Algorithmic group formation has become a flourishing research area in the computer sciences, and more recently in the field of data mining and fair machine learning. Application domains for algorithmic solutions to grouping span wide, from team-recommendation and formation in work settings to abilitygrouping in education. Recent work has also focused on fairness in groupformation. We briefly review literature on algorithmic team-formation and consider fairness in different group-formation contexts. We articulate different dimensions and constraints that are relevant for fair group-formation and discuss the tension between utility and fairness. Many problems and limitations regarding formal definitions of fairness explicated in the fair machine learning literature apply also in the context of group-formation. We suggest some limits to the relevance of fairness in general and algorithmic fairness, in particular. We argue that algorithmic fairness is less relevant to some groups because of the way they come to existence or because fairness is not a central value for them. Other central values are subjective rights; autonomy or liberty; legitimacy and authority; solidarity; and diversity, each of which can be in tension with optimal fairnessand-utility. But within acceptable limits, we argue that fairness is indeed a valuable goal that may be in tension with maximization of the relevant types of utility.
Algorithmic group formation has become a flourishing research area in the computer
sciences, and more recently in the field of data mining and fair machine learning (ML).
Application domains for algorithmic solutions to grouping span wide, from
teamrecommendation and formation in work settings
In Section Two we briefly review literature on algorithmic team-formation and consider fairness in different group-formation contexts. We articulate dimensions and constraints relevant for fair algorithmic group-formation and discuss the tension between utility and fairness. We consider different metrics for fairness and argue that many of the problems and limitations regarding the formal definitions of fairness explicated in the fair ML literature apply also in the context of group-formation.
In Section Three we discuss key concepts and ideas from political philosophy
relevant for fairness in algorithmic group-formation, and also introduce novel
viewpoints to algorithmic group-formation alongside considerations of fairness and
utility. Recent research has drawn lessons from political philosophy concerning fairness
The Team Formation Problem was first formulated in
Fairness in group-formation and team-recommendation systems has also gained
increasing interest
Decision-making is always constrained by external affordances, circumstances and contextual factors. Group-formation does not differ in this regard, in that approaches to group-formation are defined and constrained by the nuanced goals, resources and affordances, as well as limitations of context, in addition to possible ethical and legal considerations. We will next explicate some dimensions and constraints of groupformation. They include, but are not limited to the following: (i) number of tasks/projects/activities/roles to be distributed, (ii) amount of individuals to be grouped, (iii) desired amount of groups, (iv) team-composition and role flexibility (e.g., whether an individual can have several roles, perhaps in several teams); (v) appropriate criteria of inclusion or criteria according to which membership is distributed, (vi) costs and benefits, and (vii) group-level properties, such as diversity, that ought to be exhibited by some or all groups that are formed.
First, a team formation task involves one or more (sets of) objectives, tasks, resources, activities, etc., to be assigned. Sometimes there is one task, such as a single case in a law firm to be assigned to a legal team. In other situations, there may be numerous assignments or projects, e.g., different essay topics on a philosophy course.
Second, the number of individuals to be grouped, or from which a subset of individuals is to be assigned to a single task, may vary (e.g., size of overall personnel, department sizes, course attendees).
Third, there may be a constraint as to how many groups can (or should) be formed. This will usually, but not necessarily, depend on the number of tasks or projects available as well contextual affordances. In certain contexts, there may be an optimal or desirable number of groups (e.g., number of groups in child day-care) due to resource constraints (e.g., personnel and facility affordances). This may be more or less flexible, however (e.g., there is no principled constraint on how many learners can be grouped for a certain project in a philosophy class).
Fourth, depending on the situation, individuals may be grouped into only one group at a time or they may belong to several groups simultaneously. For example, in some cases, it might be required that workers split their time between different projects, and in others, workers may be assigned to only one group/task at a time.
Fifth, the inclusion criteria for group-membership may vary from context to context.
In product development tasks, a given project may require a certain heterogeneous set
of attributes, such as range of different skills. Workers with rare skills or high-level
expertise may be in a position of advantage in the competition for a place in the team.
Sometimes criteria for inclusion may not be skill related. In education, group essay
topics, for example, might be assigned to groups based not on their skills but
groupmembers’ (aggregated) preferences. The question regarding the selection of inclusion
criteria is, of course, significant from the point of view of fairness, provided that certain
individual attributes, such as ‘race’, are commonly excluded from the criteria for ethical
and/or legal reasons.
Sixth, there may be varying costs and benefits associated with specific aspects of
group-formation. Different kinds of errors may bring about different costs or harms in
algorithmic decision-making. As such it may be appropriate to prioritize the mitigation
or elimination of certain errors, such as false positives in recidivism risk assessment or
false negatives in algorithmic medical diagnosis.1 This applies also in group formation:
assigning individuals into groups that are a poor fit for them or excluding them from
groups that they would have been best suited for may bring about different costs. In
algorithmic team-formation, coordination or communication costs are often estimated
when forming collaborative groups
Furthermore, certain group compositions may be more optimal and/or just than
others. There is a long debate in the educational sciences regarding ability-grouping,
for example, which has centered around the question of whether homogeneous or
heterogeneous learning groups are most beneficial for learning
Lastly, the grouping process, and the quality of its outcomes, may be evaluated along
several lines.
This brief overview of relevant considerations provides different viewpoints to
fairness considerations in grouping, although it is not by any means exhaustive.
Furthermore, algorithmic fairness cannot be considered meaningfully without
considering a variety of sociotechnical factors, such as contexts of development and
use, institutional practices, accountability and transparency, and the moral value and
justification of particular technologies
Historical and technical biases in training data and in algorithms may lead to unfair outcomes and discrimination in algorithmic decision-making processes (Angwin et al.,
2016; d’Alessandro et al., 2017). Furthermore, once built into the system, biases may
be continuously reproduced and amplified through feedback-loops
In addition to possible bias, the fairness of group-formation also depends on whether
the used data is suitable to predict task-performance, suitability, or other relevant
qualities in the first place. For example, team-formation in the context of work has been
conducted on the basis of individuals’ personality profiles as measured with the
MyersBriggs Type Indicator (MBTI)
A plethora of metrics and formal definitions for fairness have been introduced in the
fair ML literature for measuring unwanted biases in processing and outcome
distributions. Common approaches to measuring fairness in ML models include
estimating outcome class equity, error rate disparities, and the illegitimate or undesired
effects sensitive attributes have on the generated outputs
In team-formation, when the goal is to form a single team from a set of individuals (e.g., one team of experts), several metrics introduced in the fair ML literature prove applicable. This is because the formation process is, in these cases, formally analogous to those described above (e.g., binary classification). When this is the case, we can treat equity in the formed group as a commodity to be (fairly) distributed between the individuals, akin to other goods or benefits. (The desirability of equity in the group may vary depending on whether being assigned to the group is a burden or a benefit.) When there are multiple groups to be formed and multiple goods or activities to be distributed to those groups (e.g., in multiclass classification or clustering tasks), there are other considerations, such as diversity or proportionality of shares both within and across groups, that matter for fairness. Before we move on to consider distinct metrics and definitions for fairness, it should be noted that the objective (or desirable outcome) of group-formation is in many cases maximal utility. In work and education, utility may be understood, e.g., as teams’ efficiency in solving a task, their aggregated skill-level or the coverage of a required set of skills – or, more generally, productivity or efficiency. This is the case with many approaches in the computer science literature, which do not necessarily consider fairness in team-formation or diversity within and across teams. We consider some exceptions below. In Section Three, we consider other aspects of group-formation which bear on the normative considerations regarding algorithmic grouping (and grouping in general).
A first definition for fairness to be considered here – and plausibly one aligning with
common intuitions about non-discrimination – is fairness through unawareness
The underlying intuition behind fairness through unawareness may be more
appropriate to understand in terms of conditional independence or counterfactuals. For
example, we might want that an individual’s predicted outcome will not differ in a
possible world where she does not belong to a sensitive group (other factors remaining
identical). This notion of fairness is captured by counterfactual fairness
Unawareness and/or conditional independence of sensitive attributes may be laudable
in many cases, but it may be inconsistent with explicitly promoting diversity; equitable
group-formation may require accounting for individuals’ sensitive attributes. Statistical
parity - a simple definition for equal equity in outcome classes - is satisfied when
members of the relevant groups (typically protected groups, e.g., gender groups) are
equally likely to receive a positive prediction
Enforcing statistical parity may result in outcomes which are “blatantly unfair” for
individuals, however, as it does not guarantee that the most suitable individuals are
selected
Notably, equity or diversity is a placeholder term in the formal sense; i.e., there are multiple dimensions or “currencies” of diversity in any given group. Typically, diversity is discussed mainly in terms of ethnicity or gender, perhaps due to a lack of diversity in those regards being a persistent problem in many contexts. The currency of diversity may, nonetheless, also be one of skill, vocation, etc. In other words, the notion of diversity in itself has no predetermined content but, rather, functions as a formal property of a formation. Hence, a group may be diverse along one dimension but not in another. A product development team may be diverse in terms of skill (e.g., it is interdisciplinary), but homogeneous in terms of gender (e.g., exclusively males), and vice versa. As such, the relevant question regarding fairness is whether groupformations are diverse in morally significant ways – i.e., what kinds of similarities and dissimilarities we ought to find within and across the formed groups2.
Fairness in group-formation may range beyond considerations of equity and diversity.
For many groups, diversity is no stringent moral requirement. It may not be morally
required from, e.g., interest-groups that serve and promote rights of certain
demographic or vocational groups. (However, diversity along some dimensions of
identities may still be morally praiseworthy in these cases.) Alongside diversity, fair
distributions of tasks both within and between groups seem significant from the point
of view of justice. For fair team-formation in collaborative work it might be desirable,
for example, to have an individual fairness constraint requiring that each individual has
a reasonable workload (irrespective of the overall workload of her team), but also a
2 See Green & Hu (2018) for a critical discussion on the concept of similarity in fair ML.
formation-level constraint requiring that different teams’ burdens are roughly equal
One can also approach fairness from the point of view of preference-satisfaction.
Political philosophers leaning towards welfarist and utilitarianist stances, in particular,
argue that the extent to which distributions of goods and opportunities are just depends
on whether individuals’ preferences are appropriately respected and/or satisfied
Whether individuals’ preferences are satisfied, and to what extent, is arguably
significant when we consider how, e.g., product development teams or learning groups
should be formed. We might deem it appropriate in an educational context that each
group of students receives, from a bucket of different essay topics, a topic which they
prefer the best. The extent to which individuals (and by extension, groups) are satisfied
in the given group they are assigned to, or in the overall formation of groups, can be
measured via self-assessment questionnaires, for example
Preference-satisfaction can also play a part in fairness considerations, as
system literature as a way of measuring the fairness of package-to-group
recommendations at the level of both individuals and groups
A limitation of preference-based notions of fairness is that they are not sensitive to entitlements. Sometimes certain individuals may have priority to have their preference satisfied above someone else’s. Institutional entitlements that come with, say, seniority or work-related merits, may warrant deviations from fair allocation (e.g., a priority in choosing which projects to work on). It may also be that some preferences should not be recognized as legitimate claims to membership in a group (e.g., a preference to work only with individuals of a certain gender or ethnicity). 3
The phenomenon of group-formation has a long and rich history of debates in political philosophy. In the subsections that follow we start from these debates. We argue that algorithmic fairness is irrelevant to many forms of groups, either because of the way the groups come to existence or because fairness is not a central value for them.
To anticipate, the values that come closest to fairness and utility are solidarity and diversity. They can be seen as good-making features in group-formation, and, arguably, of both intrinsic and instrumental value: groups may perform better when high levels of solidarity and appropriate degree of heterogeneity or diversity is present (figure 1). But arguably, there are other considerations (from individual rights and liberties to legitimate authority) that either pre-empt or override questions of utility, fairness, solidarity and diversity, or concern the question of whose decision the group-formation is (figure 2). Groups come in many shapes and sizes. Some groups (call them “feature-based groups”) consist of people with a certain property - the group of all left-handed people includes people who are left-handed. Some groups (call them “emergent” groups) emerge out of interaction, say, a group of people who regularly meet for cigarettes outside a library or who share a train commute and chat at the station waiting for the train. For such groups, the problem of managing group-formation (algorithmically or otherwise) cannot directly arise (of course, managing the features or interactions will indirectly affect the constitution of these groups).
Only some groups are such that membership is independent of the features of individuals of their patterns of interaction. Some groups (call them “birthright groups”) we are born to (a family, a state in contemporary understandings; see below), and only some memberships are granted intentionally or entered into voluntarily later in life (call them “intentionally formed groups”). The issue of group-choice or managed teamformation is at home concerning such groups. Fairness, algorithmic or otherwise, can be action-guiding only in such contexts. (We can, nonetheless, in a backward-looking sense, assess the fairness or utility of membership-allocations even in contexts where they are not action-guiding: see section 3.6 below). It is however to be balanced with other considerations, such as rights, autonomy or liberty, solidarity, legitimate authority, and diversity even in those contexts. Thus, the conflict between (kinds of) utility and (kinds of) fairness does not capture the whole normative shape of matchmaking and group-formation. 3.2
Michael
For those who are stateless or children without a family, a question of rights is the most relevant consideration. They have the right to become a member of a state, to then have the package of rights that the state grants to citizens. Corresponding to the rights of the stateless individuals, each state may have a duty to naturalize stateless person, although there may be questions of fair sharing of bearing the burden.
Plato’s Republic implicitly thematizes the conflict between fairness-and-utility and modern subjective rights, by neglecting the latter. Plato suggests that newborn children are collectively raised outside families and then distributed to societal tasks that are optimal to them, thus fulfilling justice (understood as everyone being in their right place). This violates such modern subjective rights as the right of parents to raise their children (and the corresponding rights of children), and the right of everyone to choose their career, and the right of everyone to freely choose their spouse. For example, Hegel in Philosophy of Right (1821) thinks that a rational whole (e.g. in terms of fairness and utility) should be formed so that also such modern subjective rights are respected - via the exercise of such rights. That prevents the state from being a totalitarian matchmaker allocating the right foster parents to the right children, or the right spouses to each other. That would violate subjective rights, and however optimal the allocation, it is practically irrelevant.
It is not only such high stakes decisions as career, family or state-membership that modern rights govern; there is a general freedom of association that modern constitutions declare. This takes us to the very closely related principle in groupformation: liberty or autonomy. Note how these values significantly lessen the practical relevance of optimal matchmaking in many contexts of modern life.
Many groups have, moreover, the right to choose their members. This has been discussed in the debates on group rights. The extent to which groups have a right to choose their members limits the extent to which outsiders have subjective rights to become members. It also, in a different way, may limit the relevance of utility and fairness: if a group has a right to choose its members, it has the right to do so in a nonoptimal and to some extent unfair manner. And if two groups have a right to choose their members, they have a right to take into consideration the utility and fairness from their own perspective, not optimizing what is optimal for the whole system of two groups and a set of applicants. It is possible that the group’s right is limited by the rights of individuals though.
It is important not to jump to the conclusion that utility or fairness would not matter: in some cases (outside birthrights) rights concern who has the right to make the decision, whereas utility and fairness help determine what is the optimal decision that should be made.
The relevance of rights may thus be threefold: (i) birthrights may pre-empt any deliberation of how to intentionally form groups; (ii) sometimes subjective rights my override considerations of utility or fairness in group-formation; and (iii) subjective and group rights may point to a distinction between two questions: who has a right to make a decision and what decision should be made. 3.3
One principle for group-formation is voluntariness: individuals are free to form new associations, and the membership profile of different groups is based on who freely enter or exit.4 Importantly, in modern contexts individuals have a freedom to choose their spouses and occupations (together with the choices of others). Similarly, within an established group, a new taskforce may be formed, and members chosen via volunteering for the task. This may lead to suboptimal formations: the volunteers may not be the most suitable, and unfairness may accumulate via voluntary choices. And this typically does not pre-empt the need to manage the team-formation: there may be a different number of volunteers than slots available. And so, fairness and utility may be action-guiding after questions of voluntariness have been taken into account. Voluntariness need not always override utility and fairness - if a leader or manager has the call, they may decide to go for the optimal solution even when volunteering has not been at stake.
So, in addition to pre-empting and overriding (in cases where rights are at stake), the considerations (fairness, utility, and voluntariness) may be in conflict as separate values to be jointly optimized. The manager may choose to prioritize voluntariness even when the individual would not strictly speaking have a corresponding right; such decisions may be motivated by the expected utility via motivational patterns etc. 3.4
In political philosophy, the difference between legitimacy and justice (or fairness) has been fruitfully discussed in recent decades. The interim upshot is that the question of legitimate governance depends on input legitimacy (whether the governor has been chosen in a legitimate procedure, and whether the governor has legitimate authority to make decisions in some realm), and output legitimacy (whether the decisions respect individual rights, and are sufficiently good in terms of utility and fairness), and some add also throughput legitimacy (how the decision-making process proceeds). (Schmidt & Wood, 2019.)
One special case of authority is the democratic authority of the group to make
binding decisions concerning itself: the decisions are illegitimate if they do not respect
4 Some liberties are afforded by memberships (citizenship, organizational role, marital status),
some may be independently grounded human rights.
the rights of individuals. But to the extent that they are legitimate, they bind everyone
- even those that voted against.
Another special case is a hierarchical organization such as military order of rank. If
a captain has authority over a group of soldiers, then the captain’s decision gives the
soldiers an overriding reason to act accordingly. Even if a soldier would know a better
route from A to B, it is irrelevant, if the captain has ordered to take another route. The
captain’s command is a stronger reason. The whole point of authority-relations is to
enable such orders being overriding reasons
There is ongoing debate about the extent to which normal workplaces should be like democracies or like military units in that respect, but what is common to both is that questions of legitimate authority are different from questions of fairness and utility. They concern the question of who is to make a decision, and not the question of which decision would be optimal. The flipside of the coin is that they do not diminish the relevance of fairness and utility in assessing which decision to make. 3.5
The concept of solidarity has a long history in the vocabularies of political philosophy
and the social sciences
Solidarity typically exists when individuals have shared interests and needs,
alongside possible responsibilities and inclinations to promote and partake in projects
of others they identify with
In many cases, however, group solidarity is an emergent feature of a group with a history, and thereby more like a desideratum than an active principle of membershipdistribution. Of course, higher levels of solidarity can be anticipated and worked for, and especially known hostilities and obstacles for solidarity should be taken into account in group-formation.
Our suggestion is that for the purposes of this paper, solidarity is to be treated of one aspect of “utility” – one aspect of functioning teams, rather than a principle that might override or conflict with such aim. It may be in tension with other aspects of utility, nonetheless, stressing the importance of pluralism in defining utility: utility-andfairness-and-high-level-of-solidarity can be a meaningful goal.
The concept of diversity is to some extent similar
Further normative considerations, such as rights, liberties, autonomy, legitimate authority, may concern the questions of whose the decision is, rather than what is the optimal decision to make. They may also be considerations that pre-empt (e.g. in the case of birthrights) or override (in case of some other rights) questions of fairness, utility, solidarity or diversity. It does not mean that the fairness or utility of the group compositions cannot be assessed in such cases. Analogously how natural beauty of sunsets or wildernesses can be assessed even though these values have not made a practical difference in their formation, we can assess fairness and optimality in groups that emerge while not being guided by such values. It would be wrong to say that utility or fairness does not matter in such cases; what can be said is that they are not practically and effectively guiding the group-formation. 4
In this paper we discussed algorithmic fairness in different group-formation contexts, and the limits that other normative considerations (rights, autonomy and liberty, legitimate authority, solidarity, diversity) pose. Extending the discussion of fairness to algorithmic group-formation, we argued that many technical notions of fairness introduced in the fair ML literature, such as equal equity, counterfactual fairness and envy-freeness, can be applied in the context of group-formation. The specific nature and setting of a group-formation task as well as the respective computational approach will determine the extent of their applicability. Assessment at the level individuals and comparisons both within and between groups may be relevant, and the limitations of technical fairness approaches – the informational scope of distinct metrics and tradeoffs between values of interest – should be recognized and carefully considered.
Furthermore, drawing on debates in political philosophy, we argued that fairness is not action-guiding in all contexts of group-formation because questions of rights and legitimacy may override claims to fairness or maximal utility or render them less relevant. Even if not action-guiding in all cases, fairness is a value to be jointly optimized alongside others and may serve as a lens for assessing decisions regarding the formation of groups. Green, B., & Hu, L. (2018). The myth in the methodology: Towards a recontextualization of fairness in machine learning. Proceedings of the Machine Learning: The Debates Workshop.
Hegel, G.W.F. (1991 [1821]) The Elements of Philosophy of Right. Cambridge UP. Cambridge. Hellman, D. (2019). Measuring Algorithmic Fairness. Virginia Public Law and Legal Theory Research Paper No. 2019-39; Virginia Law and Economics Research Paper No. 201915; Virginia Law Review, Forthcoming. Retrieved from https://ssrn.com/abstract=3418528.