Museums and galleries must have breathed a sigh of relief when James Purnell signalled an end to the era of top-down government targets or "targetolatry" that has accompanied the Labour government's investment in the arts.

In his first speech as secretary of state for culture, media and sport, Purnell argued that while targets had served their purpose by encouraging galleries and museums to demonstrate that they are reaching a wider public, government policy had been guilty of focusing too much on measuring the instrumental benefit of the arts.

While a release from the tyranny of targets will always be welcome, with a tight spending round likely, galleries and museums are still under pressure to demonstrate their value and make their case for funding. Increases in the Olympics budget have only added to concerns that the culture part of the Department for Culture, Media and Sport is being squeezed.

This problem is not unique to the arts. Managers in all public institutions grapple with finding a way to demonstrate the value of the services they provide without being overly reductive or skewing their purpose with targets.

The limitations of New Public Management, with its narrow focus on monetary value and efficiencies, and the pitfalls of target-driven policy are all too familiar. That neither takes into account the intrinsic value of the arts or the quality of visitors' experience indicates the limitations of these mechanisms for this sector. It also hints at a question of legitimacy; what and who are publicly funded art institutions for?

One answer is "public value", a theory of management that places the public back at the heart of what publicly funded institutions do. Put simply, it states that public value is advanced to the degree to which an organisation is responsive to citizens' refined preferences and destroyed to the extent that it is unresponsive.

The gist of the theory is that the public should be thought of in a similar way to stakeholders in a private company. The Work Foundation's two-year research programme into public value argues that this goes beyond performance measurement and helps identify how a public institution authorises, creates and measures its value to the public.

An important aspect of this is recognising that citizens are not passive consumers of public services, but active participants who should shape not just the outcome of general elections, but also the ongoing, day-to-day managerial process of decision-making.

The concept of public value acknowledges that public services flow from our democratic choices and civic culture. Those in charge of museums and galleries are becoming aware that they need to co-create public services and ensure that citizens take part in the decisions over the use of resources.

Being responsive is, of course, not the same as pandering to ill-informed prejudices or paying undue attention to single issues. Rather, preference-refinement is a two-way, ongoing dialogue of exchange and iteration, with an understanding that different choices produce different results.

No organisation has a comprehensive methodology for measuring the value it creates. The best-known example is the BBC, which has developed a public value test for assessing new areas of activity. In the arts, the Royal Opera House, sensitive to tabloid charges of elitism, has looked at what the public think about the value of the organisation not just as users, but also as citizens.

But there is scope for public input on far more than the "end product", from decisions on how to allocate funding to shaping collection development.

One of the criticisms of public value is its lack of absolute measures. Putting a number on what are intangibles - values such as fairness that are not easily captured through the market or by a price mechanism - is precisely not the point. Public value argues that only the processes of democracy can help to determine what is valuable and that this process is a vital part of keeping public institutions relevant and accountable.

Public value offers the more imaginative way of improving performance that Purnell has called for. It offers an ultimate purpose to public management and a managerial road map for how to run an organisation and is unquestionably a "big idea". It asks the question about how to serve the public better, and answers it by saying efficiency and effectiveness are a matter of how close an organisation is to the public it serves.

In recent years, museums and cultural institutions have found themselves under accountability pressures on several fronts: government demands for "delivery"; changing public attitudes to institutions; and fashion in the measurement of outcomes. It might not be a magic wand, but when public-value generation is put at the heart of the public-service mandate, permission is immediately given to manage more autonomously and innovatively.

Will Hutton is the chief executive of the Work Foundation and a former editor-in-chief of the Observer. He will deliver a keynote speech on museums and the cultural economy at the Museums Association conference on 22 October