A comprehensive guide to conjoint analysis

1. Attributes and levels

The attributes included in a conjoint analysis represent the key features or characteristics of the product or other object of interest (e.g. a government policy) being studied as seen from the perspective of the intended participants in the survey, e.g. consumers or citizens.

Fewer than a dozen attributes is usually sufficient for most applications though more are possible, and four to eight attributes is typical for most conjoint analysis studies.

Example:

For a conjoint survey of consumers about smartphones, the attributes might be: camera quality, size, price, screen quality, operating performance and battery life (Table 1).

As illustrated in the detailed example later in the article, some conjoint analysis software includes the option of showing participants a potentially long list of possible attributes (e.g. 20) and asking them to select the ones that are most important ones to them for their conjoint survey (whose results are still easily interpreted).

Levels

Each attribute usually has three or more levels (or categories) for describing the performance of alternatives on the attribute, though just two levels is also possible for binary attributes, e.g. “Android” and “iOS” operating systems for smartphones. There is usually no requirement for the attributes to have the same number of levels – some attributes can have three levels, others four, five or six levels, etc.

Depending on the attribute, the wording for its levels can be in quantitative or qualitative terms, including in generic qualitative terms, e.g. “good”, “very good”, etc.

Example:

• Camera quality: “ok”, “good” or “very good”
• Price: $600, $700, $800, $900 or $1000

2. Utilities

Utilities – also referred to as part-worths or part-worth utilities – are weights representing the relative importance of the attributes and their levels.

These values are derived from the choices expressed by survey participants and reflect how they feel about how much each attribute matters relative to the others.

Example:

If the utility (weight) for camera quality is 0.284 and for screen quality it is 0.112 (shown as 28.4% and 11.2% in Table 1), then camera quality is 2.5 times – i.e. 0.284/0.112 – as important as screen quality.

3. Alternatives

Alternatives – also known as profiles or concepts – are the underlying products or other objects of interest (e.g. a government policy) being studied in the conjoint analysis, represented as combinations of attribute levels.

Depending on the application, the number of alternatives can range from as few as a couple to a dozen, hundreds or even thousands, or potentially all possible combinations of the levels on the attributes.

Example:

Eight phone configurations (A to H) on the six attributes are shown in Table 2.

Attributes + utilities + alternatives

These three components – attributes, utilities and alternatives – form the basis of conjoint analysis.

The participants in your conjoint analysis survey, whose preferences you are seeking to elicit and codify, are also important. Depending on the application, potentially many hundreds or thousands of decision-makers or other stakeholders – e.g. consumers, employees or citizens – can participate.

As discussed later, most contemporary conjoint analysis methods involve participants being repeatedly shown “choice sets” comprising two or more hypothetical alternatives, each described by a combination of levels on the attributes, and asked to choose from them.

The simplest possible example of a choice set – with just two alternatives defined on two attributes – appears in Figure 1a. Choice sets with more alternatives and attributes are considered below.

Depending on the number of attributes and levels and the conjoint analysis method used, participants might be shown 10 to 30 choice sets each.

Analysis of their choices yields utilities for the attributes and levels, quantifying their relative importance (weights), representing people’s preferences. These scores are used to produce a ranking of the alternatives (Table 3).

Two example conjoint analysis surveys

A great way to understand conjoint analysis is to experience a survey yourself from the perspective of a participant.

Please try the conjoint surveys below – created using 1000minds conjoint analysis software (that you are very welcome to try too).

The first survey is about smartphones and is the source of the illustration above and the detailed example later. The second is a more light-hearted example to help you to choose a breed of cat as a pet!

• Smartphone conjoint survey
• Cat breed conjoint survey

Choice modeling and random utility theory

Choice modeling emerged in the 1920s when US psychologist Louis Thurstone developed the “Law of Comparative Judgment” (Thurstone 1927). This idea, later termed Random Utility Theory (RUT), introduced a probabilistic perspective on preferences and choice that would become central to many later developments.

Central to RUT is the idea that when a person is choosing between alternatives, each alternative has a true but unobservable “utility” – i.e. value or amount of satisfaction – to the person, comprising a systematic and a random component respectively. Thus, the person’s choices are made probabilistically in the sense that the option with the highest expected utility is most likely to be chosen.

Trade-off and conjoint analysis

A major theoretical advance followed with US mathematicians Duncan Luce and John Tukey’s theory of conjoint measurement, which established axiomatic conditions under which preferences over multi-attribute alternatives can be represented as additive utility or value functions (Luce & Tukey 1964).

Luce and Tukey’s work established the formal basis for decomposing overall preferences into attribute-level components and linked utility theory with empirical measurement.

Originally known as “trade-off analysis” (e.g. Johnson 1976), the term “conjoint analysis” was popularized in the early 1970s by Paul Green, Vithala Rao and V “Seenu” Srinivasan. These researchers introduced practical methods for estimating part-worth utilities from ratings or rankings of full product profiles, typically using regression-based techniques (Green & Rao 1971, Green & Srinivasan 1978).

These early applications were widely adopted in marketing research and demonstrated the practical feasibility of conjoint methods. The history of conjoint analysis in marketing is traced out in Green & Srinivasan (1978, 1990) and Green, Krieger & Wind (2001).

During the 1980s, conjoint analysis expanded in response to practical challenges such as high responder burden and increasing attribute complexity. Methods such as Adaptive Conjoint Analysis (ACA) were developed to accommodate larger numbers of attributes (e.g. Green & Srinivasan 1990).

Discrete choice models and experiments

Another important methodological milestone was US econometrician Daniel McFadden’s formulation of a “discrete choice model” (DCM), specifically a multinomial logit model, which embedded Random Utility Theory within a rigorous econometric framework for analyzing people’s choices (McFadden 1974).

By showing how choice probabilities could be derived from stochastic utility functions, McFadden made RUT empirically tractable and provided the foundation for modern discrete choice modeling.

This framework, for which McFadden was jointly awarded the 2000 Nobel Prize in Economic Sciences, established the theoretical basis on which later experimental choice methods were built.

Choice-Based Conjoint (CBC) / Discrete Choice Experiments (DCE)

From the 1990s onward, Choice-Based Conjoint (CBC) – methodologically equivalent to Discrete Choice Experiments (DCE) – became increasingly prominent.

These methods involve participants choosing between alternatives and directly implement McFadden’s (1974) RUT-based framework using multinomial logit and later mixed logit and hierarchical Bayes models, enabling the analysis of preference heterogeneity and predictive choice simulation (Train 2009).

Jordan Louviere, with colleagues, helped translate discrete choice theory into practical stated-choice experiments suitable for survey-based research in marketing, transport, health and environmental economics (Louviere, Hensher & Swait 2000).

Louviere’s work also played an important role in unifying the conjoint analysis and discrete choice literatures, showing that choice-based conjoint methods are formally equivalent to discrete choice models estimated from experimental data.

Other modern conjoint analysis methods

Since the 2000s, conjoint analysis has continued to diversify. Best-Worst Scaling (BWS; Marley & Louviere 2015), also known as MaxDiff (for “maximum difference”), and Adaptive Choice-Based Conjoint (ACBC; Orme 2007) – superseding Adaptive Conjoint Analysis (ACA) – extended choice-based approaches.

Other methods designed to minimize responder burden such as PAPRIKA – an acronym for Potentially All Pairwise RanKings of all possible Alternatives – use pairwise trade-off comparisons to construct additive value functions efficiently (Hansen & Ombler 2008).

Together, these developments reflect ongoing efforts to balance cognitive burden, statistical efficiency and interpretability.

Today, conjoint analysis can be viewed as a family of related methods for decomposing preferences into utilities for attributes and levels differentiated by how preferences are elicited and utilities inferred. This diversity reflects both the theoretical foundations established over the past century and the wide range of contexts in which conjoint analysis is now applied.

Number of alternatives in choice sets

Most conjoint analysis methods are based on choice sets with just two alternatives (profiles), such as in Figures 1, whereas other methods involve participants choosing from choice sets with three or more alternatives.

As can be seen, as well as having two alternatives, the choice set in Figure 1b has just two attributes, whereas for other methods the alternatives would be represented on more than two attributes (e.g. Figure 2 below). This issue of how many attributes are used for representing alternatives is discussed later.

Number of attributes for representing alternatives

As well as the number of alternatives in choice sets, another differentiator of conjoint analysis methods is the number of attributes used for representing the alternatives people are asked to choose between.

In this respect, there are two types of choice set: full profile and partial profile.

Non-adaptive versus adaptive conjoint analysis methods

Another key difference between conjoint analysis methods is how the particular choice sets presented to survey participants are selected: non-adaptively or adaptively.

Utility inference methods

Based on people’s choices from the choice sets, utilities for the attributes in the form of weights, representing the relative importance of the attributes, are inferred.

Modern methods for calculating utilities are mostly based on statistical estimation, which models choice behavior probabilistically, or linear programming, which infers utilities by solving systems of constraints implied by people’s choices.

Summary of distinguishing characteristics

Rating- and ranking-based conjoint analysis (traditional conjoint)

Preference elicitation

Preferences are elicited via ratings or rankings of alternatives, where each alternative is defined on all attributes (full profiles). Choice tasks are typically non-adaptive, with all participants evaluating the same set of profiles.

Utility inference

Utilities are most commonly inferred using regression-based methods, such as ordinary least squares or monotonic regression. Estimation is typically conducted at the aggregate level. Individual-level utilities are possible but unstable unless sufficient data per participant is available.

Why it’s popular

Traditional conjoint analysis remains in use due to its simplicity, transparency, and long-standing acceptance in applied research.

Strengths

• Simple survey design and analysis
• Intuitive for participants in small conjoint analysis studies
• Modest sample-size requirements

Limitations

• Full-profile alternatives are cognitively demanding
• Rating and ranking data are prone to scale-use and context effects
• Limited capacity to model individual-level preference heterogeneity

Further reading

Green & Rao (1971), Green & Srinivasan (1978)

Choice-Based Conjoint (CBC) / Discrete Choice Experiments (DCE)

Preference elicitation

Participants repeatedly choose their preferred option from a choice set of full-profile alternatives, often including a “none” or “status quo” option. Choice sets are typically non-adaptive, although designs may be blocked or optimized.

Utility inference

Utilities are inferred using random utility models based on Random Utility Theory (RUT), most commonly multinomial logit, mixed logit and hierarchical Bayes (HB) estimation. Estimation may be conducted at the aggregate level (e.g. aggregate logit) or at the individual level, particularly when HB methods are used.

Why it’s popular

CBC/DCE aligns closely with economic theory and observed choice behavior, making it a common method in economics, health, transport and environmental research.

Strengths

• Strong theoretical foundation
• Supports prediction, simulation and welfare analysis
• Flexible modeling of preference heterogeneity

Limitations

• Requires relatively large sample sizes
• Design and estimation are statistically complex
• Choosing from full-profile choice sets is cognitively demanding with many attributes

Further reading

Louviere, Hensher & Swait (2000), McFadden (1974)

Adaptive Choice-Based Conjoint (ACBC)

Preference elicitation

ACBC uses preliminary tasks, such as specifying a preferred combination of attribute levels (“build-your-own”) and screening out of unacceptable options, followed by tailored choice sets. Early stages often involve partial profiles, with later stages presenting more complete profiles.

Utility inference

Utilities are inferred using random utility models, typically estimated at the individual level using hierarchical Bayes methods.

Why it’s popular

ACBC extends CBC to complex products and configuration problems with more attributes and levels, where standard choice sets would be inefficient or overly burdensome.

Strengths

• Efficient handling of many attributes and levels
• Retains choice-based realism
• Explicit modeling of individual-level preferences

Limitations

• Longer and more complex surveys
• Greater design and estimation complexity
• Less suited to very large samples

Further reading

Orme (2007)

Best-Worst Scaling (MaxDiff)

Preference elicitation

Participants identify the most and least preferred alternatives from choice sets containing three to six alternatives. Alternatives are usually partial profiles and choice sets are non-adaptive.

Utility inference

Utilities are inferred using logit-based random utility models or simpler counting approaches. Estimation may be performed at either the aggregate or individual level, depending on the modeling approach and data availability.

Why it’s popular

MaxDiff is efficient in the sense that it reduces the number of decisions required to determine multiple pairwise rankings (from which utilities are derived).

Strengths

• Scale-free preference information
• Efficient elicitation of relative importance
• Flexible estimation options

Limitations

• Tasks may be less intuitive and cognitively demanding for participants
• Less direct behavioral interpretation than CBC
• Design can be complex for profile-based variants

Further reading

Marley & Louviere (2005), Louviere, Flynn & Marley (2015)

PAPRIKA method

Preference elicitation

PAPRIKA – an acronym for Potentially All Pairwise RanKings of all possible Alternatives – elicits preferences using pairwise trade-off comparisons between partial-profile alternatives defined on only two attributes at a time, though more attributes are also possible. Each participant’s choice sets are adaptive, with new ones based on earlier choices.

Utility inference

Each participant’s utilities are inferred directly from the implied preference constraints revealed by their choices, rather than statistical estimation.

Why it’s popular

PAPRIKA identifies a stable, individual-level value function for each participant, and is well suited to applications where transparency, easy interpretability and low responder burden are important.

Strengths

• Choice sets are cognitively simple and fast to choose from
• Efficient with many attributes and no “design” issues
• Produces transparent, participant-specific utility functions

Limitations

• By design, less suited to probabilistic choice prediction
• Requires internally consistent trade-off judgments (checkable as part of data quality control)

Further reading

Hansen & Ombler (2008); PAPRIKA method

Which method should you use?

Your choice of conjoint analysis method is likely to be influenced by these considerations:

• Your research goals, including the desired levels of validity and reliability of your study (which likely depends on your research question and its significance)
• Your product’s complexity, as reflected in the number of attributes and levels to be modeled
• Responder burden for participants: the conjoint survey’s cognitive complexity, length and participant engagement
• The number of participants you want to survey, and how you are going to recruit them
• The type of conjoint analysis output you want: e.g. aggregate versus individual-level utilities
• Time, logistical and budget constraints: e.g. in-person, online or mobile survey delivery, surveying costs, software licenses

A very important practical consideration is how are you planning to implement your preferred method, in particular eliciting participants’ preferences via a conjoint survey and inferring utilities from those elicited preferences?

Your two options are:

• Use specialized conjoint analysis software for running your survey and taking care of most of the method’s technical and analytical aspects for estimating and interpreting utilities
• Use more of a DIY (Do It Yourself) approach involving designing and administering the survey yourself and using a general statistics package to estimate utilities

If you are going to use specialized conjoint analysis software, what method does it use? Most software is based around a particular method or group of related methods. Not all methods are available in all platforms.

If you are going to use a DIY approach, do you have – or have access to – the requisite technical skills and knowledge (and time) to create and run the survey and estimate the utilities yourself?

Most people opt for using specialized conjoint analysis software.

Specifying attributes and their levels

After having defined the research question you want to address – such as designing a product (e.g. a smartphone) or shaping a public policy – an important next step is specifying your conjoint survey’s attributes and their levels.

Sometimes you will already have a good idea of the attributes and levels you want to use – e.g. because you’ve done this kind of research before – but other times you’ll be starting from scratch.

Here are possible approaches for coming up with potential attributes and levels, depending on your application:

• Literature review: Review existing conjoint analysis or DCE studies, or market research on similar products and extract commonly used attributes and levels as a starting point.
• Expert consultation: Run interviews or workshops with industry experts, engineers or marketers (etc) with the expertise and experience to identify relevant attributes.
• Focus groups or consumer interviews: Conduct qualitative discussions with potential users and explore what features matter most to them.
• Observation or ethnographic research: Observe how people use or choose between products in real-world settings, thereby identifying attributes that drive choices naturally.
• Product decomposition: Break down existing products (e.g. smartphones) into measurable components and analyze features that vary meaningfully between brands or models.
• Market or competitor analysis: Compare specifications and pricing of competing products to infer relevant attributes and realistic level ranges.
• Brainstorming and Delphi methods: Use structured group processes – e.g. Delphi panels – to generate and refine candidate attributes and reach consensus among stakeholders. (You might like to check out our guide to the Delphi method.
• Pilot-testing and attribute refinement: Run small-scale pilot surveys or rating tasks to test participants’ understanding of the attributes and levels and their realism.
• Text and data mining: Analyze online reviews, social media posts or customer feedback to identify frequently mentioned product features or pain points.
• “Noise auditing”: Have participants rank real or imaginary alternatives to reveal judgment variability (“noise”) and stimulate discussion of attributes for choosing between them.

If you are using 1000minds conjoint analysis software, an AI Assistant is available to suggest attributes and levels – and alternatives too, if desired – to get you up and running quickly, e.g. to create a proof-of-concept or “starter” model to build on.

Desirable properties of attributes and levels

When specifying attributes and levels for conjoint analysis surveys (e.g. about smartphones) it’s essential they are well-defined and relevant. The quality of your attributes/levels directly affects the validity and reliability of your survey results.

Here are eight desirable properties of attributes and levels. You might like to use them as a checklist as you go about specifying your own ones.

1. Relevance and Importance

Each attribute should be salient and meaningful to survey participants – something they genuinely care about when making real-world choices. Including unimportant or trivial attributes adds noise, unnecessary complexity and distracts from what truly drives preferences.

2. Independence (avoiding double-counting)

Attributes should be conceptually and empirically distinct from one another. Overlapping or redundant attributes – such as both “battery life” and “battery capacity” for smartphones – can lead to double-counting, where similar concepts are measured twice and their utilities become confounded.

3. Comprehensibility and Realism

Attributes and their levels should be easy for participants to understand and reflective of realistic trade-offs. People should be able to meaningfully evaluate each combination of attribute levels. Avoid overly technical jargon or attributes that produce incomprehensible or unimaginable profiles.

4. Manageable number of attributes

Specifying too many attributes can overwhelm participants and cause fatigue or inconsistent answers. Fewer than a dozen attributes is usually appropriate, and four to eight is typical, depending on complexity. Fewer, well-chosen attributes are generally preferable to many weak ones.

5. Controllability and Policy relevance

Each attribute should correspond to something that can be influenced, changed or designed – by a business, policymaker or decision-maker. Including attributes that can’t be controlled, such as “brand loyalty” or “friend recommendations”, reduces a survey’s practical value.

6. Balanced level ranges

The levels of each attribute should cover the full realistic range of variation: not too narrow (making it hard to detect preferences) and not too wide (making scenarios unrealistic). For example, phone “battery life” levels could range from 8 to 20 hours, i.e. reflecting plausible differences.

7. Mutual exclusivity and Exhaustiveness

Attributes should be mutually exclusive (not overlapping in meaning) and collectively exhaustive (covering all important aspects of the decision). Satisfying these two properties helps ensure the model captures all relevant dimensions of preference without redundancy or gaps.

8. Neutrality and lack of bias

Descriptions for attributes’ levels should be value-neutral so that they do not lead participants toward a particular choice. For example, “budget-friendly price” is likely to introduce bias, whereas, in contrast, “price: $100” is neutral and measurable.

An illustrative set of six attributes and their levels for a conjoint survey about smartphones appear in Table 6.

Optional attributes

In most conjoint analysis surveys, usually for reasons of administrative convenience, participants evaluate the same set of attributes, such as the six in Table 6 above.

Alternatively, the 1000minds software used for illustrating the example allows you to set up the survey so that each participant gets shown up to 30 possible attributes and asked to select the most important ones to them for their conjoint survey (Figure 4).

The survey administrator can also specify some attributes as mandatory (instead of optional) in the survey – e.g. price – if desired.

This “optional attributes” approach eliminates the pressure when you are setting up a conjoint survey of having to specify a definitive and potentially restrictively small set of attributes capable of universal relevance to all participants, while generating easily interpretable survey results.

Self-explication

For many conjoint analysis methods, including PAPRIKA, the ranking of the levels for each attribute needs to be defined before each participant sees a choice set – so that the choice sets involve trade-offs between the attributes.

In practice, most attributes have levels with an inherent and incontrovertible, or automatic, ranking. For example, all else being equal, a low-priced phone is always more desirable than an expensive one; a great camera is always preferable to a basic one (again, all else being equal).

On the other hand, the levels for some attributes do not have an inherent and incontrovertible ranking. Instead, their ranking depends on each individual’s idiosyncratic preferences.

An example is phone size: some people prefer large phones, whereas others prefer medium or small phones, e.g. because they fit better in people’s pockets or are easier for people with small hands.

For such attributes, the ranking of their levels needs to be “self-explicated”, or explicitly stated, by the participant before they are presented with their choice sets (Figure 5).

If you have not already done so, you can experience this self-explication exercise in the smartphone DCE.

Who should take your conjoint survey?

The ideal participants are people who represent the population you are studying – such as, depending on your application, your target customers, patients, citizens, employees or stakeholders.

In general, you want people who will understand the choice set scenarios you’re testing and whose preferences will inform meaningful decision-making based on your survey’s results.

For example:

• A product designer testing pricing options should survey actual or potential customers.
• A health economist evaluating treatment trade-offs should solicit responses from patients or clinicians.
• A government agency seeking input on infrastructure plans should involve members of the public.

How many participants do you need?

There’s no one-size-fits-all answer. A rule of thumb for most conjoint studies is to aim for at least 100 people to get statistically robust results – more participants if you are segmenting your data by sub-groups (e.g. age, gender, region). Checking with a statistician and/or an online statistical power calculator is likely to be worthwhile.

As well as the sample size, how the sample is selected is also critical to the validity of your results – specifically, random versus non-random sampling.

• Random sampling means that each individual in the population of interest has the same chance of being selected for the survey, which helps ensure the sample reflects the true diversity of the population (age, gender, opinions, etc).
• Non-random sampling, e.g. “convenience” sampling – such as surveying people in your networks, or “snowball” sampling, where participants share the survey in their networks, can over-represent some groups and under-represent others, introducing “selection bias”.

The power of conjoint analysis software like 1000minds is that there are major economies of scale. Having created a 1000minds conjoint survey, whether you send it to 200 or 400 people (or 5000) has little effect on the overall cost and effort involved – contingent on how you go about recruiting your participants.

How to recruit participants

There is a variety of ways to reach participants for your conjoint analysis survey. Depending on your application, here are some ways you can get your survey in front of the right people.

Email invitations to your own list

This approach reaches a known audience directly, and is ideal when surveying existing users, stakeholders or internal teams, e.g. customers, employees.

If you know where people hang out

If you know what your audience looks at – e.g. a Facebook page, Reddit, your customer portal, a train station or a milk carton – you can share a link to your survey there and ask people to click it or enter it into their device.

Social media or website links

Share your survey link through your organization’s social channels or embed it on a website to reach a wider or more organic audience.

In-person recruitment

Ideal for research involving specialized groups, such as clinicians, patients or community stakeholders, particularly in the public sector or health care settings.

Advertising

You can use Facebook advertising, Google AdWords, etc to create targeted advertisements for your survey. This can be useful if your survey is interesting enough, or if your advertisement offers a reward, e.g. to be entered into a draw for a grocery voucher or an iPad.

Snowball sampling

At the end of your survey ask participants to share it with others on social media or by email (to create a snowball effect with your survey rolling along gathering momentum).

Convenience sampling

If you do not care who does your survey – e.g. because all you want is feedback for testing purposes – you can ask anyone who is easy to contact via your personal and professional networks like friends, family and colleagues.

Survey panels and online recruitment platforms

You can purchase a sample of participants from a panel provider or market research company offering access to large pools of pre-enrolled participants.

This approach allows you to target participant panels by their characteristics such as age, gender, location, occupation, interests and more, and is especially useful if you need to access specific groups or regions.

Some providers offer self-service dashboards so you can easily control the targeting, pricing, how much you spend, and reporting process.

Here are four global panel providers:

• Cint: “access to millions of respondents across 130 countries from over 800 integrated suppliers”
• Dynata: “a global reach of nearly 70 million consumers and business professionals”
• PureSpectrum: “provides researchers instant access to multi-source respondents from high-quality global panels”
• Cloud Research: “provide academic and market researchers immediate access to millions of diverse, high-quality respondents around the world”

Data quality control

Especially if you are surveying members of the general public or people recruited via panel providers (who are usually rewarded in some way), you should be mindful of the quality of their responses. Maintaining high data-quality standards is important so you can have confidence in the validity and reliability of your results.

Ideally, the conjoint survey software you are using will make it easy to identify and exclude low-quality responses that are indicative of participants’ failure to understand or sincerely engage with the survey.

1000minds, for example, includes customizable “exclusion rules” for identifying and excluding participants who when choosing from their choice sets exhibit these potentially “telltale” behaviors:

• They contradict themselves when at the end of their survey, unbeknown to them, they are re-presented with two or three choice sets they chose from earlier, i.e. a consistency check
• They make their choices unreasonably quickly – known as “speeders”
• They choose the same option for every question, suggestive of just clicking through

It’s also good practice to ask participants at the end of their survey about the extent to which they felt they understood the choice-set questions they were asked.

In addition, each participant can be shown their own survey results with respect to their ranking of the attributes and, as a face validity test, asked if they think it matches their intuition, and if it is different, in what way.

Utilities, and their interpretation

The utilities (also known as part-worth utilities or simply part-worths) for Bao, Neha, Peter, Sajid and Susan are reported in Table 7. Also reported are the group’s mean utilities and standard deviations (SD), as calculated in the usual way.

In short, these utilities codify how Bao, Neha, Peter, Sajid and Susan – as individuals and on average – feel about the relative importance of the six smartphone attributes.

For each participant and the group overall (means), each utility value captures two combined effects with respect to the relevant attribute and level:

• the relative importance (weight) of the attribute:
  • represented by the bolded values in Table 7
  • these values sum to 100% (1), and see the donut chart in Figure 6

• the level’s “degree of performance” on the attribute:
  • the lowest level = minimum (“worst”) possible performance: always worth 0%
  • the highest level = maximum (“best”) possible performance: the attribute’s overall weight (as above)
  • levels between these two extremes = some fractional value of the attribute’s overall weight

A shortcut to appreciating these two combined effects is available by studying Table 8. This table shows an equivalent representation of Table 7’s mean utilities decomposed into “normalized weights and scores” respectively, corresponding to the two main bullet points above. This equivalence can be easily confirmed by multiplying for each level the associated weights and scores to get the utilities.

What matters most?

As revealed by the weights in Tables 6 and 7 and Figure 6, on average, the most important attribute is camera quality (28.4%), followed by size (21.5%), then price (21.2%), screen quality (11.2%) and operating performance (9.6%), and the least important is battery life (8%).

It can also be said that “camera quality’s importance is 28.4%” and “battery life’s importance is 8%” (and so on for the other attributes).

An attribute’s importance – its weight or utility – depends on how its levels are defined: the broader and more salient the levels, the more important the attribute will be to people.

For any of the non-price attributes, they would be revealed as more important – having higher utility – if their highest level were specified as “spectacular” instead of just “very good”. For example, a “spectacular” camera is more desirable than a “very good” one and so if the former description were used the camera-quality attribute would end up with a higher weight (utility).

Top-ranked alternative scores 100%

As will be explained in detail later (don’t worry if this point is unclear now), for each participant and on average, the theoretically top-ranked (e.g. “best”) alternative – i.e. the one with the highest levels on all attributes – has a total utility of 100%, for example here from the means: 28.4 + 21.5 + 21.2 + 11.2 + 9.6 + 8 = 100 (due to rounding to one decimal place, these reported weights sum to 99.9).

This point that the top ranking alternative scores 100% means that out of a maximum total utility (“score”) of 100%, on average, 28.4% is going on camera quality, 21.5% on size, and so on for the other attributes, down to 8% for battery life (Tables 6 and 7, Figure 6).

At the other extreme, the lowest-ranking (“worst”) alternative, with the lowest levels on all attributes, has a total utility of 0%, i.e. the sum of six zeros.

Thus, each of the possible combinations of the levels on the attributes, corresponding to all possible configurations of the alternatives (phones) – i.e. 3 × 4 × 5 × 3 × 3 × 3 = 1620 combinations – receives a total utility somewhere in the range of 0% to 100%.

Attribute rankings

Consistent with the relative magnitudes of the utilities for each participant in Table 7, their rankings, as well as median and mean rankings and standard deviations (SD), are reported in Table 9.

Attribute relative importance

Dividing one attribute’s weight by another attribute’s weight reveals the relative importance of the two attributes. In some fields, such as Economics, these ratios of relative importance are known as “marginal rates of substitution” (MRS).

These relative-importance ratios are reported in Table 10, where the cell values (relative importances) are calculated by dividing the mean utility (weight) of the attribute on the left by the mean utility of the attribute at the top. Notice that corresponding pairs of ratios in the table are inverses of each other.

For example, camera quality is 3.6 times (28.4/8) as important as battery life; and battery life is 0.3 times (8/28.4), or three-tenths, as important as camera quality.

Rankings of alternatives

Our focus so far has been on the conjoint survey participant’s utilities, which are fundamentally important because they capture how people feel about the attributes.

Utilities are also usefully applied to predict people’s behavior with respect to their ranked choices of the alternatives of interest as described on the attributes.

An obvious business application is predicting consumers’ demand for products when designing new products or improving existing ones in pursuit of larger market share. Possible product configurations – known generically as “alternatives”, “concepts” or “profiles” – can be modeled using the utilities.

Table 11 shows how eight smartphone alternatives (concepts or profiles) are ranked when the mean utilities from the survey are applied to each phone’s ratings on the attributes. The ranking is based on the ranking of the alternatives’ “scores”, as calculated by adding up for each alternative the relevant utilities for its levels on the attributes.

For example, Phone E’s score of 75.4% is calculated by adding up the mean utilities for “very good” on the first four attributes and a “$1000” price and “large” size: 9.6 + 15.4 + 8 + 11.2 + 15.9 + 15.3 = 75.4

In addition, Table 11 shows how the eight phones are ranked when each participant’s utilities (Table 7) are applied to the eight phones in Table 11. These rankings are predictions of the five people’s phone choices based on their individual utilities.

The mean ranking of the eight phones in Table 12 is slightly different to the ranking in Table 11 because of the difference in how the two rankings are calculated.

Market simulations (“What ifs?”)

If the conjoint analysis software you are using has one, you can use a “market simulator” to convert participants’ utilities from a conjoint survey into predicted market outcomes by simulating people’s choices between competing products (e.g. phones), enabling the modeling of:

• market shares
• elasticities and demand curves

Because the objective is to simulate the demand side of an entire market, more than just five participants, as in the smartphone example so far, are required for your conjoint survey.

It’s important to bear in mind that a simulation is just that: a simulation. Market simulators are not omniscient crystal balls capable of predicting real-world market outcomes with 100% accuracy.

Simulation results depend on who participated in the conjoint survey and how they were selected, i.e. randomly versus non-randomly, as discussed earlier. Different samples are likely to produce different simulation results.

Also, simulations don’t account for “frictions” in many real-world markets, such as consumers not being fully aware of all the products being compared and being unable to choose freely among them. To be tractable, market share predictions are usually based on “ideal world” assumptions, as summarized in the “reality checks” box below.

Predicted market shares

The focus in market simulations is on each product’s predicted market share based on participants’ predicted 1st choices – i.e. the product each participant is most likely to choose based on their utilities from the conjoint survey.

For example, as illustrated in Table 13 (from 1000minds’ market simulator), the predicted market share, or “share of preferences”, for each phone is calculated by dividing the number of participants for whom that phone is their 1st choice by the total number of survey participants (e.g. 140 in the example). The sum of market shares across all phones is 100% (1).

(This aggregation of participants’ 1st choices is analogous to an election in which citizens vote for their preferred candidate, with the votes tallied to get each candidate’s vote share or percentage – equivalent to their “market shares”.)

To perform a simulation, all you need to do is change any of the phones’ ratings on the attributes, and see what happens to their market shares, i.e. compare their shares before and after your changes.

Such before-and-after evaluations (i.e. comparative statics) are useful for:

• Head-to-head comparisons: create competing phone profiles on the attributes and see how each performs – e.g. how might your phone be improved to become the “market leader”?
• Imaginary product testing: before launching a new phone, test different configurations in the simulator to predict consumer uptake
• “What-if” analysis: simulate what happens if a competitor were to reduce their price or add a premium feature (and how might you respond?)

Simulate your survey participants’ choices and find out!

For example, as modeled using 1000minds’ market simulator (Table 13), suppose “New phone model X’s” operating performance and screen quality were upgraded to “very good” while its price was increased by $200. Its market share would triple from 15% to 45.7% – to become the market leader over Apple, Google, OPPO, Samsung and Xiaomi!

Name	Market shares Participants’ 1st choice (n=140)			Attributes
	Before	After	Change	Operating performance	Camera quality	Battery life	Screen quality	Price	Size
Apple model A	30%	15.4%	−48.8%	very good	ok	very good (13+ hours)	very good	$1000	large (6″)
Google model B	21.1%	10.4%	−50.8%	very good	good	good (11–12 hours)	very good	$900	medium (5.5″)
New phone model X	15%	45.7%	+204.8%	good → very good	very good	good (11–12 hours)	ok → very good	$800 → $1000	large (6″)
OPPO phone C	10.4%	11.4%	+10.3%	good	good	ok (10 hours)	good	$600	medium (5.5″)
Samsung model D	16.4%	11.4%	−30.4%	good	very good	very good (13+ hours)	very good	$1000	small (5″)
Xiaomi phone E	7.1%	5.7%	−20%	ok	good	ok (10 hours)	good	$600	large (6″)
Total	100%	100%	0%

Elasticities and demand curves

As well as modeling market shares, 1000minds’ market simulator allows you to:

• Measure price sensitivity: test how responsive – referred to as “elastic” – your product’s demand, or market share, is to price changes, both for your product and competitors’ products
• Plot demand curves: represent the relationship between a product’s price and its market share at various prices

“Elasticity” is a mathematical concept related to the responsiveness, or sensitivity, of a variable of interest to a change in another variable, where both variables have numeric values so that their changes are measurable in proportionate, or percentage, terms.

The word “elasticity” derives from the notion of variables “stretching” like an elastic band to varying degrees in response to changes in other variables.

Own-price elasticity of demand

Own-price elasticity of demand is measured using an own-price elasticity coefficient (ε), which is simply the ratio of the percentage change in quantity demanded to the percentage change in price.

Thus, own-price ε for a product – let’s call it “Product A” – is defined as:

own-price ε = $$\frac{\text{\% change in Product }\text{A}\text{’s quantity demanded}}{\text{\% change in Product }\text{A}\text{’s price}}$$

For example, if Product A’s price rose by 2% and its quantity demanded fell by 4%, then:

own-price ε = −4% / 2% = −2

See the technical note about how percentage changes for elasticity coefficients are estimated using the arc method.

Own-price elasticity coefficients are negative because price and quantity demanded typically move in opposite directions: when a product’s price rises, some consumers decide not to buy it, buy less of it, or switch to an alternative, resulting in the quantity demanded falling. This negative relationship is reflected in downward-sloping demand curves (e.g. Figure 9 later).

Because own-price elasticity coefficients (ε) are almost always negative (or, in rare cases, zero), what matters for interpretation – in particular, for pricing decisions – is their relative magnitudes.

There are three main ranges of ε values, corresponding to three types of own-price elasticity, to consider:

ε < −1   demand is price elastic (relatively responsive)

Example: ε = −5

This elasticity coefficient means that a 1% decrease in price causes a 5% increase in quantity demanded. Thus, quantity demanded responds proportionately more than the price change, which means demand is relatively responsive (elastic).

Conversely, a 1% price increase causes a 5% decrease in quantity demanded.

ε = −1   demand is unit elastic

This coefficient means that a percentage change in price causes an equal percentage change in quantity demanded in the opposite direction. For example, a 1% decrease in price causes a 1% increase in quantity demanded.

−1 < ε ≤ 0   demand is price inelastic (relatively unresponsive)

Example: ε = −0.4

This coefficient means that a 1% decrease in price causes only a 0.4% increase in quantity demanded. Thus, quantity demanded responds proportionately less than the price change, which means demand is relatively unresponsive (inelastic).

Conversely, a 1% price increase causes a 0.4% decrease in quantity demanded.

A special, rare case is ε = 0, which means that a price change has no effect on quantity demanded; in other words, demand for the product is perfectly price inelastic over the range being considered.

Why own-price elasticity matters for revenue

From a business perspective, appreciating the difference between the three relative magnitudes of own-price ε explained above is critically important when thinking about whether to raise or lower prices.

In short, the value of own-price elasticity coefficients (ε) – indicating whether demand is elastic (ε < −1), unit elastic (ε = −1) or inelastic (−1 < ε ≤ 0) – determines how price changes affect revenue earned from selling a product, where revenue = price × quantity demanded.

Corresponding to the three own-price elasticity types introduced earlier are three possible scenarios related to the effect of price changes on revenue:

ε < −1   demand is price elastic (relatively responsive)

Example: ε = −5

This elasticity coefficient means that a 1% increase in price causes a 5% decrease in quantity demanded; thus, quantity demanded changes proportionately more than price. Although more revenue is earned per unit sold, substantially fewer units are sold, and so the overall effect on revenue is for it to fall.

Conversely, a 1% decrease in price causes a proportionately larger increase in quantity demanded, and so the overall effect on revenue is for it to rise.

ε = −1   demand is unit elastic

In this case, price and quantity demanded change by equal percentages in opposite directions. Therefore, revenue remains unchanged following either a price increase or a price decrease.

−1 < ε ≤ 0   demand is price inelastic (relatively unresponsive)

Example: ε = −0.4

This time, quantity demanded changes proportionately less than price: this elasticity coefficient means that a 1% increase in price causes only a 0.4% decrease in quantity demanded. Although fewer units are sold, the reduction in sales is relatively small, and so the overall effect on revenue is for it to rise.

Conversely, a price decrease reduces revenue because the increase in quantity demanded is proportionately too small to offset the lower price per unit.

These three scenarios underpin why understanding own-price elasticity is so important for pricing decisions. Whether raising or lowering price is likely to cause revenue to increase or decrease (or not change) comes down to which one of the three ranges of ε applies.

Cross-price elasticity of demand

Cross-price elasticity of demand – the effect on the quantity demanded of a product in response to a change in the price of another product – is measured using a cross-price elasticity coefficient (ε), which is simply the ratio of the percentage change in the product’s quantity demanded to the percentage change in the other product’s price.

Thus, cross-price ε for Product B with respect to a change in Product A’s price is defined as:

cross-price ε = $$\frac{\text{\% change in Product }\text{B}\text{’s quantity demanded}}{\text{\% change in Product }\text{A}\text{’s price}}$$

For example, if Product A’s price rose by 2% and Product B’s quantity demanded rose by 1.4%, then:

cross-price ε = 1.4% / 2% = 0.7

See the technical note above about how percentage changes for elasticity coefficients are estimated using the arc method.

The same approach is used to measure the effects of a change in Product A’s price on demand for other products (C, D, E and so on): i.e. to calculate cross-price ε for each other product with respect to a change in Product A’s price.

Whereas own-price elasticity coefficients are almost always negative (or, in rare cases, zero), in 1000minds’ market simulator, cross-price ε coefficients are always positive or zero, corresponding to products that are either substitutes or economically unrelated:

• A positive coefficient indicates the two products are substitutes – because consumers switch between them when their prices change, and so, when the price of one product rises, demand for the other rises; and vice versa when the price falls
• A zero coefficient is for products that are economically unrelated – and so a price change for one product has no effect on demand for the other

Demand curves

A demand curve is a simple graph of the relationship between a product’s price and the quantity demanded by customers at different prices. It represents how customer demand responds across the range of possible prices.

1000minds’ market simulator generates demand curves by varying a product’s price and calculating its predicted market share (or “share of preference”) at each price point. This predicted market share is a proxy for quantity demanded, normalized by the number of participants in the simulated market.

As illustrated in Figure 9 for “New phone model X”, demand curves slope downward: as price decreases, the product’s share of preferences increases; and vice versa: as price increases, share of preferences decreases.

The reason for this negative relationship is that when the price of something increases, ceteris paribus (all else equal), people demand less of it. This is the same negative relationship captured by the negative own-price elasticity coefficients discussed earlier.

For more information about elasticities and demand curves, check out our ultimate guide to price elasticity of demand.

Marginal willingness-to-pay (MWTP)

MWTP – often shortened to WTP (willingness to pay) – is a measure of how much people would be willing to pay for an improvement in a particular attribute of a product.

For example, how much would people be WTP for a “very good” camera on their phone relative to just an “ok” camera?

The “marginal” in “marginal willingness to pay” is to remind us that the MWTP is for the change to the attribute of interest relative to the alternative’s baseline configuration, i.e. the WTP for just this (marginal) change to the attribute. As returned to later, it is usually inappropriate to add up WTPs across attributes.

Cluster analysis (market segmentation)

The mean utilities reported earlier (Table 7) are useful, but means can conceal the most interesting finding of all: that participants are not one population with one set of preferences, but a few distinct groups (“clusters”) whose preferences differ systematically – e.g. price-hunters and camera enthusiasts. If the sample contains two or more such groups, the average describes none of them.

Cluster analysis addresses whether participants fall into groups whose preferences (as captured by their utilities) are similar within the group and different between groups – and, just as importantly, how much confidence you can have in the groups you have identified.

Cluster analysis is a type of “unsupervised learning” in which the algorithm is not told in advance which participants belong together – the conjoint analysis utilities get to speak for themselves!

Note that participants are clustered on their preferences, not on their socio-demographics. Characteristics such as age, region and income play no part in forming the clusters; they come in afterwards, when you examine whether the clusters that emerged differ on those characteristics. Such information is useful for designing marketing campaigns or government policy-making.

Of course, more than just the five participants in the smartphone example are required for meaningful segmentation – the analysis illustrated below draws on a mock survey of 1000 participants.

What the analysis tells you

For each cluster it finds, a cluster analysis reports how many participants belong to it and how much its members care about each attribute – the cluster’s profile of utilities.

Read against other clusters and the sample-wide means, those profiles are what turn an abstract grouping into a description of a market segment: e.g. this cluster is obsessed with camera quality, these other two clusters are not.

As well as the profiles, three things are worth having:

• A representative member. Depending on the method, this is either a computed average profile or – with k-medoids – an actual participant whose utilities and responses can be inspected.
• A measure of fit, indicating how comfortably participants sit in the cluster they were assigned to (see silhouette below).
• A map of participants positioned so that like-minded ones sit close together, colored by cluster, which makes the shape of the sample visible at a glance.

Figure 10 shows profiles of clusters identified among the participants in the smartphone example for k = 4; Figure 11 shows a preference map of the clusters for k = 5.

The analysis can also be run on a subset of participants rather than all of them – a single region, say – if you have reason to think a sub-population segments differently from the sample as a whole.

What sets 1000minds apart?

1000minds has the following advantages relative to other conjoint analysis & DCE software.

Quick-and-easy setup

Create conjoint surveys in minutes. Easily define your attributes, customize your survey (available in any language and with images) and distribute it to potentially 1000s of participants. Need help getting started? 1000minds’ AI Assistant can help suggest attributes – and alternatives too, if desired – to get you up and running quickly.

User-friendly for all

The intuitive interface and conversational question style make 1000minds easy for both administrators and participants. This user-friendliness ensures better engagement and higher quality data and completion rates than other methods.

Automatic results and reporting

As responses come in, conjoint analysis outputs are produced instantly in real-time – no manual analysis is required. The platform generates clear, actionable results that are easy to interpret and share with stakeholders.

Scientific validity

1000minds is used at over 880 universities and research organizations around the world and regularly cited in peer-reviewed studies (see our 430⁠+ peer-reviewed publications). Its validity and reliability are widely recognized by both conjoint analysis academics and practitioners alike.

Award-winning innovation

1000minds has been recognized in 18 innovation awards, including the Consensus Software Award (sponsored by IBM and Microsoft) which praised 1000minds for “blending an innovative algorithm with a simple user interface to produce a tool of great power and sheer elegance.”

Try 1000minds today

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