts it: "Rational choice involves two kinds of guesses: guesses about future consequences of current actions and guesses about future preferences for those consequences" (p. 589, emphasis added).

If the consumer has not experienced a brand directly and must rely on others for information regarding that brand's outcome distribution, then s/he may experience some uncertainty regarding the others' ". . . perceived similarity in standards (tastes) . . . particular expertise (perceived ability to judge) with respect to that particular product category . . . as well as the number and quality of the performance/occasions which they must have experienced. . ." (Vann 1984).

Cox also identified other loci for uncertainty - those associated with the consumer's buying goals ". . . [with] their nature, acceptance levels, and importance (1967b, pp. 6-7).

However, as the focus of this paper is on outcome distributions, the type of uncertainty which is most relevant here is external uncertainty - that concerned with the stochastic nature of the system(s) generating the salient outcome distribution(s). The problem, however is how to model this uncertainty.

Characterizing the Uncertainty Associated with Outcome Distributions

Probability as a measure of uncertainty. "Uncertainty can be described as the probability that a given event will occur" (Cunningham 1965, p. 232). "The uncertainty dimension is analogous to Fishbein's likelihood of association component and measures a consumer's subjective probability that the purchase may result in undesirable consequences" (Zikmund and Scott 1973, p. 407).

Presumably as the probability of a negative outcome increases, uncertainty and perceived risk should do likewise. But, whatever the relationship between the probability of a negative outcome and perceived risk may be, probability is clearly not a measure of uncertainty. For a given perceived outcome distribution, uncertainty would be maximum when all of the possible outcome levels were equiprobable, not when the probability of one unique range or level was maximum (Wyer 1974). If probability were a measure of uncertainty, then consumers should be maximally uncertain when they perceived that a given event should occur with a probability of 1 (i.e., when they are maximally certain) (Cooley 1979, Peter and Ryan 1976).

Variance as a measure of uncertainty. The variance of a perceived outcome distribution has also been proposed as a measure of the distribution's associated uncertainty (e.g., ". . . uncertainty (called perceived risk) . . . which is a function of the shape of the probability distribution and which may include a consideration of one or more of the following descriptive measures: variance, skewness, and kurtosis" (Humphreys and Kenderdine 1979, p. 285; see also Bettman 1973, p. 185). While variance may be related to perceived risk, it is not equivalent to uncertainty - at least not according to information theory. Wyer (1974) has ably demonstrated the difference between variance and an information theory depiction of uncertainty (p. 30). Under information theory, uncertainty increases as the number of outcome levels with associated non-zero probabilities increases - as does the variance. However, variance calculations include information regarding the distance of each possible outcome level from the mean of the distribution. Increasing the distance of an outcome level from the mean increases the variance, but has no effect on information-theory based estimates of uncertainty.

An information-theory measure of uncertainty. Wyer (1974) presents an information-theory based index of the uncertainty associated with a distribution:

If the probability that an object is a member of each of" categories is known, the uncertainty of its category membership is given by the equation UO - - EPilog229 where Pi is the probability that the object belongs to the it category. According to this equation, uncertainty should be minimum if Pi-l when i-k and Pi-O when ivk . . . It should be maximum when the probability of belonging to each of the" categories is the same (=1/N) (pp. 29-30).

This formulation is essentially the same as that used by Herniter (1973) as a measure of entropy.

While it is unclear how this measure of uncertainty is related to perceived risk, there is some evidence that it is related to perceived uncertainty (Driscoll and Corpolongo 1980, Wyer 1973).


Just because the variance of a distribution is not the equivalent of uncertainty does not mean that it is unrelated to perceptions of risk ascribed to an outcome distribution. In fact, the variance of outcome distributions has long been used to model the risk inherent in choice alternatives:

The various approaches to the study of risk share three basic assumptions. 1. Risk is regarded as a property of options, (e.g., gambles, courses of action) that affects choices among them. 2. Options can be meaningfully ordered with respect to their riskiness. 3. The risk of an option is related in some way to the dispersion, or the variance, of its outcomes (Pollatsek and Tversky 1970, p. 541).

Several consumer researchers have proposed that the variance of a perceived outcome distribution is an appropriate measure of the distribution's shape to incorporate into risk models (e.g., Bettman 1973, Humphreys and Kenderdine 1979). Since the variance is a measure of the average squared deviation from the mean of a distribution, models of risk which depict the risk associated with an alternative as being positively related to the variance will predict increases in perceived risk with increases in the dispersion of the possible outcome levels about the mean of the distribution.

Bettman (1974) used the standard deviation of the distribution of belief strengths for brand-outcome associations across brands to characterize the associated risk. This measure was used as one element in a threshold model for the degree of conviction that a product "attribute-- would be satisfactory. (While he used the term, attribute, it is clear that he utilized outcomes in the development of this model: the whiteness, cavity prevention, economy, breath freshness, and taste associated with brands of toothpaste.) Since specific levels of outcomes were not utilized in the model (or the questions), it is likely that level of outcome and likelihood of outcome could have been confounded in the subjects' responses. For example, a mid-scale response could indicate the respondent thought that the particular toothpaste had a moderate likelihood of whitening teeth or that the toothpaste would lead to moderately white teeth (See Ahtola 1975).

While the variance and standard deviation reflect the dispersion of an outcome distribution, they are independent of its location. Models of risk based on the variance or standard deviation of outcome distributions would predict the same perceived risk for any two alternatives which had perceived outcome distributions with the same variance/standard deviation even if one had a very high mean and the other had a very low mean. Variance-based models are also insensitive to the skewness of outcome distributions. (This point will be further discussed later in the paper.)


Measures of central tendency were used to characterize outcome distributions in some of the earliest models of risk. Their use was based on two assumptions: "... that people choose the 'best' alternative, a concept used to justify the search for some rational measure of best, and . . . the principle of mathematical expectation, as the measure of best-- (Payne 1973, p. 442). These models incorporated an expectancy term and a value term, and varied by whether either or both of the terms were subjectively determined (Pruitt 1962, Payne 1973, Sarel 1982b). Structurally, the Ahtola vector model (1975) fits this conceptualization as a model of decision making under risk. However, this model was developed to portray the effect of differing levels of attributes rather than of outcomes on the assessment of the "best" alternative.

Measures of central tendency clearly reflect the location of an outcome distribution. However, unlike the variance or standard deviation, they are unaffected by the dispersion of the distribution. Thus, two alternatives with perceived outcome distributions which had the same value on the appropriate (to the particular theory) measure of central tendency would be presumed to be equal in perceived risk even if they varied widely in their dispersion.


As operationalized by Pras and Summers (1978) the semistandard deviation of an outcome distribution is equal to the square root of the average squared deviations of possible outcome levels from the mean of the distribution for only half of the distribution (either above or below the mean) (p. 431, footnote). They incorporated the upward semistandard deviation into their model for risk takers and the downward semistandard deviation for risk avoiders. Their rationale was that: "Risk avoiders should be more sensitive to the downside portion of the distribution and risk takers more sensitive to the upper side" (p. 430). Their model has the following form: Pij = uij + rikosij.

Where. Pij = the risk-adjusted index for attribute i and brand i. uij = the mean of the distribution for brand i on attribute i, rik = the consumer's tolerance for risk for attribute i with respect to the range of possible rating (k), and asij = the semistandard deviation of the distribution (attribute i for brand i) with respect to the mean (p. 431). [Even though their model is characterized as an attribute model, their "attribute" list includes some outcomes.]

While risk is presumed to increase with increases in either the negative or the positive semistandard deviation, it is assumed to affect evaluation positively for risk seekers and negatively for risk avoiders since rik is positive for risk seekers and negative for risk avoiders.

Since this model utilizes either the upper or the downward semistandard deviation, but not both, it assumes that risk takers and risk avoiders will employ decision strategies that consider only one end of a distribution rather than trading-off the possibility of negative outcomes against the possibility of positive outcomes (Vann 1984). In addition, since the semistandard deviation ignores half of the distribution, it is insensitive to the skewness of the distribution. The half of the distribution which is not represented in the model could be the mirror image of that which is represented or it could be very different. Furthermore, as with the mean and variance models (to be discussed in the next section) while the use of the mean anchors the distribution to the scale, the model does not explicitly consider any minimum performance thresholds which the consumer may hold. For example, the entire upper portion of an outcome distribution (which is represented by the upper semistandard deviation) may be below a consumer's minimum acceptable performance threshold.


Pollatsek and Tversky (1970) proposed a theory of risk which incorporated both the variance and the mean of the outcome distribution:

R(A) - 0V(A) - (1C0)E(A). . . Thus, in a regular risk system, the risk ordering is generated by a linear combination of expectation and variance. Put differently, the risk of any option can be readily computed, once a single parameter, 0, is determined. Furthermore, 0 is attainable from a single judgement of risk-equality between two distinct distributions, and its value determines the relative contribution of the expectation and the variance to the riskiness of an option (p. 547).

Meyer (1981) proposed an attribute-level model of perceived risk which utilizes information regarding both the mean and the dispersion of a brand on each attribute. However, his model differs in several ways from that suggested by Pollatsek and Tversky. First, it includes the addition of a third term in which the measure of dispersion is multiplied by the mean (ant by a scaling constant). Second, the measure of dispersion which Myer uses is not the variance (squared deviations from the mean are summed, but not averaged). Finally, the "mean' and the "dispersion" measures used in the model are composites in which the expectations for the brand and the expectations for the product class are weighted depending on the consumer's familiarity with the particular brand's performance (uncertainty). If the consumer is totally ignorant regarding the performance history of the particular brand, then the measures of "mean" and "dispersion" used in the model take on the perceived values for the product class (i.e., default values (Crocker 1984)). Again, as with the Ahtola vector motel, attributes are not outcomes - but both models could be adapted to an outcome-oriented approach.

Models of perceived risk which include information regarding a measure of central tendency and the dispersion of an outcome distribution eliminate some of the major shortcomings of the separate, variance-only or central-tendency-only models. There are at least two remaining shortcomings. First, as with the Pras and Summers model, while a measure of central tendency anchors the distribution to a location on the scale, it does not directly reflect minimum-performance thresholds which consumers may hold. The second remaining shortcoming is that the variance is insensitive to the skewness of an outcome distribution (as is the semistandard deviation). For example, if two highly skewed distributions were mirror images of each other (same mean and variance, but one positively skewed and the other negatively skewed), then variance-only or variance-and-central-tendency models would predict that both distributions would elicit the same level of perceived risk.


Threshold models of perceived risk reflect the location of a perceived outcome distribution relative to either an explicit or an implicit performance threshold level that is relevant to the consumer. The model may consider the portion of the distribution below the threshold or above it. In addition, more than one threshold may be posited. Threshold models characterize the relevant portions of outcome distributions by using probabilities or a semivariance approach.

Single Threshold Models Utilizing Probabilities

Explicit thresholds. The original explicit-threshold model in the marketing/consumer behavior tradition was that proposed by Cunningham (1965). Briefly, the operational definition of uncertainty . . . was intended to measure the respondent's certainty that an untried brand . . . would work as well as her present brand" (p. 232, emphasis added). While uncertainty is not probability, the curious response categories which he used (i.e., frequency of uncertainty) appear to reflect the proportion of the product class outcome distribution which the consumer perceives to lie above the performance level of the ' present brand": "Would you say that you are: Very certain, usually certain, sometimes certain, or almost never certain that a brand of headache remedy (floor wax, dry spaghetti) you haven't tried will work as well as your present brands?" (p. 232, footnote). (The greater the number of brands which the consumer perceives to perform as well as the present brand, the more "frequently" s/he should be certain that an unknown brand would work as well as the present brand.) This measure was then multiplied by the response to the following question:" Compared to other products would you say that there is: a great deal of danger, some danger, not much danger, or no danger, in trying a brand of headache remedy (floor wax, dry spaghetti), you have never used before?" (p. 233, footnote).

It seems that to answer the second question, the consumer would have to consider the frequentistic information requested by the first question. In effect, the danger question, itself, may be a surrogate measure of risk. This probably accounts for the fact that "there is some evidence to suggest that the consequences component may be weighted more heavily than is the certainty component" (Cunningham 1967, p. 86). (Bettman, using a modified Cunningham scale, was later to report: ". . . we may conclude that uncertainty and danger are definitely not independent for this study" (1972, p. 401).) Nevertheless, Cunningham contended that "some combination of these two questions should represent perceived risk" (1967, p. 84).

Cunningham's work has had a tremendous impact on research in the area of perceived risk. The Cunningham frequency-of-certainty/danger format was used intact or in modified form by other researchers (intact: Arndt 1967; modified: Bettman 1972; Hisrich, Dornoff, and Kernan 1972; Hoover, Green, and Saegert 1978). Others claimed that their approaches were based on the Cunningham approach, but it is either unclear what uncertainty response categories they used (e.g., Gronhaug 1972), or they used a straight uncertainty scale (e.g., Deering and Jacoby 1972), or a straight certainty scale ( e.g., Schiffman 1972, Dash, Schiffman and Berenson 1976).

Straight uncertainty/certainty scales are conceptually very different from the scale used by Cunningham. If the consumer were "almost never certain" (the opposite of "very certain on Cunningham's scale) that an untried brand would perform as well as the present brand, then there should be a high level of certainty as to whether any untried brand will perform as well as the present brand -- it almost certainly won't!

Bettman (1975) experimentally compared the Cunningham format to another explicit-threshold, probability model which he had developed in Bettman (1973). Bettman's characterization was . . . the percentage of brands falling above an acceptable level of quality for a consumer. . ." (1975, p. 381).

Implicit thresholds. For some threshold probability models a threshold value is not specified, but is rather implied by the questions asked of consumers. There are many examples of such models in the marketing/consumer behavior literature: ". . . probability that the purchase will fail . . ." Roselius (1971, p. 56); ". . . subjective probability that the purchase may result in undesirable consequences" (Zikmund and Scott 1973, p. 407); "I think that it is .. . [seven-point improbable/probable scale]. . . that the purchase of (brand) would lead to a performance loss for me because it would run extremely poorly" (Peter and Tarpey 1975, p. 35, see also Peter and Ryan 1976); Sow likely is it that this product is of poor quality?" (Vincent and Zikmund 1975, p. 1975).

A Double-Threshold Model Utilizing Probabilities

Sarel (1982a) proposed a double-threshold model which he experimentally tested against a central-tendency model and a mean-variance model. His double-threshold model divided the perceived outcome distribution into three segments: unacceptable, neutral, and outstanding (p. 6). While the thresholds which were utilized in his study were derived to maximize the degree of fit between predicted and observed evaluations, subjects could be asked to specify their thresholds (p. 13).

Sarel's model has the following form: PT = V(U)P(U) + V(O)P(O), where U represents the unacceptable region of the distribution, O represents the outstanding region, V(U) and V(O) represent the values associated with the unacceptable and outstanding regions, and P(U) and P(O) represent the probabilities associated with the unacceptable and outstanding regions of the outcome distribution (p. 8)

All of the threshold models which utilize probabilities to characterize the region(s) beyond the relevant threshold share a common shortcoming. They fail to represent the dispersion of the distribution beyond the threshold(s). They would make the same predictions regarding perceived risk regardless of whether the possible outcome values beyond the threshold(s) were closely bunched near the threshold(s) or if they were widely dispersed beyond the threshold(s). Threshold models which utilize the semivariance overcome this shortcoming.

Threshold Models Which Utilize the Semivariance

The negative semivariance is a measure of dispersion which represents the average squared deviation from some threshold value for possible outcomes below the threshold. While the negative semivariance has been proposed as a measure of perceived risk in the finance literature (e.g., Markowitz 1959), the author is unaware of any applications in the marketing/consumer behavior tradition. The obvious counterpart to the negative semivariance is the positive semivariance. The author has seen no proposals for incorporating the positive semivariance into models of perceived risk.

Threshold risk models which utilize the negative semivariance incorporate more information regarding the outcome distribution than do probability threshold models in that they are sensitive to the dispersion of possible outcome values below the threshold. If two alternatives both generate perceived outcome distributions which have the same proportion of their respective distributions below the threshold, but one has more extreme possible values below the threshold, probability threshold models would predict that both would elicit the same level of perceived risk, while a negative semivariance model would predict that the one with the more extreme values below the threshold would have the higher associated perceived risk.


A logical extension of the negative semivariance model, which would also incorporate the ability of Sarel's dual threshold (probability) model (1982a) to capture the influence of both the positive and the negative ends of outcome distributions, is a model utilizing both the negative and the positive semivariance. The negative and the positive semivariance could be calculated relative to the same threshold or to two thresholds as were used in the Sarel model.

Such a model would appear to overcome all of the shortcomings of the other approaches to partitioning outcome distributions in modeling perceived risk. It would be anchored to the scale in a manner which explicitly considers minimum acceptable performance thresholds. It would reflect the dispersion of the outcome distribution, both at the positive and the negative ends. It would thereby be sensitive to both variability and to skewness. It would provide for trade-off decision strategies on the part of consumers, in which they could simultaneously consider both possible negative consequences and possible positive consequences (which could represent potential opportunity losses) associated with an alternative. In addition, the negative and the positive semivariances could be weighted in a fashion which reflects the risk-seeking versus the risk-avoiding preferences of the consumer.

The model could take the following form: Risk(A) w1(Neg. Semivar(A)) - w2(Pos. Semivar(A)) where w1 and w2 are weights which reflect the risk avoidance and risk seeking preferences respectively. This model would predict that perceived risk would increase with increasing negative semivariance and with decreasing positive semivariance. Consumers who are risk averse would be expected to emphasize the negative semivariance and to de-emphasize the positive semivariance. Risk seekers would be expected to do the opposite.


Various ways of partitioning perceived outcome distributions to model the perceived risk inherent in them have been examined. The strengths and weaknesses of each approach have been discussed. It is unclear exactly how to characterize the uncertainty inherent in a distribution. However, if an information-theory approach is used, then the extent of the distribution's dispersion is not fully represented. If a distribution is characterized by its variance or standard deviation, then its dispersion is represented, but skewness and location are not. If a measure of central tendency is used to characterize the risk inherent in a distribution, the location is represented, but all information regarding shape is not. Characterizations which utilize both the mean and the variance capture both location and dispersion information, but fail to represent skewness or minimum acceptable performance levels. Characterizations employing the semistandard deviation fail to represent half of the distributor Probability threshold models anchor the distribution relative to minimum acceptable performance levels but fail to fully reflect the dispersion of the distribution. Negative semivariance models incorporate a consumer's minimum performance threshold and reflect the dispersion of the distribution below that threshold, but fail to reflect the shape of the distribution above the threshold. A model was proposed which appears to have the strengths of the other characterizations while avoiding the weaknesses. This model utilizes both the negative and the positive semivariances in a way which also reflects the consumer's risk-seeking/risk-avoiding tendencies.


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