The scheme, described internally as "re-balancing" the pension system, would mean that those who paid the most National Insurance contributions throughout their working lives would get the least income in their retirement.
Although the move would anger many middle-class voters, its defenders argue that it would protect a crucial element of the National Insurance Contribution principle - that all those who contribute are entitled to benefits.
However, the mechanism for assessing the reduction in the pension remains unresolved. The most obvious way would be to calculate pensions on the basis of total National Insurance contributions through people's working lives.
At present, all those in work pay contributions based on their income up to a ceiling of pounds 24,180. These sums, plus the money paid in by their employers, entitle workers to benefits if they lose their jobs or when they retire.
National Insurance contributions have to be paid by any employee earning more than pounds 62 a week or pounds 3,224 a year. You pay at 2 per cent on the first pounds 62 of earnings and a further 10 per cent on earnings above this figure, up to the upper earnings limit of pounds 24,180 a year. Anything above the ceiling is exempt, meaning someone on pounds 250,000 a year pays no more than someone on pounds 24,180. Employees who earn less than pounds 62 a week pay no national insurance contributions.
Under a "re-balanced" scheme, those who had paid most in would get a reduced pension on a sliding scale.
If that were based on employees contributions, it would inevitably hit the middle classes, because all those earning pounds 24,180 or more pay the maximum.
However, employers do not have a ceiling on their contributions and pay as a percentage of the salary of the individual. Such records might form the basis of the new "re-balanced" formula.
An alternative is the creation of an "affluence test", which would reduce the state pension for those with higher income.
One possibility is that the basic state pension is reduced, with poorer pensioners applying for a top-up.
The initiative comes amid further signs of tension between Ms Harman and her deputy, Frank Field, the minister of state at the department of social security.
Last week, Ms Harman raised the possibility of an affluence test to some benefits as a possible mechanism of reforming the state. This would weed out those on high incomes or with large savings, rather than penalise the poor.
However, Mr Field, a long-time opponent of means-testing, last week distanced himself from the policy in public.
Speaking after a lecture to the right-wing Centre for Policy Studies, Mr Field described affluence testing as "one of many ideas being considered" adding, "There is no suggestion it has any more status than that."Reuse content