You asked

The ONS claims that state pensions are contingent liabilities.

The dictionary definition of contingent is

  1. Subject to chance

  2. Occurring or existing only if (certain circumstances) are the case; dependent on

Which meaning does the ONS apply in the case of the state pensions?

If it is definition 2, please state what circumstances the ONS uses to omit the state pensions from the accounts.

We said

The Office for National Statistics is legally obliged to compile and publish the UK National Accounts in accordance with the European statistical law, the European System of Accounts 2010 (ESA 2010).

Paragraph 5.08 of ESA 2010, defines contingent assets and liabilities as "agreements whereby one party is obliged to provide a payment or series of payments to another unit only where certain specific conditions prevail. As they do not give rise to unconditional obligations, contingent assets and contingent liabilities are not considered as financial assets and liabilities."

This definition of contingent used in the National Accounts can be seen to be similar to the second dictionary definition you quote,

Paragraph 5.09 of ESA 2010 goes on to state that "contingent assets and contingent liabilities include:
.......
(f) pension entitlements under unfunded government defined benefit employer pension schemes or social security pension funds. Such pension entitlements are recorded in the supplementary table on accrued-to- date pension entitlements in social insurance, and not in the core accounts."

This text from ESA 2010 clearly precludes the recording of state pensions (i.e. social security pension funds) within the core National Accounts and for this reason ONS does not include the state pension liabilities within the UK National Accounts.

The full ESA 2010 text can be read at this link: http://ec.europa.eu/eurostat/web/esa-2010/overview