Formal Equality of Opportunity is the view that formal rules should not exclude individuals from acheiving certain goals by making reference to personal characteristics that are arbitrary, such as race, socio-economic class, gender, religion and sexuality. In addition, Formal Equality of Opportunity forbids reference to proper names in formal rules. Formal Equality of Opportunity is incompatible with segregating workplaces or schools along these dimensions, and rules that pick out John Smith as a subject of unique advantages or disadvantages.
The best example of Formal Equality of Opportunity concerns equality before the law. However, Formal Equality of Opportunity is only formal. It is not concerned with the content of informal rules or of private discrimination. To illustrate this, consider the case of a racist employer who hires only whites but never advertises that fact. The adverts for these positions are formally open to all individuals, but the employer will never give the job to a non-white person. We can imagine other employers who are homophobic, anti-Semitic or sexist. There is something wrong with this kind of discrimination, but it is not a fault of formal rules, so Formal Equality of Opportunity can only take us so far.
Formal Equality of Opportunity suffers from some problems in its definition. We can ask, what makes a rule properly general? On one understanding, Formal Equality of Opportunity would require all positions to be open to all human beings. However, this is implausible. We do not think that young children should be allowed to apply for the position of bar tender and we certainly forbid them from voting. The severely mentally disabled may likewise be prohibited from applying for certain positions and voting. Finally, there doesn't seem to be anything especially wrong with limiting applications to only those with certain qualifications, such as a driving license for a taxi driver. However, the more permissive formal rules become, the easier it becomes to indirectly discriminate. For instance, a hair salon may insist that stylists' hair be shown and not covered. This would rule out members of some groups who cover their hair on religious or cultural grounds.