Lee Merkhofer Consulting Priority Systems

Technical Terms Used in Project Portfolio Management (Continued)





























paired comparison

Also called pairwise comparison, a process for simplifying decisions or judgments that involves comparing options or entities in pairs and judging which element of the pair is preferred or has the greater amount of some other measurable property. The process is popular because paired comparisons are easy for people to make. The questions can be presented as pictorial scales, with numbers assigned to qualitative judgments to represent a strength of opinion. Among other applications, paired comparison is used as a method for assessing preferences, assigning probabilities, voting, and ranking decision options.

Sample PERT chart

A paired comparison scale - Which do you prefer?

Paired comparison is sometimes used as a method for prioritizing projects. Each project option is compared against each other option, and a score is assigned to each option under each comparison to indicate a degree of superiority or inferiority. The preference scores are then combined in some way (e.g., summed) to obtain an overall figure of merit for each project. The popular analytic hierarchy process (AHP) has decision makers compare the performance of pairs of options with regard to each decision objective. The preferred option is the one most consistent with the pairwise judgments.

paired comparison matrix

Also called a pairwise comparison matrix, a matrix whose elements represent the results of preference comparisons conducted as part of a multi-criteria analysis. For example, with one common pairwise comparison matrix, the entry in the i'th row and j'th column indicates judgments of the relative value of obtaining a swing in the performance specified for the i'th performance measure compared to the estimated value of obtaining a swing specified for the j'th performance measure. In another common instance, the comparisons might be conducted with regard to different alternatives. In this instance, the entry in the i'th row and j'th column might indicate a judgment of the relative desirability of the i'th alternative compared to the j'th alternative with respect to a specified performance measure.

payback period

The amount of time it takes for the cumulative cash flows from a project to equal the initial investment. An investment will have paid for itself in the year, or month, where the cumulative cash flow first becomes positive. Payback period is a popular metric for evaluating projects because of its simplicity, emphasis on liquidity, and obvious responsiveness to external financing pressures. However, because a payback period does not provide an adequate measure of project or portfolio value, it should not be used as a metric for prioritizing projects.

A major limitation of the payback period method is that it ignores cash flows after the payback period. For example, a small project may have a break-even point at six months from the start of the project. A larger project that costs twice as much may not break-even until 12 months after the start of the project. Based on the analysis of the payback periods, the company may choose to go with the smaller project. The analysis would ignore the fact that after two years, the larger project would have produced three times the dollar savings as the smaller project. Also, as no discounting is involved, the payback period overlooks the time value of money (cost of capital).

peer review

The most common approach to project selection used by organizations engaged in scientific research. Projects are evaluated by "peers," individuals with credentials similar to those who are proposing to conduct the projects and who are technically competent to evaluate them. Written project proposals are provided to three or more peers who review and evaluate each proposal independently. For example, the reviewers may be asked to assess the project's technical merit, the competence of the project team, and the adequacy of the management plan. The assessment is typically noted on an evaluation sheet, where each evaluation criterion is given a score from 1 (poor) to 5 (excellent). If one or more reviewers give the project low scores, it is unlikely to be funded. Peer review has long been criticized as being highly subjective and susceptible to bias, such as favoritism of "an old boy network."

perception biases

A category of cognitive biases (distortions in judgments) characterized by faulty perceptions. Examples of perception biases include overconfidence, anchoring, base-rate, and bounded awareness.

performance measure

On this website, I use the term to mean a metric that expresses the level of performance achieved with respect to an objective. Performance measures are useful for comparing the alternatives to a decision. For example, suppose you are shopping for a refrigerator. One objective is to have adequate space to store your food. A possible performance measure for this objective is storage capacity measured, for example, in cubic feet. Another objective might be operating cost, for which the refrigerator's average annual electricity cost might be selected as a performance measure. The number of lights that go on when the refrigerator door is open is a metric, but not likely a performance measure because maximizing the amount of light inside the refrigerator is not an important objective for most shoppers.

Oftentimes, a performance measure for an objective is calculated from other metrics that are easier for a decision maker to estimate or obtain. In such cases, a performnce model is used to estimate the performance measure. For example, a label on a refrigerator might state the amount of electric power the product consumes per year, for example, 1000kWh. If the shopper obtains from his or her electric bill price charged for electricity, for example, 10 cents per kWh, the approximate annual operating cost for the refrigerator may be calculated: 1000kWh x .10/kWh = $100 per year.

The entries in the cells of a decision matrix, if they relate to decision objectives, are performance measures. The attributes in a utility function are typically performance measures, though they don't need to be since any metric that a decision maker feels is relevant to judging preference, whether or not it measures achievement of a decision objective, may be included in a utility function. For example, a metric defined to measure project urgency might be an attribute in a utility function, though urgency may not be defined as an objective for project selection.

performance model

A model for simulating or otherwise estimating or forecasting the impacts of project decisions relevant to determining project value. Most often, project impacts are one time impacts relative to objectives as measured by performance measures or time streams of impacts that are discounted to present values that serve as performance measures. The outputs of a performance model are the inputs needed by a preference model. A performance model and preference model together make up a value model.

Performance model


In project portfolio management software, specifications of the particular users or user roles that are allowed access to secure work items and other project elements contained in the software database.

PERT chart

A diagram that graphically displays a type of network model often used to support the planning and analysis of projects composed of many interdependent tasks. PERT stands for Program Evaluation and Review Technique. PERT charts were first developed in the 1950's by the Navy to help manage very large, multi-step, non-routine projects having a high degree of inter-task dependency.

In a PERT chart, tasks are represented by nodes and task dependencies are represented by lines connecting the nodes.

Sample PERT chart

A simple PERT chart

A primary use of PERT charts is to compute the minimum time required to complete the project, where the model allows for uncertainty in the time necessary to complete each task. Project management tools typically support PERT charts and some portfolio management tools provide this capability as well.

platform project

A project that creates knowledge or capability (i.e., a "platform") for delivering other projects, such as a new generation of product or service offerings. An example would be a project for an automobile company to create its first electric vehicle. Platform projects represent significant departures from existing offerings and are often costlier and/or riskier, but may generate strategic value for the organization.


Refers to a project management guide provided by the Project Management Institute, a non-profit professional organization. PMBOK stands for Project Management Body of Knowledge. The PMBOK guide specifies widely recognized and accepted standards for project management information and practice.

PMI analysis

A simple decision-making aid wherein the pros, cons, and interesting implications of a project or other proposed action are listed and evaluated. PMI stands for plus, minus, and interesting. Positive and negative scores are assigned subjectively and the results added. A strongly positive total is interpreted as suggesting that the action should be taken and a strongly negative score that it should be avoided.

point estimate

A single numerical value selected to summarize what is, in reality, an uncertainty that could take on any value within some range of possibilities. Uncertainties are more accurately described by probability distributions.


A collection of investments or other valued assets, such as projects or securities, held by a person or organization. The investments are grouped to facilitate their management.

portfolio balancing

A term sometimes used in project portfolio management (PPM) literature to describe the last step in the process of identifying an optimal project portfolio. Portfolio balancing involves adjusting the portfolio of selected projects based on observing and adjusting the mix, or" balance," of projects across various dimensions, for example, risk versus return, long-duration versus short duration, maintenance versus asset enhancement, incremental projects versus breakthrough projects, etc. PPM tools provide portfolio mappings to support the process. Tool vendors assert that the displays allow instances of imbalance to be identified and help suggest project substitutions that improve the portfolio.

It's a bit more complicated than that. While PPM literature frequently advises portfolio balancing, there is very little real advice about how to assess portfolio balance or what changes should be made to the distribution of projects to improve balance. Organizations use many different schemes to categorize projects. Defining the scheme requires choosing project categories (e.g., Should projects be categorized based on complexity?), selecting metrics (How does one measure complexity?), and deciding how to differentiate projects based on the metrics (How many distinct levels of complexity should be identified?). Typically, the organization's project categorization scheme is multi-dimensional. Also, the scheme may be hierarchical, such that there is a primary categorization based on one project attribute (e.g., large vs. small projects) and then subsequent classifications that differ depending on where the project falls in the primary categorization. An important but rarely addressed question is whether the project categorization system used by the organization is a good one for observing and managing balance. In any case, displaying and managing balance becomes more difficult with hierarchical categorization and when the buckets are not mutually exclusive.

As I argue in my papers, the goal of PPM is to select the set of projects, subject to applicable constraints, that creates the greatest possible value, where value is defined as the worth to the organization of the consequences that would be produced by conducting all of the projects in the portfolio. A comprehensive assessment of project value must account for all of the impacts of project decisions on the ability of the organization to achieve its objectives, now and in the future, with portfolio value adjusted to account for portfolio risk in accordance with the organization's risk tolerance. If projects have not been defined so as to be independent of one another, then the value assessment for a project must be contingent on whether or not the interdependent projects are conducted as well. By definition, the optimal project mix is the one that maximizes risk-adjusted, portfolio value.

Many PPM tools include some model or logic for prioritizing projects or recommending project portfolios. For most tools, the model is very simple (e.g., a weighted scoring model). Many tools rank projects based on scoring strategic alignment, an approach that has little to do with measuring project value. Only a very few PPM tools utilize sophisticated value models and accurate optimization algorithms. The reason for this is that defensible value models need to be organization- and project-type specific, and vendors can't make as much money selling a tool that only fits a narrowly defined market.

Regardless of the tool used, because even the best models are not perfect, the project portfolio that is recommended by a tool may not actually be the value-maximizing project portfolio. Thus, it is always necessary to consider how the recommendations produced by a tool (or obtained by any other mechanism) ought to be adjusted and improved. One could call this subjective step "balancing the portfolio," but it might also be called accounting for considerations that are not well addressed by the model.

For example, if projects involve risk, but the model does not adequately account for the impact of risk diversification and/or the willingness of decision makers to accept risk when computing portfolio value, then it will be particularly important to check whether the recommended portfolio presents an acceptable level of risk and whether it reflects a bias toward either risky or safe projects. If the application includes multi-year projects or projects that generate benefits over time, but the model does not capture time preference, or if it recognizes constraints on only current-year and not out-year spending, then it will be important to check whether the portfolio provides a reasonable balance between immediate and long term costs and benefits, and to check whether portfolio cash flows are sustainable (e.g., will near term cash flows be sufficient to support investments necessary to assure returns over the long term?). If the different types of projects require different people resources (e.g., research projects versus development projects), but the model doesn't account for constraints on the specific resources needed by each type of project, then it will be important to check whether the recommended portfolio balances demand for the available types of constrained resources. If there are dependencies among projects, but the model merely ranks projects without regard to the dependencies, then changes may similarly be needed to better "balance" the portfolio so as to take such dependencies into account.

The point is that it is always necessary to examine a candidate portfolio carefully from various perspectives for the purpose of identifying changes that would increase portfolio value. Portfolio balancing may be as good a term as any for this step. In any case, a PPM tool should provide graphical outputs that assist portfolio balancing. However, absent having a better model, there is no way to measure whether a change to portfolio "balance" actually increases portfolio value. Thus, it is best to start with a quality model, thereby reducing the extent to which subjective judgment unsupported by analysis is needed to translate the "bad recommendations" made by a poor tool into choices that actually create more value for the organization.

portfolio decision analysis

The approach that I recommend for selecting projects, the most important task within project portfolio management. PDA represents a body of knowledge and formal process based on mathematical modeling aimed at helping decision makers select the best choices from a discrete set of options taking into account relevant constraints, option costs, preferences, and uncertainties. PDA is a banch of decision analysis (DA) wherein the decision to be made is the selection of a portfolio of choices.

the concern on this website is PDA where the decision to be made is the selection of a portfolio of projects. Being a form of DA, PDA is founded on decision theory and makes use of DA's well-structured, step-by-step process for building decision models, analyzing alternatives, and making choices.

PDA is a relatively new form of DA with a specialized focus. Most early applications of DA were designed to help decision makers make single-choice decisions, for example, choosing a site to drill for oil. PDA, in contrast, is intended to help decision makers make multiple, interconnected decisions, specifically, what investment alternatives to include within a portfolio. In other words, PDA is focused on portfolio project selection and the allocation of resources across available projects.

When choosing the projects to include within a portfolio, the project choices are inherently interconnected. Even if the projects are independent of one another in the sense that neither the costs nor benefits of any project depend on which other projects are conducted, the projects are interconnected because they consume or compete to consume shared resources. This means that project choices cannot be made one-at-a-time without consideration of the interconnections. It is not possible to determine whether or not a specific project should be included within a portfolio without knowing the other projects in the portfolio and the capital and other resources that those projects would consume. With PDA, the problem is defined to be the selection of the project portfolio and interconnections are taken into account.

The existence of PDA does not mean that traditional "single-choice" DA is useless for project selection. Some organizations conduct independent DA's for each and every major project that is a candidate for the portfolio. However, the fact that a DA indicates that doing a project is a better choice than not doing the project is not sufficient to conclude that the project belongs in the portfolio—there may be insufficient resources for conducting all such projects. Thus, some rule must be established for determining the subset of attractive projects to include within the portfolio (e.g., choose those projects with the highest ratios of value-to-cost). Even if the rule makes sense, if the project DA's are conducted independently of one another, inconsistencies in assumptions may result, opportunities for analytic efficiencies may be missed, and interdependencies among projects may not be captured.

If, on the other hand, DA is applied with the problem framed as choosing a portfolio, a consistent, efficient logic can be defined and used to evaluate every project. In addition, the portfolio approach allows dependencies among projects to be included within the analysis. Thus, PDA allows for a more complete and consistent form of portfolio analysis which improves the quality of decision making because it accounts for more considerations while ensuring that all options are treated equally. With PDA, for example, a marginal project won't be selected merely because it happens to be evaluated early in the year before the budget is depleted.

PDA's major strength for project portfolio selection is the ability to quantify the value of projects and project portfolios. PDA commonly uses multi-objective decision analysis (MODA) to quantify and include non-financial sources of project value. MODA allows computations of value to be expressed in equivalent dollar units while taking into account risk and organizational risk tolerance.

PDA is a particularly cost-effective form of DA since, compared to single-choice decisions, choosing portfolios is more difficult and organizations typically spend more to fund portfolios than single projects. As a consequence, a large portion of more recent, professional DA applications are PDA's.

portfolio mapping

Various graphing and charting techniques generally used to portray the "balance" of a portfolio of projects by displaying how the various projects perform on two or more dimensions or criteria. The most popular portfolio mapping diagram displays project risk and reward—the y-axis is labeled probability of success and the x-axis is labeled payoff or reward. Projects are plotted on the diagram according to their estimated success probabilities and payoffs (if successful).

A bubble diagram is a popular variant of portfolio mapping that uses a circle or ellipse to identify each project instead of a single point. The size, shape, color or shading of the circle is varied to provide additional information about the corresponding project. For example, the size of the circle may represent the initial cost of the project.

Sample Portfolio Mapping Chart

A portfolio mapping

In one popular version of the risk-reward portfolio mapping (shown above), projects are categorized according to the quadrant that they fall into. The 4 quadrants of the diagram are labeled "pearls," "oysters," "bread & butter," and "white elephants." Pearls have a high probability of success and yield high payoffs. Oysters are long shots, but with high payoffs. Bread & butter are low-risk projects with low reward. White elephants are low probability and low payoff projects.

Numerous, versions of portfolio mappings and bubble diagrams are in use and project portfolio management software often provides such displays. The chosen axes represent characteristics relevant to the specific application area. For example, for new-product-development projects, popular variations of the risk-reward plot include ease-attractiveness (plots showing the trade-offs between technical feasibility versus some measure of market attractiveness, such as growth potential), cost- timing (cost to complete versus time to benefits), and focus-benefit (consistency with organizational strengths versus some measure of project benefit, such as expected net present value (ENPV)).

Portfolio mapping tools are useful devices for displaying project characteristics, but they do not provide a basis for deciding either how to tradeoff those characteristics nor what balance or distribution among the various characteristics is best for the project portfolio.

portfolio planning matrix

Also called a portfolio grid, graphical tool sometimes used by large companies to help analyze and manage their portfolios of strategic business units (SBU's). The tool involves locating the company's SBU's within the cells of a matrix. The results, it is claimed, assist the company in deciding which businesses should receive more or less investment and help to identify businesses that should be abandoned and new businesses that should be added to the portfolio.

The original version of the portfolio planning matrix (sometimes called the BCG Growth-Share Matrix, was developed in the 1970's by the Boston Consulting Group (BCG). In this version, the matrix has four quadrants representing low versus high levels of market share and low versus high opportunities for growth. The company's SBU's are identified and placed in the matrix as follows: Mature SBU's that generate excess cash because of their dominant market shares in slow-growth markets are placed in the lower left quadrant and labeled cash cows. SBUs that consume cash but that have potential because of their high shares of high-growth markets are placed in the upper right quadrant and labeled stars. SBU's that must consume cash to remain viable and that have low shares of high-growth markets are placed in the upper right cell and labeled question marks. Finally, SBU's that simply generate enough cash to break even, but that hold little further promise because of their low shares of low-growth markets are placed in the lower right quadrant and labeled dogs.

BCG Portfolio Planning Matrix

BCG portfolio planning matrix

The location of SBU's within the BCG matrix can help suggest portfolio strategies. If the company can increase the market share for a question mark, it may turn it into a star. If investment needs to be decreased, the company could phase out or sell dogs or question marks. Cash might be increased by reducing the investments in stars that have established good market share, thereby turning them into cash cows.

A somewhat more sophisticated version of the portfolio planning matrix, referred to as the McKinsey/General Electric Matrix, uses market attractiveness rather than market growth as the y axis and competitive strength rather than market share as the x axis. Multiple indicators are used to assess market attractiveness, including market profitability, pricing trends, and entry barriers. Likewise, multiple factors are used to assess competitive strength, such as relative brand strength, market share, customer loyalty, and record of technological or other innovation. In this version, business units are portrayed on the matrix as pie charts, where the size of the pie represents the total market size and the slice size indicates the market share captured by the SBU. Arrows are added to indicate the projected direction of movement of the SBU's over time. The process for locating the SBU's within the matrix involves identifying drivers for each dimension, scoring the SBU's against the drivers, weighting the drivers, and multiplying weights times the scores. As with the BCG version of the planning matrix, the pattern of results may help to suggest strategies for improving the business portfolio.

GE Portfolio Planning Matrix

McKinsey/GE portfolio planning matrix

The main advantage of a portfolio planning matrix is its simplicity. The main limitations include the inability to compute or account for the contribution of the various SBU's to total portfolio value, failure to account for risk, and lack of consideration of the interdependencies that, in practice, often exist among SBUs. Although the portfolio planning matrix was once widely popular, its use has largely been replaced by more sophisticated project portfolio management methods, including those described throughout this website.

posterior probability distribution

In Bayesian analysis, the probability distribution of an uncertain event or an uncertain proposition that is assigned after some new relevant evidence or information is taken into account.

precedence diagram

See project network diagram (PND).

prediction interval

See confidence interval.

preference model

A model for computing the value of achieving increments of achievement relative to objectives, for example, increments of achievement as measured by performance measures resulting from the decision to conduct a project. A preference model is a representation of the value judgments needed for decision making.

I recommend using a utility function for representing preferences. The utility function may be a single-attribute utility function, in which case it represents that there is only a single decision objective (e.g., maximize financial return) or it may represent multiple decision objectives. A multi-attribute utility function may be used to represent multiple decision objectives and to express willingness to tradeoff achievement of the different objectives. A utility function may also be used to represent risk aversion (I recommend using an exponential utility function, in which case risk preference is captured by a single parameter called risk tolerance). If a decision produces outcomes that occur over time, time preference is typically represented by using discounting to collapse those outcomes into an equivalent present value, in which case the discount rate is a necessary value judgment.

Preference model

preferential independence

Also called preference independence, an independence condition regarding a person's preferences for alternatives, situations, or outcomes characterized by more than one attribute. Attribute X is said to be preferentially independent of attribute Y if preferences for levels of X do not depend on the level of Y. Mutual preferential independence (where all subsets of the attributes are preferentially independent complements) is a necessary condition for using an additive value function to measure the value of projects.

To use a common example, suppose that when ordering a meal at a restaurant you are concerned about two attributes: (1) the type of meat (fish or beef) and (2) the type of wine (red or white). Suppose you prefer beef to fish regardless of the color of wine you drink, in which case your preferences for food may be preferentially independent of wine. However, suppose you prefer white wine with fish and red wine with beef. Then your preferences for wine depends on the food you order, so wine is not preferentially independent of food.

As the example shows, one attribute may be preferentially independent of another without that other attribute being preferentially independent of it. That's why mutual preferential independence is needed. A subset of the attributes X1, X2,...,XN, (N > 3) is said to be preferentially independent of its complement (the subset composed of the remaining attributes) if the rank ordering of outcomes (with no uncertainty) that have common levels for the complementary attributes does not depend on those common levels. If this property holds for all levels x1, x2,...,xN and for all subsets of the X1, X2,...,XN attributes, then mutual preferential independence is said to hold.

For example, suppose there are three attributes, X1, X2 , X3, and suppose x1 and x'1 are two levels for X1; x2 and x'2 are two levels for X2, and; x3 and x'3 are two levels for X3. Demonstrating that each pair of attributes is preferentially independent of its complement means finding that preferences for:

  • (x1, x2, x3) compared to (x'1, x'2, x3) are the same for all levels of x3
  • (x1, x2, x3) compared to (x1, x'2, x'3) are the same for all levels of x1
  • (x1, x2, x3) compared to (x'1, x2, x'3) are the same for all levels of x2

If there are more than just a few attributes, verifying mutual preferential independence can take a lot of work. Demonstrating mutual preferential independence would appear to require showing that each individual attribute is preferentially independent of its complement, each pair of attributes is preferentially independent of its compliment, then each triplet, and so forth, which is a lot of assessments. With N > 3 attributes, the number of such assessments is 2N-2, not really that many. However, as it has been proven that if Xi and Xj can be shown to be preference independent of the remaining attributes for any fixed attribute Xi and for all other Xj attributes, then mutual preferential independence must hold.

Mutual preference independence is important because it is a necessary (but not sufficient) condition for the existence of an additive value function applicable when there is no uncertainty over the levels of attributes:

V(x1,x2...xN) = w1V1(x1) + w2V2(x2) ... + wNVN(xN)

The Vi functions in the equation are single attribute value functions over each xi and the wi are weights.

As an example of what happens when preferential independence is violated, suppose you are at a restaurant and want to select a meal with a glass of wine. As demonstrated above, your preferences for wines may not be preferentially independent of your preferences for main dishes. Thus, the combination of your favorite wine from the wine list with your favorite entree from the menu won't necessarily result in the dinner meal you'd like best.

Note that preferential independence does not require statistical independence or causal independence. Mutual preferential independence can hold even when performance against different criteria is highly correlated, provided that the criteria express separate aspects of value (e.g., tests show that people often view public health and the environment to be preferentially independent even though the quality of human health often depends on the quality of the local environment). Thus, a project that reduces pollution from company operation might simultaneously improve the health of local populations and be good for the environment. In that case, the project would produce both human health value and environmental value. Because they are separate types of value (human health and environmental health are preferentially independent), there is no double counting when adding the two types of value.

present bias

A tendency of people to give more weight to payoffs in the present and immediate future when making decisions that trade-off outcomes occuring at different points in time. Present bias causes us to over-value immediate rewards at the expense of our long-term satisfaction.

present value (PV)

The value of a future stream of costs or benefits, or their monetary values, on a specified date or at the beginning of a specified time period. Present value is computed via a discount rate and the net present value formula.


Similar to PMBOK, PRINCE2 is a process-based, project management methodology based on the application of best-practices such as continued business justification, learning from experience, defining roles and responsibilities, managing by stages, managing by exception, and focusing on products and tailored to suit the project environment. The term is an acronym for PRojects IN Controlled Environments, 2nd major revision. PRINCE2 was originally developed by the government of the United Kingdom and is now widely used there, as well as internationally and in the private sector especially in information technology (IT) environments. The term is also used to refer to the training and accreditation of authorized practitioners of the methodology who undertake accredited qualifications to obtain certification. Some project portfolio management tools incorporate PRINCE2 documents, templates, and decision points.


The process of evaluating items and ranking them. The term is not specific as to the criterion by which items should be ranked, and different criteria are common in different contexts. Perhaps most common is prioritizing items by importance, with the most important items ranked highest. If the items to be priorized are tasks, it is common for the ranking to indicate the order in which the tasks should be done. Supporting this view, the word prioritize comes from the Latin word, prioritas, which means "before". The most commmon assumption for prioritizing tasks is that they should be ranked based on urgency. However, prioritization is a prominent consideration for time management where other ranking criteria are often recommended, for example, easiest first, hardest first, quickest first, and longest first, as well as most important first.

In the contet of project portfolio management the prioritization of projects is important because there are typically more available projects than can be conducted due to limits on time, money, or other resources. Here, prioritization involves displaying in a list the order in which projects would be added or removed as constraints governing what can be accomplished are relaxed or tightened. Importantly, as described in my paper on mathematical methods, the ratio of project benefit (or value) to project cost (the ratio is called project productivity) is often used as a priority measure for ranking projects. When independent projects are ranked using this measure, selecting projects in rank order until the budget is consumed will approximately identify the project portfolio that generates the greatest total benefit (value) for the available budget.

The concept of project prioritization is less helpful in situations where there are interdependencies among projects and when there are multiple constraints that limit the set of projects that can be conducted (e.g., projects that require funding in successive years, with constraints on what can be spent in each year). In such circumstances, it is generally still possible to show as a list the order in which projects would be added or deleted from the project portfolio, but the list would change depending on the particular constraint that is adjusted. Also, the list will not be a strict ranking. For example, as the budget is increased, a project that is initially added might be dropped to accommodate a larger project with a higher benefit-to-cost ratio (see the discussion on the efficient frontiers vs. ranking curves). Thus, although the concept of prioritization is useful, portfolio optimization is a more general concept and goal.

prioritization matrix

A simple tabular format for displaying a prioritization of projects based on a multi-criteria analysis. For example:

Sample prioritization matrix

A sample prioritization matrix

If the purpose of the matrix is to aid the selection of an alternative rather than prioritizing alternatives, it is typically called a decision matrix. Some of the numerous other names used to refer to the same device are the criteria-alternative matrix, weighted-scoring matrix, and evaluation matrix.

Many project portfolio management tools use some form of a prioritization matrix to summarize project evaluations and rankings. While the matrix provides a compact way of conveying results, the quality of the tool depends on the quality of the multi-criteria method used to produce the results, including the logic for defining the criteria and the processes used to evaluate projects and assign weights.


Determined by uncertainties as described by probabilities. Typically applied to describe a model or method of analysis whose outputs account for uncertainties and their probabilities. Stochastic is another term with essentially the same meaning. Compare with deterministic.

probability distribution

Also called a probability distribution function or probability function, a graph, formula, or listing that describes the possible outcomes and associated probabilities of a random variable. If the variable is discrete; that is, it can only take on a finite number of possible outcomes, the probability distribution may be referred to as a discrete probability distribution or a probability mass function.

Discrete probability distribution

The discrete probability distribution for rolling a pair of dice

If the variable is continuous and can take on an infinite number of possible values, the probability distribution may be referred to as a continuous probability distribution or probability density function.

Continuous probability distribution

Continuous probability distribution (normal distribution, mean=2, variance=3)

Probability distributions can also be expressed as cumulative probability distributions, which provide the probabilities that each value of the variable is less than or equal to any value on the x axis.

Cumulative probability distributions

Cumulative probability distributions (outcome from a pair of dice and normal distribution)

Probability distributions that describe the simultaneous behavior of multiple random variables are called joint probability distributions.

probability density function

A function (mathematical expression or graph) that defines a probability distribution for a continuous uncertainty (as opposed to a discrete uncertainty). When the probability density function is displayed graphically, the area under the curve within an interval defined by any two values gives the probability of the uncertain variable falling within that interval.

Probability density function

A probability density function

probability encoding

A formal, interview-based process for extracting and quantifying judgments about an uncertainty in the form of a probability distribution. Probability encoding is routinely used within the field of decision analysis to convert the specialized or general knowledge held by experts into probability distributions that represent the judgments of those experts. Although there are variations, most approaches to probability encoding are multi-step and use recognized techniques for reducing errors and bias in judgments. A common approach includes stages or elements designed to motivate, structure, condition, encode, and verify.

probability mass function

A function that defines a probability distribution for a discrete uncertainty. It gives the probability the uncertain outcome will equal each of the possible values for the uncertainty.

Probability density function

A probability mass function

probability wheel

A device for facilitating probability encoding. The original probability wheel developed by the Decision Analysis Group at SRI International (see below) was a spinner for visually generating random events of specified probability. It served as a reference probability for comparing the perceived likelihood of uncertain events. Decision analysis tools and some project portfolio management tools provide virtual probability wheels or similar devices for probability encoding.

Probability wheel

Probability wheel used to facilitate encoding judgmental profiles


A productivity index useful for project prioritization; namely the ratio of the value returned by the project to the cost required to complete the project. Project productivity is the correct measure for prioritizing independent projects so as to identify value-maximizing project portfolios.

productivity index (PI)

Various metrics intended to represent the efficiency of a project, often used for project prioritization. The productivity index (PI) is the ratio of some quantity to be maximized and some quantity that is a constraining resource. For example, a construction company might select the project's "earned value" (as defined, for example, by earned value management) as the numerator for the PI. The denominator might be the number of labor hours needed to complete the project. Thus, a productivity index could be defined as:

PI = Earned value / Person-hours required

The ratio expresses the dollar earnings available from the project per hour of labor required. Projects are ranked according to the productivity index and approved from the top down until the constraining resource (in this case, labor) is exhausted. The approach is intended to maximize the productivity of the selected project portfolio, as defined by the measure used in the numerator, while staying within the constraints for the resource defined by the denominator.

As another example, if R&D budget is the presumed constraining resource, a productivity index might be defined as:

PI = Project NPV / Project R&D costs

A form of the productivity index sometimes proposed for ranking new product-development projects is the development productivity index (DPI), defined as:

DPI = (NPV x Probability of success) / Development cost remaining

This and related approaches that involve assigning probabilities to the achievement of the measure to be maximized may alternatively be described as a probability-adjusted productivity index.

The recommended project ranking metric described in our paper on mathematical methods, project benefit divided by project cost (bang for the buck), is an example of a productivity index. In contrast, note that in the above two examples the cost in the denominator is subtracted within the numerator (since NPV is project value minus project costs). Thus, these PI's do not exactly express benefit-per-unit-of-cost (the ratio typically recommended for ranking projects). However, such a PI effectively expresses a ratio of benefit-to-cost and then subtracts one unit from it, which results in the same priority rankings.

Like other ranking metrics, at best, a PI is an approximation that may, in some cases, reasonably approximate the project portfolio that would be obtained based on constrained optimization (i.e., maximizing the measure in the numerator subject to the constraint represented by the denominator). However, errors are often made in formulating the productivity index, and the approach will not work if there are dependencies that cause a project's productivity index to change depending on what other projects are conducted.

profitability index (PI)

A specific type of productivity index used to measure the financial attractiveness of a project. The profitability index (PI) is normally defined as the ratio of the present value (PV) of the project's projected future cash flows divided its required initial investment:

PI = PV of future cash flows / Initial investment

(If the required investment takes place over several years, the denominator may be replaced by the PV of required investments.) The computed PI's are used to rank projects based on projected financial value created per dollar of required investment.

Since the project net present value (NPV) includes the cash flow deduction for the initial project costs,

PI = [NPV + Initial investment] / Initial investment.

A PI of 1.0 is logically the lowest value for an acceptable project, which would correspond to an NPV = 0. Any value less than one would signal a project with a present value less than its costs.

Like other productivity indexes, the profitability index provides a simple way to rank projects that compete for limited capital. Its weakness is that it ignores project interdependencies. Also, the profitability index fails to account for project benefits other than future cash flows. The profitability index is also sometimes called the profit investment ratio or the value investment ratio.


A suite of related, interdependent projects and related work conducted in a specific order and managed as a whole to produce benefits not available from managing them individually. The table below summarizes the key differences between projects, programs, and project portfolios:

Key differences Projects Programs Portfolios
Definition A temporary endeavor to produce deliverables anticipated to produce benefits A suite of interdependent projects plus related work managed as a whole to produce benefits not available from managing them individually. The collection of projects that, at any specified point in time, an organization is doing or considering doing, managed as a whole as to best advance or protect the objectives of the organization
Example Project to produce an automotive airbag with a lower risk of false deployment Collection of related projects to produce a new model SUV Collection of projects and programs to produce an automotive company's suite of cars, trucks, and SUV's available for the new model year.
Success criteria Quality of project deliverables, timeliness relative to specified schedule, and budget compliance Degree to which the program satisfies the needs and benefits for which it was undertaken; unless all projects within the program are successful, the program will not be as successful as it could be Aggregate value of the projects and programs contained in the portfolio
Schedule Time allocated and/or taken to create the deliverables specified for the project The aggregation of the schedules specified and/or taken to complete the program's project components, which must generally be undertaken in a specified order Ongoing, with project selection and initiation coordinated with the organization's budgeting cycle.
Risk management Identification and mitigation of threats to successful project completion Identification and mitigation of threats to successful program completion Decision making under uncertainty, recognizing that risks create threats and opportunities

program management

The task of managing a program; that is, a suite of related projects. Analogous to project management, the program manager strives to achieve the triple constraints of schedule, cost, and quality, while meeting requirements on deliverables established by customers or sponsors. Typically, the program manager provides overall direction and coordination to teams responsible for the individual projects and serves as a central point of contact for the program's customer or sponsor.


A unique, temporary, often complex, endeavor undertaken by an organization to produce results (project deliverables) that create benefits (e.g., a project to enhance a product or service). Most larger projects have a duration under three years and a life cycle consisting of several phases, for example, concept, development, implementation and, termination. Thinking in terms of discrete project phases tends to facilitate the identification of appropriate project management activities and necessary skills and tools to accomplish each phase.

Projects vary greatly in size and complexity, typically involve activities outside the routine operations of an organization, and often draw on resources from different parts of the organization for the duration of the project. Typically, there are insufficient resources to conduct all desired projects, so projects typically compete for a share of the organization's scarce resources.

project-based organization

An organization that executes much of its business through conducting projects. Project based organizations typically adopt an organizational structure that facilitates the formation and support of project teams, as well as the reassignment of individuals following the completion of projects. As argued throughout this website, project-based organizations can benefit greatly from implementing project portfolio management.

project deferral risk

The risks associated with the decision to defer (delay or decline) doing a project. Maintenance projects commonly involve deferral risks, since postponing maintenance often leads to a deterioration in asset performance and/or greater risk that the asset will fail in some way. Project deferral risk can also arise if there is a limited window of opportunity for successfully conducting a project. More generally, deferral risk occurs if project benefits would decline or project costs would increase if the project were to be conducted (or completed) at a later date. See this risk demo illustrating the importance of accounting for project deferral risk in project portfolio management.

project evaluation criteria

Criteria used to evaluate, prioritize, or select projects. There are many possible arguments for and against conducting projects. As such, it can be helpful to establish and enumerate the criteria that should be systematically addressed when considering a project proposal. The major challenge for using project evaluation criteria is determining how evaluations against each criterion should be mathematically aggregated to obtain a measure of the overall attractiveness of the project.

It is easy to find lists of criteria for evaluating projects. For example:

  • Financial criteria, e.g., profitability, return on investment, impact on cash flows, payback period, size of initial investment required, upside economic potential.
  • Health, safety, environmental criteria, e.g., impact on public health, impact on public safety, impact on worker health, impact on worker safety, air/water emissions, impacts on native plants/animals.
  • Customer criteria, e.g., serving demand, impact on service quality, customer experience, customer acceptance.
  • Marketing criteria, e.g., competitive need, market attractiveness, size of the potential market to be served, likely market share attained, time until market share acquired, product/asset lifecycle duration.
  • Production/operational criteria, e.g., the ease of implementation, fit with available capabilities/resources, degree of understanding of required technology, managerial capability to direct and control, energy requirements, process safety, impact on waste generation, impact on suppliers, impact on IT systems.
  • Work force criteria, e.g., the availability of required labor skills, training requirements, opportunity for learning, level of resistance/acceptance from the current work force, impact on working conditions.
  • Regulatory/legal criteria, e.g., needed to meet standards or requirements, patent and trade secret protection, potential to create legal liabilities.
  • Image/stakeholder relationship criteria, e.g., the reaction of shareholders and other stakeholders, impact on the corporate image.
  • Strategic criteria, e.g., advancement of strategic goals, political significance, contribution to portfolio balance.
  • Risk criteria, e.g., the likelihood of missing schedule, potential for cost overrun, sensitivity to external uncertainties, probability of success.

Project evaluation criteria should be selected to reflect the specific objectives of the organization. Also, they should be expressed in terms of metrics, attributes, and performance measures that are appropriate and familiar to the business. Thus, lists such as the above are best used as starting points for the development of project evaluation criteria that are specifically tailored to the organization and the types of projects to be evaluated.

Many project portfolio management tools allow users to specify project evaluation criteria. The tools use the criteria, typically in a scoring model, to compute an overall measure of project attractiveness, which is then used to rank projects. Scoring models typically weight and add the scores assigned to the various evaluation criteria. However, with criteria similar to the examples in the above list, this would most likely not be correct, and the result would be erroneous project rankings.

If evaluations against multiple criteria are to be combined, it is essential the criteria be defined and structured in such a way as to facilitate the determination of a logical aggregation equation. For example, care must be taken to ensure that criteria do not overlap or double count the same basic benefit. Also, if ratings against the criteria will be weighted and added, the criteria must be defined so as to be preferentially independent, and scaling functions may be needed to account for differences in the value of achieving different levels of performance against criteria. The paper section on Project-Selection Decision Models describes how this may be accomplished based on developing models for measuring project value.

project management

A set of principles and practices for successfully completing projects. A major focus of project management is maintaining project quality while adhering to time, scope, and budget constraints. Typical steps in project management include initiation, planning, executing, controlling, and closing. Project management is typically the responsibility of a project manager who is supported by a project team.

The era of modern project management began in the early 1960's as organizations began to see the benefit of organizing work around projects. The Project Management Institute (PMI) has created "A Guide to the Project Management Body of Knowledge" (PMBOK), which contains well-established standards and guidelines for project management.

In contrast with project portfolio management (PPM), which is aimed at simultaneously managing whole collections of projects, project management is focused on successfully completing individual projects. Loosely speaking, project management is sometimes described as "the collection of processes and practices required to do things right," while PPM emphasizes "the process and practices needed to do the right things."

project-management institute (PMI)

A global nonprofit professional organization for project management with more than half a million members worldwide. Its work includes developing standards, conducting research, hosting conferences, and providing education, training, publications, and accreditation in project management. The PMI is the source of "A Guide to the Project Management Body of Knowledge (PMBOK Guide)", which has been recognized by the American National Standards Institute (ANSI).

project management software

Software intended to support project management, particularly the management of larger or more complex projects. Hundreds of project management software tools are available, and there is much variation in the features and capabilities provided. Most often, the tools provide functionality aimed at day-to-day project planning, scheduling, tracking, monitoring, and change management. Often, the tools include capabilities for organizing resource pools and supporting the development of cost estimates. The tools typically help project teams and stakeholders collaborate and increase transparency through milestones, Gantt charts, budgeting, calendars, timesheets, and progress tracking. The main benefits are cost control, quality management, resource allocation, and reporting.

project manager

Also called project leader, the person with responsibility for leading a project from inception through execution. This includes managing the people, resources, and scope of the project. The project managers primary focus is ensuring the success of a project by minimizing risk throughout the project's lifecycle. The project manager may be considered a professional in the field of project management.

In addition to the traditional responsibilities of a manager (e.g., decision making, planning, and controlling work), the project managers activities include communication (exchanging routine information and processing of paperwork, human resource management (including motivating, disciplining, managing conflict, staffing, and training) and networking (socializing and interacting with those outside the project team.

project network diagram (PND)

Also called a project precedence diagram, a graphic representation of the activities that make up a project and their interdependencies. PNDs can aid project planning, and the capability is provided by many project management tools and by some tools for project portfolio management tools. The diagrams are similar to Gantt and Pert charts but contain more detailed information about project activities.

To construct a PND, necessary project tasks are identified. These tasks may then be further broken down into more detailed activities, as in a work breakdown structure (WBS). Each activity is examined to determine which other activities need to be conducted before it can start (its predecessors). Likewise, other activities that must be delayed until the activity is completed are identified (its successors). Typically, the dependencies include "discretionary dependencies," based on industry best-practice or previous experience, as well as mandatory dependencies inherent in the nature of the work.

The project activities are represented by nodes in the diagram. Each node is typically displayed as a rectangular box containing information about the activity. The boxes are arranged according to activity order; left to right or top to bottom. Arrows are drawn to connect the boxes according to the successor/predecessor relationships

A project network diagram.

A project network diagram

PND software automatically computes the critical path and other project statistics, but you can manually construct the diagrams using paper stickies on a white board. Either way, the resulting diagram illustrates the entire project plan from a high-level view, and you can drill down to obtain more detailed information about each task, including how long it will take, the earliest and latest times it can start and end, and float; the time available to perform the activity less the time needed.

project planning

The process of creating a plan for conducting a project, recognized as a critical, initial step of project management. Like other types of business planning, project planning is aimed at obtaining the greatest benefit from the project while minimizing risk and making the wisest use of available resources.

Key steps in project planning include establishing project goals, defining project deliverables, creating a list of project tasks and a work break down structure (WBS), identifying the people and other resources needed to carry out each task, creating a project schedule, and identifying risks and developing a risk management plan. The amount of effort and detail appropriate to each step depends on the size and complexity of the project. Gantt charts and PERT charts are often used to plan and subsequently report progress with regard to project tasks. Inadequate project planning is often cited as the main reason that high percentages of projects fail.

project portfolio

The collection of projects and perhaps related work, that, at any specified point in time, an organization or element of the organization is doing, is committed to doing, or is considering doing. The projects are grouped together to facilitate effective decision making and management of that work so as to best advance or protect the objectives of the organization. The projects within a portfolio will necessarily share or compete to consume the organization's limited resources.

project portfolio management (PPM)

A formal, tool-supported process for selecting projects and managing project portfolios with the goal of creating the greatest possible value. A project portfolio is a collection of projects (and, perhaps, other work) grouped together to facilitate the effective management of that work.

PPM is similar in some ways to financial portfolio management. The goal of financial investing is to select the best portfolio of available stocks, bonds, and other financial investments. By analogy, the goal of a project-based organization is to invest in the best possible set of projects. In both cases, the "best" portfolio is the one that is expected to return the most value, taking risk into account. Good financial portfolio management requires monitoring investment performance and periodically restructuring the portfolio. Poor-performing investments, for example, may be sold and the proceeds redirected to other investments that are expected to perform better. Similarly, with PPM, projects are monitored and those that are performing below expectations (e.g., because of cost overruns, benefit erosion, or changing needs) may be terminated so that the resources may be directed toward new or other existing projects. In the case of both financial investing and project investing, the key to success is making sound, high-quality decisions, and the best way to achieve that is through a disciplined, well-reasoned, decision-making logic. (Despite the similarities between financial portfolios and project portfolios, be aware that there are some important differences—see the discussion under modern portfolio theory).

The tools available to support PPM vary greatly in their capabilities. However, a common characteristic is that all PPM tools collect and organize into a central database pertinent information about proposed and ongoing projects (data such as project names, objectives, resource needs, timelines, etc.). The tool gives users (typically managers or senior executives) a bird's eye view of projects, making it easier to spot inefficiencies in the project portfolio (for example, redundant projects). Being able to quickly and easily access, review, and compare a large number of projects aids project funding decisions and other key financial and business choices that the organization must make.

Of course, financial portfolio management involves much more than simply putting the information sheets for candidate investments in front of the decision maker. Professional investors rely on sophisticated models to forecast the performance of individual investments. Many also use mathematical optimization techniques to construct investment portfolios that maximize expected risk-adjusted return, accounting for the risk tolerance of the investor.

Likewise, most PPM tools include models for estimating project performance and logic for recommending projects. However, very few PPM tools employ methods as rigorous as those routinely used for financial investing for valuing projects, assessing project and portfolio risk, or optimizing the project portfolio. Instead, many PPM tools use simplistic, unreliable methods for prioritizing projects. For example, one common approach, called strategic alignment, involves ranking projects based on the degree of judged alignment between the project and elements of corporate strategy. Strategic alignment, of course, has little if anything to do with project value or risk. PPM customers should take care to not be misguided by faulty recommendations provided by inadequate PPM tools.

project portfolio management office (PPMO)

Also called the project portfolio management team, one or more people in an organization assigned responsibility for project portfolio management (PPM). Activities include evaluating project proposals, estimating the value of the project to the organization based on the degree to which the project will help the organization obtain its objectives, assessing the risk of obtaining the assessing the risks of not doing the project, and making recommendations to senior management regarding what projects to conduct, recognizing the limitations on available resources. The PPMO is distinct from a project management office (PMO) in that the latter is focused on improving project management performance as it relates to individual projects. See the section of the of the paper on the project portfolio management office for more detail.

project portfolio management (PPM) software

Software for aiding project portfolio management (PPM). In addition to the many custom software applications developed internally by organizations and by consultants to support PPM, there are more than 100 commercially available PPM software products. PPM tools take many different forms, but the common element is an electronic database for storing data on proposed and ongoing projects. Most PPM tools also provide reporting and graphing capabilities that make it easy to view the project portfolio, compare the characteristics of different projects, and roll up project information.

Beyond the basics, PPM tools differ considerably. Some are designed for use by organizations in specific industries, others are general purpose. Many apply only to specific types of projects, for example, IT (information technology) projects. PPM tools differ in their functionality and the degree to which they support project management (e.g., project planning and tracking of project status) and resource assignment (e.g., resource utilization tracking)

PPM tools are available as standalone applications installed on a single computer, applications installed on the organization's client server and allowing simultaneous access to multiple users over a local network or the web, and PPM tools available "on-demand" wherein the service provider hosts the application and makes it available to customers for a per month, per user fee.

Importantly, tools differ significantly in their analytic capabilities, especially the quality of the algorithms (if present) used to assess project benefits, evaluate projects, account for risk, and provide decision-making recommendations. The vast majority of commercially available tools lack the analytics needed to accurately prioritize projects or identify value-maximizing project portfolios.

A list with links to vendors of PPM tools is provided here. There is also a downloadable Aid for Comparing and Evaluating PPM Tools.

project portfolio manager

The manager responsible for the project portfolio. Usually supported by a team. The project portfolio manager typically establishes the rules, and procedures for making portfolio decisions. The portfolio manager analyzes projects and portfolios proposed by other managers and either makes or recommends to more senior decision makers, portfolio decisions.

project portfolio selection

The process, conducted periodically by a project-based organization, of selecting a project portfolio from available project proposals and projects currently underway. The aim of project portfolio selection is to choose the collection of projects that will creaate the most value without exceeding available resources or violating other constraints.

project productivity

The ratio of project value to project cost; in other words, the value produced per dollar of cost. Project productivity is the natural metric for ranking projects.

There are other, related uses of the term, for example, labor productivity (value per hour worked) and earned value per dollar of cost or per labor hour worked.

project proponent

An individual, group or organization that submits or proposes a project for review and can be expected to advocate for the acceptance of the project.

project selection model

A model intended to aid the selection of projects. Assuming the goal is to select project portfolios that create the greatest possible value for the organization given the constraints that exist on resources, a project selection model needs to include a value model (model for computing the value of projects). A project selection model also needs a means to identify value-maximizing portfolios subject to constraints.

On this website, I recommend building a project selection model using the model-building approach known as multi-objective decision analysis (MODA). In many situations, an acceptable, transparent, accurate, and practical approach for obtaining the value-maximizing portfolio of projects is to (1) define projects so as to be independent of one another, (2) use a value model to compute the value of each project, and (3) rank projects by the ratio of value to cost. However, if there are project interdependencies or constraints in addition to the constraint on capital, constrained optimization may be used.

Project selection system.

Components of a project selection model


A multi-criteria analysis method that, like ELECTRE, is based on comparing potential actions while applying different criteria. A so-called outranking method characteristic of the "European school" of multi-criteria methods, PROMETHEE does not require a utility function for quantifying decision-maker preferences. Instead, it ranks options and determines which is most preferred by systematically analyzing the results of the individual comparisons.

PROMETHEE was originally developed in Belgium in the early 1980's and stands for Preference Ranking Organisation METHod for Enrichment Evaluations. Like ELECTRE, it comes in various "versions." The PROMETHEE family of outranking methods includes PROMETHEE I for partial ranking of the alternatives and PROMETHEE II for complete ranking of the alternatives, which were developed and presented for the first time in 1982. A few years later, additional versions of the PROMETHEE methods included PROMETHEE III for ranking based on intervals, PROMETHEE IV for complete or partial ranking of the alternatives when the set of viable solutions is continuous, PROMETHEE V for problems with segmentation constraints, PROMETHEE VI for the "human brain" representation of the decision process.

PROMETHEE has been around for many decades and its ease of use has kept it popular as its iterations have improved. Its applications areas include prioritizing activities in environmental management, hydrology and water management, transportation, manufacturing and assembly, energy management, and agriculture. Several project portfolio management tools advertise that they support the method.

prospect theory

A theory for explaining biases people exhibit when selecting between probabilistic alternatives that involve risk. The theory states that people make decisions based on the potential value of losses and gains without regard to probability distributions and that people evaluate these losses and gains using certain heuristics.

proxy measure

Also called proxy indicator, a measure defined to approximate some difficult-to-quantify characteristic of concern, such as an attribute relevant to evaluating decision alternatives. For example, suppose the concern is the impact of a proposed project on the culture of an Indigenous Tribe of Native Americans. There is no obvious, single metric for measuring cultural impact. However, a possible proxy variable might be the percent of school-aged children who are learning the Tribe’s traditional language. At best, the proxy variable only approximates the attribute of concern, but it is something that might be readily measured or estimated.