Elements of Measurement Design

The Alkire-Foster (AF) methodology is a general framework for measuring multidimensional poverty—an open-source technology that can be freely altered by the user to best match the measure's context and evaluative purpose.

Traditional unidimensional measures require a set of parallel decisions with normative content.^[185] For example, should the variable be expenditure or income? What indicators should comprise the consumption aggregate? How should ‘missing' prices be set? What should the poverty line(s) be? If it reflects a food basket, how many calories should it total, and should it exclude cheap unhealthy foods? Choices to create comparability can likewise be important for final results, such as the construction of Purchasing Power Par­ityvalues or urban-rural adjustments, or adjustments for inflation. Robustness standards are crucial for all poverty measures, as they ensure that the results obtained are not unduly dependent upon the calibration choices (whether these are normatively based or not).^[186]

The flexibility in AF measurement design means that measures at the country or subnational level can be designed to embody reasoned priorities or norms of what it means to be poor. For example, if dimensions, weights, and cutoffs are specified in a legal document such as the Constitution, the identification function might be developed using an axiomatic approach, as was done in Mexico.^[187] Qualitative and participatory work can significantly enrich and substantively complement other analyses.^[188] The weights can also be developed by a range of processes: expert opinion or coherence with a consensus docu­ment such as a national plan, focus groups, survey data, or human rights.

This section introduces the purpose of a poverty measure and the normative choices that inhere in measurement design.^[189] We cover eight design elements. The first five serve to structure a poverty measure; the last three calibrate key parameters (cutoffs and weights).

1. Purpose(s) of the measure: The purpose(s) of a measure may include its policy applications, the reference population, dimensions, and time horizon.

2. The choice of space: The choice of space determines whether poverty is measured in the space of resources, inputs and access to services, outputs, or functionings and capabilities.

3. The unit(s) of identification and analysis: These are unit(s) for which the AF method reflects the joint distribution of disadvantages, identifies who is poor, and analyses poverty.

4. Dimensions: Dimensions are conceptual categories into which indicators may be arranged (and possibly weighted) for intuition and ease of communication.

5. Indicators: Indicators are the building blocks of a measure; they bring into view relevant facets of poverty and constitute the columns of the achievement and deprivation matrices.

6. Deprivation cutoffs: The deprivation cutoff for an indicator shows the minimum achievement level or category required to be considered non-deprived in that indicator.

7. Weights: The weight or deprivation value affixed to each indicator reflects the value that a deprivation in that indicator has for poverty, relative to deprivations in the other indicators.

8. Poverty cutoff: The poverty cutoff shows what combined share of weighted depriva­tions is sufficient to identify a person as poor.

In practice, these design choices are not made in a linear fashion but rather iteratively, and in combination with consultations and empirical work.

6.3.1 Purpose(S)Ofameasure

The purpose(s) of a measure clarify the way(s) in which the measure will be used to describe and understand situations, to make comparisons across groups or across time, and to guide policy or monitor progress. The purpose shapes the choice of space and many of the calibration decisions that will follow and so should be explicitly formulated and stated. The Stiglitz-Sen-Fitoussi Commission drew attention, in the case of quality of life measures, to the fundamental importance of the purpose of the measure to the identification of dimensions and indicators. ‘The range of objective features to be considered in any assessment..will depend on the purpose of the exercise...the question of which elements should belong to a list of objective features inevitably depends on value judgements (2009).

The purpose may also identify constraints and shape processes. For example, if the purpose includes legitimacy to the wider public, then public consultations may be essential; if it is performance monitoring, involvement with the concerned agencies and institutions may be useful. While a measure may have a single purpose, it is more common for measures to seek to fulfil multiple purposes.

For example, a national poverty measure might aim to assess the population-wide levels and trends in capability poverty across regions and population groups in ways that are regarded as legitimate and accurate by the citizenry. Note that this statement of purpose has scope (population-wide), space (capability), relevant comparisons (across population groups and time trends), and popular legitimacy (which affects procedures).

The purpose of the measure will often also include political economy and institutional issues and constraints that are pertinent to the measure fulfilling its purpose, such as timescale, data, budgetary resources, political and legal procedures, updating procedures, and so on.^[190] For example, will a given dataset be used or will a new survey be designed and implemented and if so what is its budget and frequency? Are particular committees, commissions, or institutional processes to be involved in measurement design and what is their authority? If a measure will be updated over time, what is its legal or institutional basis, which institution(s) or person(s) have the authority to update the measure, and when and how is occasional methodological updating to take place? Clarity on such issues during measurement design can greatly streamline design procedures.

6.3.2 Choiceofspace

As mentioned in section 6.1 another preliminary choice is the space in which measure­ment is to proceed. Will it be in the space of income, of resources and access to resources, of functionings and capabilities, or of subjective utility? There are well-known arguments in favour of each space, and purposes for which each space might be appropriate.

Following Sen, we may take the space that is of central interest to be the space of functionings and capabilities (they are the same space). Functionings are the beings and doings that people value and have reason to value, and capabilities are the freedoms to achieve valuable functionings. This implies that measurement should focus on valuable activities and states of being that people can actually achieve, given their values and their varying abilities to convert resources into functionings. The choice of space may have implications for the interpretation of variables' scales of measurement. In some cases, for example, capability measures use indicators that reflect achievements in other spaces (or subjective and self-reported states), if these can be justified empirically as proxies of functionings or capabilities.

An essential step at this stage is to revisit the scales of measurement introduced in section 2.3. To summarize, any achievement matrix may contain data having categorical, ordinal, or cardinal scales (which may be binary, interval, or ratio scale). In measures requiring cardinal data, the indicator's scale of measurement has to be reassessed after the space of measurement has been chosen. For example, years of schooling may seem to be a ratio-scale variable. But in terms of human functionings, is it? Or do the earlier years of education confer marginally more capabilities than later years, or the completion of the twelfth year (with a diploma) more than the eleventh year (without a diploma)? In using M₀, we dichotomize variables at a deprivation cutoff. This obviates the need to rescale indicators to construct an appropriate normalized gap in different spaces, but still requires that the deprivation cutoffs (discussed in section 6.3.6) reflect deprivations in the chosen space.

Not all measures focus on the capability space—or need to. They might reflect social rights, social exclusion, access to services, social protection, or the quality of services. And most poverty reduction requires, as intermediary steps, institutions that effectively deliver resources and services to people and communities. Thus, even if the goal is capability expansion, this might be stimulated or monitored in part by a multidimensional poverty measure that is framed in an intermediary space of inputs or outputs. The choice of space specifies how a given measure will advance the purpose.

6.3.3 UNITS OF IDENTIFICATION AND ANALYSIS

The unit(s) of identification or of analysis^[191] may be a person, a household, a geographic area, or an institution (such as a school or firm or clinic). A common unit of identification for a poverty measure is a person (any adult, a child, a worker, a woman, an elderly person). This permits a poverty measure to be decomposed by variables like gender, age, ethnicity, occupation, and other relevant individual characteristics. It may also permit analysis of intra-household patterns of poverty or of group-specific poverty (indigenous groups, youth unemployed, urban slums). Alternatively, household members' information may be considered together, which has advantages in terms of supporting intra-household sharing and getting an overview of households. In this case, household members' combined achievements are used as a unit of identification for a population-wide measure, and all household members receive the same deprivation score.

The unit of analysis—meaning how the results are reported and analysed—may still reflect each person. That is, even if the unit of identification is the household, one can report the percentage of people who are identified as poor (by using individual sampling weights), rather than the percentage of households that are identified as poor (which is used if the household is the unit of analysis).

Where data are not available at the household level or where the measure focuses on topics such as infrastructure, poverty can be computed for data zones or geographic areas, so long as there is a justification for overlooking within-region inequality. Other measures may use a particular institution such as a school or clinic or firm as a unit of identification and/or analysis.

What is essential is that data for all variables must be available for (or transformed to represent) each unit of identification (see also Chapter 7), that the definition of applicable populations be transparent and complete, and that the unit of analysis be explicitly and clearly stated and justified.

There are ethical considerations in choosing and justifying a unit of analysis. For example, using the person as the unit of identification coheres with human rights policies, can show gendered or age disparities, and may permit intra-household analysis (Alkire, Meinzen-Dick, et al. 2013). Yet using the household as a unit of identification acknowledges intra-household caring and sharing—for example, educated household members reading for each other and multiple household members being affected by someone's severe health conditions. Policies targeting or addressing the household may also strengthen or at least not weaken the household unit. Normative and policy assessments may be supplemented by participatory insights regarding the appropriate unit of identification and the ensuing focus of policy interventions.

The justification of a unit of identification may include empirical assessments of bias and comparability. For example, if the unit of identification is the household, then indicators that draw on individual-level achievements may be checked for biases according to household size and composition (Alkire and Santos 2014). If the unit of identification is the person, then the comparability of indicators across diverse groups requires analysis—as in the case of education and health indicators for people of different ages (infants and toddlers, school-aged children, adults, and the elderly). The scale of errors that could be introduced if household-level variables are presumed to be equally shared by all household members is a further fruitful topic of empirical scrutiny.

For some policy purposes it could be useful to construct a set of measures, in which each measure takes a nested unit of identification that includes or is included by related measures: for example, the person, the household, the village or neighbourhood, and the district. The nested measures permit further analysis of the interactions between deprivations at different levels. For example, the individual-level data may have health and educational functionings, household data may have living standard and housing-related functionings, and village-level data may have environmental, in­frastructure, and service delivery information. Analyses may explore the extent to which health- and education-deprived people live in living-standard-deprived households, for example, and whether these live in services-deprived villages. Alternatively one may study which poor children live in poor households. Analyses using nested measures can be compared to analyses of a multidimensional poverty index at the individual level that applies relevant household- and village-level deprivations to each individual.

In sum, although often data constraints will require that the household be the unit of identification, when other options are feasible, then this choice can be considered, made, and justified using different kinds of reasoning to assess the ‘fit' between the proposed measure and its purpose.

6.3.4 DIMENSIONS

When these structural choices have been established, poverty measures require the selection and valuation of deprivations. Sen introduces the task as follows: ‘In an evaluative exercise, two distinct questions have to be clearly distinguished: (1) What are the objects of value? (2) Howvaluable are the respective objects?' (Sen 1992: 42). These two tasks of selecting focal deprivations (using dimensions, indicators, and cutoffs), and setting relative values for them, recur in poverty measurement.

The term ‘dimensions' in this chapter refers to conceptual categorizations of indicators for ease of communication and interpretation of results. By ‘indicators' we mean the d variables that appear in columns of the achievement and deprivation matrices and are used to construct the deprivation scores and to measure poverty.

A multidimensional poverty measure is constructed using indicators. In some cases, these indicators may each represent distinct facets of poverty. In other cases, it may be useful to talk about several indicators as forming a ‘dimension' of poverty. Why use dimensions? Dimensions may reflect the categories defined by some deliberative or synthetic processes. For example, a dimension might be children's education; indicators might include a child's years of completed schooling and their achievement scores last period. In this case the indicators may be the best possible approximation of those dimensions from an existing dataset. It may also arise from a theory or policy source. Noll (2002) develops a systematic conceptual framework for social indicators in Europe by reviewing concepts of welfare and common policy goals, then identifying fourteen dimensions that fit the measurement's purposes. Grouping indicators into dimensions may facilitate the communication of results because there are likely to be fewer dimensions than indicators and they are likely to be intuitive and accessible to non-experts.

Grusky and Kanbur argue that the selection of dimensions merits active attention because ‘economists have not reached consensus on the dimensions that matter, nor even on how they might decide what matters' (2006: 12). Yet the extensive and historic discussions about the post-2015 development agenda have been tremendously useful in illuminating areas of agreement across different interest groups with respect to widely varying national and international considerations.

Unusually, the selection of dimensions does not necessarily rely on empirical or technical analysis. Naturally, sometimes analysts explore or confirm the extent to which dimensional grouping of indicators is corroborated statistically. Such statistical explorations should not determine the selection of dimensions or grouping of indicators; they may, however, contribute to their justification and expose interesting relationships that should be considered.

In addition to the inevitable consideration of data constraints, there are at least three overlapping kinds of information that may inform the selection of dimensions: deliberation and public reasoning, legitimate consensus, and theoretical arguments (Alkire 2008a).

The first approach is a repeated deliberative or participatory exercise, which engages a representative group of participants as reflective agents in making the value judgements to select focal capabilities. Deliberation may involve online assessments as well as face-to-face focus groups; it may also consolidate the body of recent and similar participatory work that has been undertaken for other purposes. In a supportive, well-informed, and equitable environment, participatory processes seem to be ideal for choosing dimensions, but not, however, if deliberation is dominated by conflict or inequality or misinformation, or coloured by the absence or dominance of certain groups. Furthermore, the process of aggregating the values of a diverse assembly of groups and people, whose deliberative processes may vary in quality, is neither elementary nor void of controversy (indeed it is an appropriate topic for further research). Even if a new set of deliberative exercises is not possible, it may be possible to consider documentation of previous such processes, be it from a previous measurement consultation, participatory exercises, a widely debated national plan, high-profile legal documents, the media, or a respectable set of life histories of disadvantaged people and communities (Leavy and Howard et al. 2013; Narayan et al. 2000). So it may be rare for a set of dimensions to be justified without any reference to participatory studies and public debates.

In writing on the selection of capabilities—which relate to dimensions and indicat­ors^[192]—Sen calls for deliberative engagement rather than using a pre-ordained list. ‘I have nothing against the listing of capabilities,' Sen writes, ‘but must stand up against a grand mausoleum to one fixed and final list of capabilities' (2004: 80). A central reason against promulgating a fixed list is that to be relevant, the dimensions (and indicators) should reflect the purpose of the measure. ‘What we focus on cannot be independent of what we are doing and why' (Sen 2004: 79). The deprivations in international measures will rightly differ from a national measure or a measure of child poverty or of an indigenous community, for example. A further motivation for not fixing a list of capabilities even for a given purpose—including poverty measurement—is that a fixed list would crowd out debate and public reasoning, which can play an educational and motivational role. It also would not catalyse constructive debate that may influence people's values. ‘To insist on a fixed forever list of capabilities would...go against the productive role of public discussion, social agitation, and open debates' (Sen 2004: 80). Also, as technology advances and social values change, the list might become outdated (Sen 2004: 78). For example, recent approaches to poverty often incorporate environmental and energy considerations that were lacking previously.

A second approach to the selection of dimensions is the use of an authoritative document or list that has attracted a kind of enduring consensus and associated legitimacy. Examples include a constitution, a national development plan, a declaration of human rights, or some time-bound international agreements such as the MDGs. Most official multidimensional poverty measures have some transparent link to such a policy process or document. The use of a set of dimensions that already have a kind of visibility and legitimacy is useful for international or global measures (where public deliberation is difficult), as well as for those that are clearly designed to monitor policy processes. It also naturally connects measurement to policy management.

A third potential source of dimensions is a conceptual framework or particular theory—which may range from Maslow's hierarchy of human needs to a religious framework such as the Maqasid A-Sharia, to lists like Martha Nussbaum's set of central human capabilities. These approaches are particularly relevant for communities where the theory enjoys widespread approval and/or is consistent with lists generated by alternative theories or processes (Alkire 2008a).

Comparing the lists that groups generate by these and additional processes, one finds a striking degree of commonality between them. Table 6.1 lists dimensions generated by these processes that pertain to multidimensional poverty measurement. Indeed there are a plethora of similar resources for the selection of deprivations, which may contribute towards standards supporting multidimensional poverty measurement design. And whilst the particular names and grouping of indicators differ, the universe of options is not too great, and this fact itself may be of no little comfort to those designing multidimensional poverty measures.

sections. See Alkire (2002a, 2002b), Nussbaum (2003), Robeyns (2003,2005), Sen (2004), Burchardt (2013), and Burchardt and Vizard (2007, 2011).

Table 6.1 Dimensions of poverty

* Narayan et al. (2000)

** United Nations Development Group (UNDG) (2013)

It should be borne in mind that the selection of dimensions and indicators affects the selection of weights. In a book supporting the development of national poverty plans in Europe, Tony Atkinson and colleagues point out the convenience of keeping weights in mind when selecting dimensions and indicators. In particular, they commend choosing indicators (or, possibly, dimensions) such that their weights are roughly equal to facilitate policy interpretations: ‘the interpretation of the set of indicators is greatly eased where the individual components have degrees of importance that, while not necessarily exactly equal, are not grossly different' (Atkinson et al. 2002). Sen also emphasizes the interconnection between these choices: ‘There is no escape from the problem of evaluation in selecting a class of functionings in the description and appraisal of capabilities, and this selection problem is, in fact, one part of the general task of the choice of weights in making normative evaluation' (Sen 2008). Elsewhere we observed that this linkage holds not only for dimensions that are selected but also for those that are omitted: ‘choosing one out of several possible variables is tantamount to assigning that dimension full weight and the remaining dimensions zero weight' (Alkire and Foster 2011b). And it is to the selection of indicators that we now turn.

6.3.5 INDICATORS

Indicators are the backbone of measurement. Their quality, accuracy, and reach determine the informational content of a poverty measure. Given data constraints, the process through which these are selected may include participatory and deliberative exercises, legal or political documents, statistical explorations, robustness tests, or theoretical guidelines.

While a considerable amount of attention, discussion, and practice has focused on the normative selection of dimensions of poverty and well-being, there is a paucity of comparable normative literature on the selection of indicators. The literature on indicator selection is, however, richly arrayed with a plethora of empirical considerations, which must be considered alongside normative and policy issues. Some of these will be raised in Chapter 7. These include:

• statistical techniques to assess aspects such as the reliability, validity, robustness, and standard errors of economic and social indicators;^[193]

• indicators' comparability across time and for different population subgroups;

• dataset-specific issues such as data quality, sample design, seasonality, and missing values;

• the justification of indicators as proxies for a hard-to-measure variable of interest.

Such analysis of each component indicator is fundamentally important for building rigorous measures, and, while these are not covered here, we presume readers will learn relevant techniques and consider how best to apply them.

Alongside these, numerous guidelines seek to match indicator selection with policy purposes (IISD 2009; Maggino and Zumbo 2012). For example, Atkinson and Marlier (2010: 8-14) provide an insightful overview of the purposes for which appropriate indicators should be stock or flow, subjective or objective, relative or absolute, static or dynamic, input or output or outcome, and so on. When statistics are used by the public, issues such as ease of interpretation also affect the choice. Still, as we saw in Chapter 4, the literatures on existing practices of addressing these technical, policy, and practical concerns are dispersed.

Naturally, the cost of data collection, cleaning, and preparing an indicator are also likely to influence indicator selection, especially when new surveys are fielded or regular updates are anticipated. This is a very important and underdocumented consideration, given the need both for better and more frequent data, and for timely, thorough analysis of new data (Alkire 2014).

The selection of indicators should be transparently justified—as many counting measures are. The criteria for selection will vary, however. For example, Atkinson and Marlier (2010: 45) outline five criteria for internationally comparable indicators of deprivation in social inclusion:

1. An indicator should identify the essence of the problem and have an agreed normative interpretation.

2. An indicator should be robust and statistically validated.

3. An indicator should be interpretable in an international context.

4. An indicator should reflect the direction of change and be susceptible to revision as improved methods become available.

5. The measurement of an indicator should not impose too large a burden on countries, on enterprises, or on citizens.

As the field of multidimensional poverty advances, we anticipate that conventions and standards will be further developed to facilitate the selection of indicators and the calibration of parameters described in the following sections, much as has been done for monetary poverty.^[194] These will reduce although not eliminate the value judgements in measurement design. In the case of monetary poverty, conventions did not make the creation of a consumption aggregate mechanical, imputation of housing costs easy, or the comparison of rural and urban monetary poverty lines uncontroversial. There remain animated debates, such as whether to include popular sugary drinks in the food poverty basket or elite goods in the consumer price index. Yet conventions still serve to streamline and legitimize key choices during the design process and reflect an ongoing and evolving technical consensus (or partial consensus) regarding sound measurement principles.

6.3.6 DEPRIVATION CUTOFFS

Deprivation cutoffs are fundamentally normative standards. They define a minimum level of achievement, below which a person is deprived in each indicator or subindex.^[195] As we saw in Chapter 2, the deprivation cutoffs, together with the deprivation values, create cardinal comparability across indicators for M₀ measures and may be interpreted as creating a ‘natural zero’. Deprivation cutoffs for each indicator are a distinguishing feature of multidimensional poverty measures that reflect the joint distribution of deprivations (Bourguignon and Chakravarty 2003). This is because, by the property of deprivation focus, having more than the deprivation cutoff achievement level in one dimension—for example, clean water—does not ‘erase’ the deprivation in another dimension (like malnutrition). This coheres with a human rights approach, among others.

Deprivation cutoffs may be justified with reference to international or national standards.^[196] They may be set to reflect ‘basic minima’ or ‘aspirations’ that have arisen in participatory, consultative, or deliberative exercises. They might reflect the ‘targets’ of national development plans or of some international agreement or legal guidelines—for example, on compulsory schooling and social protection—or a social contract or, in some cases, medical standards (e.g. for anaemia, micronutrients, stunting, wasting, and so on).

Note that in indicators that use the household as the unit of identification, deprivation cutoffs must be defined such that they combine individual-level data when it is available for multiple household members. For example, if the household is the unit of identification, a deprivation cutoff for an educational variable may consider data for some or all household members. This can be done in many ways. Alternative deprivation cutoffs for the variable ‘years of schooling among adults aged 15 and above’ could be: if any household member has achieved a certain level, if any adult lacks a given level, if the women of the household reach a certain level, if a certain proportion of adults achieve that level, if (all or some) household members have levels that were appropriate when they were of school-going age, or if the educational achievements for at least one male and at least one female (or some other combination) each meet a certain standard. Empirical implementation and analysis of several definitions can be useful to understand the patterns of educational deprivations within households—and their accuracy, for example, given the gender composition of households.

In other cases, deprivation cutoffs are set across subindices, such as defining housing deprivations if a person has substandard housing construction in terms of any two of: roof, flooring, walls. Again each subindex design requires independent and careful validation, which this chapter does not cover.

Having fixed one set of deprivation cutoffs, a second vector of cutoffs may be constructed in which at least one indicator reflects more (less) extreme deprivation. This second vector can be implemented across the same indicators, weights, and poverty cutoff as previously to identify a subset of the poor who are in more (less) extreme poverty according to these more (less) exacting standards.^[197]

In practice, it is common in multidimensional poverty design to construct indicators and candidate multidimensional poverty measures using various cutoff vectors, in order to assess the sensitivity of measures to a change in deprivation cutoffs, and also, in the case of uncertainty about which cutoff to choose, to clarify the implications of a choice to policy users. For example, Alkire and Santos (2010, 2014) implemented cutoffs such as ‘stunting', ‘piped water into the dwelling', or ‘flush toilet' to understand whether country rankings changed dramatically if these standards were used instead of the chosen MDG cutoffs.

The selection of deprivation cutoffs enables the computation of uncensored headcount ratios for all indicators. Reasoned consideration of these ratios is quite important for cross-checking indicator selection and for weighting. For example, if the uncensored headcount ratio for an indicator is much lower than other indicators, that indicator will be unlikely to influence the measure; however, if changes in this indicator would be quite precise and if its normative importance is high, a large weight can be attributed to it, returning it to prominence. Also, suppose the indicators have been selected, following Atkinson et al. (2002), such that their importance and hence weights are ‘roughly equal'. If deprivation rates across indicators are exceedingly variable, then equal weights across indicators will produce a measure that is dominated by the indicators having the highest censored headcount ratios. We might do well to remind readers of the need to consider design issues iteratively rather than sequentially in practice.

6.3.7 values Andweights

Another key component of normative choices is the relative weight placed on dimen­sional deprivations. In multidimensional poverty measures, weights could be applied (i) to each indicator (thus determining the relative importance of each indicator to the other as interpreted from the ratio of the weights); (ii) within an indicator (if a subindex such as an asset index or housing index is constructed); and (iii) among people in the distribution, for example to give greater priority to the most disadvantaged. This section focuses solely on the first of these.

As people are diverse and our values differ both from each other and from ourselves at different points in time, the relative values that people place on different indicators of disadvantage vary.^[198] This is no catastrophe. Sen observes, ‘It can, of course, be the case that the agreement that emerges on the weights to be used may be far from total', but continues, ‘we shall then have some good reason to use ranges of weights on which we may find some agreement. This need not fatally disrupt evaluation of injustice or the making of public policy... A broad range of not fully congruent weights could yield rather similar principal guidelines' (2009: 243). Thus, as Chapter 8 suggests, robustness tests should be undertaken to assess whether the main policy prescriptions are robust to a range of weights or to show their sensitivity to alternative weighting structures.

The weights applied in the M₀ measure differ radically from weights in ‘composite' indicators and are, for that reason, easier to set and to assess normatively. Critics of M₀ at times overlook the dramatic simplicity of M₀ weights in comparison with composite measures or multidimensional poverty measures that require cardinal data, so we begin by clarifying this important distinction.

Weights in composite measures are applied to quantities (achievement levels), and the marginal rates of substitution across indicators are usually assumed to be meaningful at all achievement levels.^[199] We elsewhere clarified that, unlike M₀, composite indices, including the Human Development Index (HDI), require ‘strong implicit assumptions on the cardinality and commensurability of the three dimensions of human development. The key implication is that after appropriate transformations, all variables are measured using a ratio scale in such a way that levels are comparable across dimensions' (Alkire and Foster 2010). This is rather stringent. To take a very straightforward case, in the original arithmetic HDI the weights govern the effect that an improvement in one dimension has on the overall HDI. The weights must accurately reflect the value of such a change, whether the increment occurs at the highest or the lowest level of achievement in that dimension. That is, changes from each starting level must be able to be justified separately and independently. Weights also govern trade-offs across all variables for every increment of each variable. That is, the trade-off between an increment in variable A from any starting achievement level and corresponding increments in variables B and C would need to be justified—whatever the starting level those variables take (Ravallion 2012). Weights are thus used to compare changes in the same indicator at any level of achievement and trade-offs across variables. We might refer to them as ‘precision weights’.

Precision weights are also used in multidimensional poverty methodologies that require cardinal (normally ratio-scale) data, such as those proposed by Chakravarty, Mukherjee, and Ranade (1998), Tsui (2002), Bourguignon and Chakravarty (2003), Maasoumi and Lugo (2008), and Chakravarty and DAmbrosio (2013), among others. Ratio-scale data are also required for M_α measures when a > 0. In M_α measures when a > 0, the deprivation cutoff creates a ‘natural zero’ and the normalized gaps for each indicator are understood to be cardinally meaningful. In this situation, in a manner similar to composite indices, the weights govern the impact that each increment or decrement in a deprived indicator has on poverty. Also similar to composite indices, weights govern trade-offs across all variables at all deprived levels of every variable.

In M0 and other dichotomous counting approaches, weights are almost completely different. We may refer to them as deprivation values to mark this difference verbally. They are applied to the 0-1 deprivation status entry. Their function is to reflect the relative impact that the presence or absence of a deprivation has on the person’s deprivation score and thus on identification and, for poor people, on poverty. Correspondingly, the weights affect how much impact the removal of a particular deprivation has on M₀. Thus, they create comparability across dichotomized indicators (see section 2.4). But because deprivation values are applied to dichotomous 0-1 variables, they need not calibrate different levels of deprivations in a single variable. Further, because all indicators are dichotomous, the only possible trade-offs across deprivations (presence or absence) take the value of the relative weights. Put differently, because M₀ uses dichotomized deprivations rather than normalized gaps, deprivation values are not required to govern trade-offs across different levels of achievement in different variables as they are in the measures requiring precision weights. They only reflect the presence or absence of a deprivation. This greatly simplifies their selection and justification, and is worth noting clearly as the distinction between precision weights and deprivation values is often overlooked.

Due to an appreciation of democratic debate, and to permit values to evolve, as in the selection of capabilities, Sen does not commend any fixed-and-forever vector of weights: ‘The connection between public reasoning and the choice and weighting of capabilities in social assessment...also points to the absurdity of the argument that is sometimes presented, which claims that the capability approach would be usable—and “operational”—only if it comes with a set of “given” weights on the distinct functionings in some fixed list of relevant capabilities’. In contrast, Sen advocates occasional public discussion for similar reasons to those given in the selection of dimensions: ‘The search for given, pre-determined weights is not only conceptually ungrounded, but it also overlooks the fact that the valuations and weights to be used may reasonably be influenced by our own continued scrutiny and by the reach of public discussion. It would be hard to accommodate this understanding with inflexible use of some pre-determined weights in a non-contingent form' (2009: 242-3). In practice, for measures used to compute changes over time, it can be useful to fix the weights and other parameters for a given time period, such as a decade, and update them thereafter.

The selection of deprivation values also reflects the purpose of the exercise. For example, if the purpose is to evaluate changes in poverty, weights might reflect the fundamental importance people place on each indicator, whereas if the purpose is to monitor progress in the short or medium term, the relative weights might partly depict the relative priority of reductions in indicator deprivations. For example, if a region has very high levels of educational achievements but deeply rutted roads, then a long-term poverty measure may give a higher weight to education because of its importance and value. But a measure used for participatory planning may give higher priority weights to roads because of the pressing need for progress in this area.

The potential value of public discussion does not mean that weights must be created by participatory processes—although Sen would suggest that they be made transparent in order to catalyse such discussion. Weights may also be corroborated or justified using expert opinion; analyses of survey data, such as perceived necessities (see Chapter 4); subjective evaluations; or the input of policymakers and relevant authorities. They may reflect values implicit in a legal document or national plan, or use some socially accepted value structure that has been applied in poverty measurement or similar exercises previously.

The justification of weights is explored extensively both theoretically and practically by Wolff and De-Shalit, who reach the conclusion that, ‘...even though disadvantage is plural, indexing disadvantages is possible, despite various theoretical and practical problems.(2007:181). Their proposal is to use multiple methods and create measures whose key policy proposals are robust to them. Let us unpack this. In terms of setting weights, for example, they (like Sen) point out the need for a democratic procedure, but also recognize ‘that individual valuations might be liable to distortion, false consciousness, or the result of limited experience and thus ignorance of the real nature of various alternatives’. Hence they justify including additional inputs. ‘Keeping both sides in play is sensitive to the fact that legitimacy in a democracy builds out of people’s voices’ while at the same time recognizing potential weaknesses of participatory processes (2007: 99).

In the end, Wollf and De-Shalit commend the creation of orderings that are robust to a range of plausible weights: ‘A social ordering is weighting sensitive to the degree that it changes with different weighting assignments to different categories. A social ordering, therefore, is weighting insensitive—robust—to the degree it does not change with different weighting assignments to the different categories’ (2007: 101-2).

So, first of all, the deprivation values that are used to create ‘relative weights' across 0-1 deprivations are fundamentally straightforward, which simplifies matters. But there are plural ways to make and justify weights, which seems to reconstitute complexity. Happily, in fact, the plurality of potentially justifiable weights means that weights can be justified and cross-checked against different sources. Technically, given the legitimate pluralism in values, it would be desirable to implement a poverty measure with a range of weighting vectors and to release measures whose relevant policy implications were robust (Chapter 8 and Alkire and Santos 2014).

6.3.8 POVERTY CUTOFF k

The cross-dimensional poverty cutoff k identifies each person as poor or non-poor according to the extent of deprivations they experience, which are summarized in their deprivation score. It establishes the minimum eligibility criteria for poverty in terms of the breadth of deprivation. Normatively it reflects a judgement regarding the maximally acceptable set of deprivations a person may experience and not be considered poor. Thus the value of k can only be justified after fully articulating the parameters described previously.

Like the income poverty line, the final choice of k in most cases should be a normative one, with k describing the minimum deprivation score associated with people who are considered poor and consider themselves to be poor (Sen 1980). For multidimensional measures the normative content could come from participatory processes in which poor people articulate the conditions and combinations of deprivations that constitute poverty. They may be informed by subjective poverty assessments and qualitative studies.^[200] As noted by Tsui, ‘In the final analysis, how reasonable the identification rule is depends, inter alia, on the attributes included and how imperative these attributes are to leading a meaningful life' (2002: 74). If, for example, deprivation in each dimension meant a terrible human rights abuse and data were highly reliable, then k could be set at the minimal union level to reflect the fact that human rights are each essential, have equal status, and cannot be positioned in a hierarchical order.

In some circumstances, the value of k could be chosen to reflect priorities and policy goals.^[201] For example, if a subset of dimensions were essential while the rest may be replaced with one another, the weights and k could be set accordingly. For example, suppose d = 4, and w₁ = 2, and w₂...w₄ = 2/3. A cutoff of k = 2 would then identify as poor anyone who is either deprived in dimension 1 or in all the remaining dimensions, while a slightly higher value of k would require deprivation in the first dimension and in one other.^[202] Alternatively, one could select a k cutoff whose resulting headcount identified the poorest segment of the population that the budgetary resources could address. Thus, the weights and poverty cutoff allow for a range of identification constellations.

To justify and communicate the poverty cutoff, the relative values of deprivations (or possibly dimensions) should be explicitly considered. While technically the poverty cutoff can be set at any level, in practice a range of poverty cutoff values may identify the same group as poor. For example, if there are five equally weighted indicators, then a poverty cutoff of 21% will identify the same set of persons to be poor as a cutoff of 25%, 33%, or 40%. Given these weights, any person who has at least two deprivations will be identified as poor by any poverty cutoff taking the value 20 < k < 40%. Yet if communication is a priority, then a poverty cutoff value of 40% might be chosen, as it most intuitively conveys the fact that poor people are deprived in at least two out of the five (2/5) deprivations. When deprivations take different weights, of course, the distribution may be smoother, but communicating the poverty cutoff in terms of indicators or dimensions may remain relevant.

No matter which technique is finally employed in selecting the parameter k, as in the case of income poverty lines, it should be routine to construct the poverty measure for a range of poverty cutoffs, to publish robustness results for alternative poverty cutoffs, and/or to explore dominance tests across relevant values of k. Techniques for doing so are set out in Chapter 8.

6.4