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Looking for ways to calculate equal opportunity

The centrist tenet of egalitarianism holds that members of a society should have equal opportunity. But what does equal opportunity mean, and how can it be measured?

In the last post we looked at what might constitute a fair society and why it is difficult to work out what people should be equal in. While there is not yet a consensus on which principle of distributive justice a rational society should favour, the most convincing principles tend to agree that opportunity should be distributed equally. But before we can enforce equal opportunity, we must first agree on how to measure it.

Equality of opportunity (where everyone has an equal chance of achieving happiness, fulfilment, wealth etc.) is much more difficult to measure than things like equality of voting rights or equality of law1. Equality of opportunity is more complicated because ‘opportunities’ to achieve happiness and fulfilment tend to be intangible and immeasurable. Opportunities for an individual might include things like being born with a photographic memory, having access to role models, discovering hidden talents like playing the piano, meeting individuals by chance, and so on. These opportunities, which may be random or coincidental, are complicated to measure, even for a single person. To compare these opportunities between two individuals is even more difficult — a single really useful opportunity for one person (meeting a family friend who offers you work experience) might be equal to many lesser opportunities for another (say, reading an advert in a magazine for work experience and having an enjoyment of music and being interviewed by someone who’s son happens to play in a band, ultimately results in being offered work experience). Despite this, because we only care about opportunities being equal (not measuring them exactly), equal opportunity can be measured — albeit in a roundabout way.

  • First, we know that an individual’s opportunities, whatever they are, are likely to influence his or her outcomes (the extent to which individuals have happiness, fulfilment, wealth etc2).
  • Second, we know that a single factor often causes a number of opportunities: more years in education might cause opportunities such as greater contact with role models, better literacy skills, increased access to career advice and higher self-esteem; while access to current affairs when young might cause exposure to opposing views and popular culture and lead to better debating skills. We term these factors that might cause opportunities as opportunity variables.

Opportunity variables can be any measurable aspect of an individual’s life: the number of siblings they have; whether they are left or right handed; the number of yogurts they ate as a child; etc. Given the above two bullet points, we can infer that outcomes are dependent on opportunities and that opportunities are dependent on opportunity variables. What happens if we get a positive or negative correlation between an opportunity variable and an outcome like wealth? Provided we can’t establish any other causal link between our opportunity variable and outcome, a correlation will arise only if people’s opportunities are unequal. When opportunity variables are not causing opportunities, or the intervening opportunities are equal with respect to the outcomes they cause, there will be no correlation. We will refer to those opportunity variables that can be empirically shown to correlate with outcomes as opportunity covariates. Over a large enough sample size:

  1. Finding a correlation between opportunity variables and outcome in a society will tell us that opportunity must be unequal in that society.
  2. We also know the root cause of this inequality, namely the opportunity covariate itself.

A society in this situation can be considered unfair because, under the definition in the last post (“a fair society refers to any society where the principles of distributive justice have been agreed, and are thereafter enforced”), we have an asset (opportunity) which is not equal in our society even though we’ve agreed it should be.

Admittedly this all sounds a bit theoretical (thanks for staying with us this long) so we’ll consider an example. We take an outcome (such as wealth or happiness) of a population, and see if we can find an opportunity covariate for it — if we can, then we know the society has at least some unequal opportunity. A plausible potential opportunity covariate might be the number of school years that children are required to attend. The actual instances of opportunities caused by this variable would be the intangible aspects of children’s school lives: inspiring teachers; more academic knowledge, and friends to network with as an adult etc. In conclusion, if there is a correlation between an opportunity variable and an outcome, it is statistically likely that the outcome is being affected by the opportunities caused by this variable, and the society is thus unfair.

Imaginary years-in-education/income graphs

In the above fictional examples, ‘years of school education’ are plotted against adult income for a number of individuals in three different countries. Country A’s school-years and income follow a linear correlation, suggesting that more years in education give rise to more opportunities to earn wealth. A similar story can be derived from the second example, Country B, except that the correlation attenuates with the growing number of school years (so past a certain point, extra years make no difference to what you earn). We can infer that both these countries have unequal opportunities, arising from an opportunity covariate whereby adults with fewer school years do worse in later life. There would be several ways to equalise opportunity in these countries; the easiest probably being to make sure every child spends the same time in school. Country C, by contrast, has no years-in-education opportunity covariate, because years are uncorrelated with wealth. This country has more equal opportunity than the other two, with respect to schooling at least, and would not require any government intervention in this area, assuming you felt income was a good enough approximation of happiness and fulfilment.

School years actually turns out to be a strong opportunity covariate for income (Card, 1999), and this inequality is the reason why measures such as raising the compulsory school leaving-age in the UK to eighteen are being considered. Whether things like government-sponsored apprenticeships (where an individual is trained in a vocational skill instead of academic subjects) are a good idea also depends on this correlation: if apprenticeships turned out to weaken the correlation between the number-of-school-years covariate and outcome, then they are probably a good idea because they are giving extra opportunities to those children who wouldn’t otherwise continue education.

We can now talk about equality of opportunity as something measurable, even if this is indirectly through the medium of opportunity covariates, and even though a number of approximations have to be made. For instance, outcomes like ‘happiness’, ‘contentedness’ and ‘fulfilment’ are subjective, so studies into inequality use other definitions as approximations, like material wealth, profession, or number of cars3. We also have to keep in mind that, as with all statistical analysis, we must be careful what we can infer from correlations. Overlap between the opportunities caused by different covariates (for example, the years-in-school covariate and size-of-class covariate) may mean that we could come to the wrong conclusion about what is responsible for certain opportunities. But this is a problem in all scientific correlation studies, and common sense can reduce it.

A different complication comes from trying to decide whether opportunities that stem from choice should be equalised. Plenty of people (including the philosopher John Rawls who first attempted to formalise the idea of fairness in society) maintain that choices are heavily influenced by non-choice factors for which we cannot be held responsible. Others take the stance that choice-based opportunities (opportunities gained as a result of hard work, enthusiasm and patience etc.) should not be distributed equally, because society would be forced to equalise opportunities (and thus the chance of better outcomes) to people regardless of how hard they work. In these posts, we adhere to the second view: that there is such a thing as free-will, and people should be rewarded with more opportunities if they decide to put in the effort4. Thus opportunity covariates based on choice (like hard-work and patience) should not be decorrelated from outcome.

Having determined that (non-choice) opportunity covariates should be unwelcome in a society, we are now in a position to look at equality of opportunity in a wider context. Gender and ethnicity are two classic examples of non-choice opportunity covariates that have historically influenced outcome. Other less politicised opportunity covariates have also been found: height seems to restrict your opportunity to a similar extent as gender and skin-colour (Persico, Postlewaite and Silverman, 2004). Other potential opportunity covariates are more complicated to measure; for instance, whether you have access to information (the internet, newspapers) as a child, or whether your family was socially excluded or isolated5. Provided the statistics are done properly, there are an infinite number of opportunity variables we could measure. If any of these (non-choice) variables are found to correlate with outcomes, it means that the society under consideration is unfair, and its government would have an obligation to try to mitigate this, for instance by passing laws that manually undo the correlation. Anti-discrimination laws in employment (for non-choice factors like sexuality and gender) are one example of such a law. Likewise, laws for full-time education and against child-labour are passed partly in order to reduce the imbalance generated by the education-level covariate. Reducing the effect of opportunity covariates can also be achieved in other ways: taxes for instance (which, in the education case, redistributes the wealth of the rich towards the education of the poor). Some commentators have even suggested such levies may be effective in curtailing the height opportunity covariate (i.e. Mankiw & Weinzierl, 2010). Happily a tax on people over six foot may be avoidable in the UK; there is evidence that opportunity covariates such as gender, ethnicity and sexuality are decorrelating as people become more tolerant, something also true of height (Heineck, 2007). While this is encouraging, it is not necessarily universally true — some claim that the correlation between the US’s ethnicity opportunity covariate and wealth outcome, by contrast, has grown more pronounced over the past twenty years (see sources).

We have described a way to measure whether members of society are equal in opportunity. In the next post, we will look in more detail at an opportunity covariate of particular importance: that of parents’ wealth.

1Equal voting rights and equal legal rights can measured simply by checking that everyone gets a single vote at elections,  and that everyone is subject to the same set of laws.
2Outcome can be measured using censuses (“how much do you earn?”, “how happy are you?” etc.). Happiness measures are arguably subjective (although a number of organisations try to find ways to sidestep this, the New Economics Foundation and the Centre for Bhutan Studies being two).
3There are also more complicated measures of outcome, such as social capital (the number of friends and acquaintances and individual has, and the form these relationships take), human capital (measures of education and skills), and emotional wellbeing (in the form of psychological questionnaires). Many of these could be studied as potential opportunity covariates as well.
4How to measure effort is something we’ll discuss in other posts.
5Depending on whether your family was ostracised by society (socially excluded) or chose not to interact with it (socially isolated).


Since this post was written, the Equality and Human Rights Commission has published its first Triennial ReviewHow fair is Britain?’. It gathers together the figures relating seven different opportunity variables (gender, age, ethnicity, religion, socio-economic group, sexual orientation and disability) to more than forty outcome measures. From a centrist viewpoint, this is a very welcome document: gathering such figures is a necessary obligation of the state, because the correlations they produce can be used to work out if equality of opportunity is (or isn’t) being met. While the report is well written and contains references to a lot of useful data, it also shows why the analysis of equal opportunity must focus on the relevant correlations and not just the bare numbers. The review’s frequent reluctance to properly calculate the correlation between the opportunity variables and the outcome variables result in some rather misleading (and occasionally plain wrong) statements. Take this assertion: “Whereas a generation ago almost all the students on the university campus were White British, today 1 in 5 are from ethnic minority groups” (p. 299). In the context this statement is set, it gives the impression that equal opportunity has risen. In fact, the ratio of ‘ethnic minorities’ to ‘whites’ in that age-group is 1-in-10 (Source: Census, April 2001, Office for National Statistics), meaning the most reasonable interpretation of the 1-in-5 statistic is that being a member of an ethnic minority now gives you an unfair advantage in achieving a university place (and quite a large one at that). We would also argue that religion/belief is not a relevant covariate, as it is a choice; and that some of the variables (the ‘ethnicity’ opportunity variable and a number of the ‘outcome’ variables) are highly subjective due to being self-diagnosed. Despite this, the review is a great introduction to the available data on equality of opportunity, and a welcome start — we recommend you give the report a read if you are interested in this subject.


  • ‘The impact of school years on outcome actually turns out to be a strong opportunity covariate…’ Card, D, ‘The causal effect of education on earnings’. Handbook of Labor Economics, Volume 3, (1999) Elsevier Science
  • “…whether your family was socially excluded (if your family was ostracised by society) or socially isolated” Postlewaite & Silverman (2005) Social isolation and inequality. The Journal of Economic Inequality 3:3, 243-262
  • …some […] maintain that choices are heavily influenced by non-choice factors for which we cannot be held responsible.” Rawls, A Theory of justice 1971 Havard Universty press p. 312
  • Others take the stance that choice-based opportunities (opportunities gained as a result of hard work, enthusiasm and patience etc.) should not be distributed equally…” For instance Dworkin, R. (1981a). “What is Equality? Part 1: Equality of Welfare,” Philosophy and Public Affairs, 10, 3, 185-246. (1981b). “What is Equality? Part 2: Equality of Resources,” Philosophy and Public Affairs, 10, 4, 283-345. Arneson, R. (1989), “Equality and equal opportunity for welfare”, Philosophical Studies, Vol. 56, pp. 77-93; Cohen, G.A. (1989), “On the currency of egalitarian justice”, Ethics, 99, pp. 906-944; Roemer, John (1998), Equality of Opportunity, Harvard University Press, Cambridge MA.
  • “...infamously, height is a comparably restricting factor for jobs as gender or skin-colour…”. Persico, Postlewaite and Silverman, The Effect of Adolescent Experience on Labor Market Outcomes: The Case of Height [Journal of Political Economy, 2004, vol. 112, no. 5]
  • “…Some have even suggested this might be done with height…” Mankiw & Weinzierl (2010) The Optimal Taxation of Height: A Case Study of Utilitarian Income Redistribution.
  • “…including, at the last check, of height …” Guido Heineck, A note on the height–wage differential in the UK – Cross-sectional evidence from the BHPS American Economic Journal: Economic Policy 2:1, 155-176 (2007)
  • “…the US’s ethnicity opportunity covariate […], by contrast, has grown more pronounced over the past twenty years.Where the wealth outcome is, more specifically, the ‘total financial assets excluding home equity’ outcome, although we can’t find a peer reviewed version of this: http://iasp.brandeis.edu/pdfs/Racial-Wealth-Gap-Brief.pdf
  • Weale, A ‘Equality’ The Shorter Routledge Encyclopaedia of Philosophy, Routledge [2005]