The Mathematics of Integrity

Professor Jonathan Wolff

Integrity, considered at the level of an individual, is a virtue. But what is to be a virtuous person? Consider how three types of people might respond to the dilemma of whether or not to take a bribe. The first type of person calculates the benefits and costs of the alternatives and decides to follow whatever best furthers their self-interest, which in this case, let us suppose, means taking the bribe. The second understands that self-interest will be best served by taking the bribe, at least in this case, but nevertheless has the strength of character to do the right thing and decline. For this person morality overrides self-interest. But the third type of person – the truly virtuous – doesn’t even do the calculation. Morality ‘silences’ self-interest. It just doesn’t occur to them to consider whether it is worth taking the bribe. And this we can say, is the person of true integrity.

Cynics, and economists if the categories are distinct, may suggest that the distinction is illusory. All actors are – must be – following self-interest in their own different way. The first obviously so. The second has a powerful interest, perhaps based on psychological comfort, in following the rules, and when the mental costs of breaking them are factored in too, the scales are tipped. And the third is just like the second, but the calculation is automatic or unconscious because the mental costs of accepting the bribe would be so high.

Certainly, it is possible to describe the different cases in this way. But what distinguishes them may be, at least for our purposes, more important than what they have in common. For one, although not the only, strand in considering integrity at the level of an institution, is working out how to design it so that people are instinctively motivated to follow the rules, without even considering whether it would profit them to break them. In a system of integrity, taking a side-profit becomes unthinkable.

In saying this I might be challenged from a different direction, based on a paradoxical claim discussed by Robert Klitgaard, that the optimal level of corruption in an organisation is not zero. What is meant is that if you are trying to clean up a corrupt organisation, there comes a time when you will have reached the point ‘enough is enough’. Chasing down the last pockets of minor corruption could be so expensive, and intrusive in individual lives, that it is a waste of energy and resources, given the minor benefits to be gained. It would be better to spend time and money on other priorities. Hence living with some corruption could be an optimal use of resources. However, this assumes that we are starting from a very corrupt situation. It would be very odd to criticise a completely clean, yet lightly policed, organisation for having a lower than optimal level of corruption.

How, though, can you build a system of integrity where breaking the rules is unthinkable? That will rely on many factors, no doubt. But here is a clue about how to make breaking the rules at least not worth thinking about.

Suppose you have a safe and three guards. How do you set things up to minimize the chances that the guards will rob the safe? If there is one lock and each guard has their own key, then it only needs one of three to fall to temptation. Suppose each guard is likely to suffer from temptation one day each year. With one lock and the same key, you can expect to be robbed every four months, on average. But if there are three locks, with different keys, all three guards must fall to temptation at the same time. If the guards act independently, and a single guard will fall to temptation again just one day a year, then the chances of all three coinciding on falling to temptation on the same day is 1 in 365 to the power of 3 (rather than divided by 3), or approximately once in every 133,000 years. This seems an incredibly powerful result.

Of course, though, this is a very artificial example. Corruption in a group is not a matter of coincidence of temptation, but influence and pressure. Still, the general point remains. There are situations in which you are as weak as your weakest point, and there are others where you are as strong as your strongest point. The trick of institutional design to resist corruption is to build structures that are analogous to a safe with three locks. This is sometimes put in terms of the need to divide tasks, so that no one individual has final sign-off control, and therefore corruption requires collusion. If there is mutual influence, and, a charismatic and influential potential rule-breaker, then bigger groups than three may well be needed, but cases will differ.

Notice, also, that where systems are successfully designed to avoid rule-breaking, then it is wasted time and effort for an individual to consider breaking the rules, other than as an idle daydream. The person determined to find a way to be corrupt will need to leave and join a different, more vulnerable, organisation, which is one way in which systems of integrity achieve stability. It is too much to say that systems of integrity will generate the virtue of integrity in individuals. But they may well encourage it, and will certainly encourage people to act as a virtuous person of integrity would do.


The discussion in the first paragraph is inspired by John McDowell “Are Moral Requirements Hypothetical Imperatives?” Proceedings of the Aristotelian Society, Supplementary Volume, Vol. 52 (1978), pp. 13-29.

The safe and lock example is taken from Joseph S. Fulda “The Mathematical Pull of Temptation” Mind 101 (402):305-307 (1992).

For the example of dividing tasks, and the “optimal corruption” argument see Robert Klitgaard Controlling Corruption (Berkeley: University of California Press, 1988).

Jonathan Wolff is the Blavatnik Chair in Public Policy in association with Wolfson College. He was formerly Professor of Philosophy and Dean of Arts and Humanities at UCL. He writes a monthly column on higher education for The Guardian.


How auditing can be directed against corruption: the case of Brazil’s municipality-facing auditing programme

Sérgio Seabra and Michael Barzelay

Following on from Anna Petherick’s post on corruption revelations in Brazil, Sérgio Seabra and Michael Barzelay preview their latest research on auditing policy and efforts to curb public-office corruption. Using case study evidence from Brazil, they show the intrinsic difficulties of obtaining two ‘necessities of auditing-against-corruption’: preventing corrupt activity while forestalling political pressure.

The wrongful exercise of authority over the use of public money is a major issue for public governance in many countries.  As a tool of public governance, auditing is often directed against public office-holders’ corrupt activities and behaviour.  This study seeks to advance professional knowledge about applying auditing to this purpose.  It clarifies two broad necessities of auditing-against-corruption: (a) preventing and detecting the corrupt activities and behaviour of a target population of public office-holders, and (b) forestalling political pressure against the audit agency’s independence in government and/or the professional discretion of its auditing staff.   These twin necessities of auditing-against-corruption sit uneasily together, posing a challenge for audit agency leadership – satisfying the former makes it more difficult to satisfy the latter.  This study shows how this characteristic challenge of auditing-against-corruption can be neutralised, through a case study of a nation-wide auditing program of Brazil’s Controller-General Office, where the target population was the pool of 5,570 municipalities, which together execute much of the Federal budget.

The programme began in 2003 and by 2015 more than 2,200 municipalities had been audited at least once. The effectiveness of the programme in preventing local government corruption has been confirmed by several empirical studies.  A special feature of the program was the random selection of the municipalities, which was conducted in a public event, by the same organisation, method and place used to draw the numbers of the National Lottery – the difference being that instead of win a large amount of money, they “luck” municipalities will receive a team of federal auditors eager to inspect the “actual” use of almost every money transferred from federal government’s departments. Both the periodic random draw and the announcement the results of the “lottery” were dramatised to a large degree, in collaboration with national and local media outlets. Another important feature of the program was the frequency, depth/scope and the short timeframe of the audits. Just a few days after the selection events a team of 10 to 15  auditors arrives at the selected municipalities for a week of intense field work. They conduct inspections and tests to check whether the grants transferred had been used as expected, ranging from visits to schools to check the purchase and quality of foods served to children at public schools, to inspections to check if the equipment to fight the Aedes Aegypti mosquito (Zika virus) was actually and adequately purchased.  Few weeks later the reports are released and published at the internet.

While there is no ready-made program theory, or theory of change, of auditing against corruption, ideas about deterrence, well established in fields like criminology, provide a good starting point for elaborating a program theory of auditing-against-corruption. This theory proposes that a corrupt behaviour tends to reduce when the likelihood of apprehension and the severity of penalty increase. Thus, in order to activate deterrence effects of this nature, auditing must generate a generalised perception among those of its targets – e.g. officials with control over the use of public funds – that corruption has high likelihood of being detected and, when that occurs, the resulting corruption case will hold up in tribunals with the authority to impose sanction. The case study analysis demonstrated that the effectiveness of the program can be attributed to a series of features of the program that, within an enabling context, activated three mechanisms needed to generated the “fear of detection”: selection, detection and sanctioning mechanisms.

Selection mechanism. This mechanism is responsible for the perception among potential offenders that the likelihood of being audited has increased. This perception was evoked by three features of the program: the auditing focus on municipality; the “dramatized” public events to select municipalities; and the frequency of the selection events.

Detection mechanism. The perception that a corrupt act could be detected was activated by program design features such as the widespread in loco inspections, and the fact that the scope of a municipal audit encompassed almost all grants transferred to the municipality. Another important program design feature was the use of information provided by citizens, via CGU’s ombudsman channel, to feed audit planning.

Sanctioning mechanism. A program design feature that contributed to the activation of this mechanism was CGU’s close liaison with other organisations responsible for criminal investigation and prosecution, namely the Federal Police and Public Prosecutors Office. Once indications of corruption are detected through auditing, a “joint-operation” with these organisations can be initiated. With judicial authorisation, auditors participate in most of the phases of the investigation, including the execution of the operation, when “search and seizure” and temporary arrests are conducted, with some media coverage. The joint-operations program at CGU gave the missing “teeth” to auditing, so that it could generate a deterring effect.

Auditing-against-corruption requires also the satisfaction of the other twin necessity: forestalling political pressure against the audit agency’s independence and/or the professional discretion of its auditing staff. We contend that the satisfaction of this necessity was due to the legitimacy of CGU, as a Federal organisation with constitutional mandate to oversee the use of federal funds, and to a meaningful “social front” – the idealisation of a set of activities performed by the organisation and the program. A meaningful social front was a result of the attributes of the “front stage” (e.g. audits’ reports and the selection events) and the ‘backstage” process/context factors (e.g. auditing review procedures, governance arrangements, etc.), functioning in an integrated manner. On the one hand, attributes of the CGU’s reports and the public selection events assured outsiders that the auditing process was grounded in procedures that guaranteed expertise, independence, balance and an unbiased, fair selection of municipalities. On the other hand, the CGU was portrayed an institution staffed by apolitical, well-paid and skilled auditors, whose activities and decision-making process are regulated by impersonal procedures and insulated from political interference.

In summary, the analysis demonstrated that the result can be attributed to a series of features of the program that neutralised the challenge involved in satisfying the twin necessities inherent to auditing against corruption. By providing an account on how the program features worked to satisfy these inherent necessities, this study contributes to advance professional knowledge on stock solutions to this form of undertaking. As such, it can be used as a precedent by practitioners for program implementation and organisational leadership in other settings where auditing-against-corruption is the part of the audit agency’s strategy.

Sérgio Seabra is the Lemann Visting Fellow of Practice 2017 at the Blavatnik School of Government, University of Oxford. Outside of academia, Sérgio has been a Federal Auditor of the Office of the Comptroller General of Brazil (Controladoria-Geral da União – CGU), since July 1996. Michael Barzelay is Professor of Public Management, within the Department of Management at the London School of Economics.

Two sides of transparency: how audits sometimes help, sometimes harm, women’s political representation


Anna Petherick

In this blog post, Anna Petherick inspects the relationship between corruption revelations and women in politics within Brazil. Her work highlights the importance of how corrupt activity is conveyed to citizens, and the unforeseen consequences of anti-corruption efforts on participation.

It seems reasonable to assume that progressive policies help each other along. That, for example, programs to improve transparency and lower corruption go hand in hand with efforts to encourage more women to stand for political office. But is this assumption justified? And what if the opposite were sometimes the case?

Unfortunately, the academic literature doesn’t offer a straightforward answer to the first question. There are two schools of thought. On the one hand, feminist institutionalists argue that corruption and its conceptual cousins (like clientelism and patrimonialism) tend to block women’s access to power. These scholars see institutions themselves as gendered because the norms and practices that they perpetuate often affect men and women differently, and reproduce gender-based inequalities.

On the other hand, political scientists who study stereotyping and voting behaviour anticipate that corruption might open the door to women who wish to enter politics, at least while women are rare among incumbents. This is because voters generally stereotype women as more trustworthy than men. A corruption scandal might therefore prompt voters—consciously or otherwise—to temporarily view female candidates as more electable than they usually do.

My research seeks to clarify these arguments. It suggests that the two perspectives are not actually in conflict, and that the mechanisms that they propose probably coexist in a lot of countries. To understand how this might work, you need to think about who is aware of the ins and outs of local corruption. What matters is whether these details become common knowledge, or whether only the politically connected or exceptionally interested—‘elites’, in political science parlance—learn about what has been going on.

To illustrate the point, consider Brazil, a land with plenty of double-dealing and no fewer than 5,570 local governments, of which only about 10% are headed by a woman. In 2003, a few months after Luiz Inácio Lula da Silva first won the presidency, the comptroller general’s office began a programme to air the dirty laundry of Brazil’s municipal administrations. But, with a continental-sized country to monitor and a limited budget, there was no way of checking the books everywhere. So the comptroller general decided to select municipalities at random.

The selection process is demonstrably as well as theoretically fair. Municipalities are picked using the wheels of a national lottery, in which jammy Brazilians win cash prizes. Re-deployed by the comptroller general, each numbered ball that tumbles around in a lottery wheel represents a municipality. If a ball is selected, that municipality can expect an audit. To many an incumbent mayor, these are unlucky lotteries.

On most occasions, sixty municipalities are plucked at once. Auditors then fan out across the country within the week, prepped to investigate every monetary transfer from every federal government department to the selected municipalities back to 2001. The auditors interview residents about the availability of public goods and services. They measure public toilet blocks to see if these are smaller than described in invoices. Sometimes they even invite themselves into hospitals to verify that individual items of equipment really were purchased. Whatever the auditors uncover appears in an online report.

It takes a certain amount of endurance to get through one of these reports. (I’ve read many and they are usually long and boring.) So learning the contents requires either personal motivation, or moving in the kind of circles where somebody will fill you in. Of course, this is not the case if your municipality has a news outlet that reports on local politics. Indeed, Brazilian researchers have shown that AM radio stations seem to do a decent job of disseminating news about the lottery audits’ findings.

My research considers locales with and without indigenous media separately. I have found that in municipalities where an AM radio station is the main source of local news, a corruption scandal involving a male incumbent gives women an electoral boost. Sensing opportunity, women are more likely to stand in the mayoral election after the comptroller general’s auditors have visited, and they also receive more votes than they did in the previous election. Where voters’ broadly know about the auditors’ findings, stereotyping appears to provide an invisible, female-friendly, electoral escalator for those who wish to challenge the incumbent.

Conversely, among Brazilian municipalities with no media outlet, women are less likely to stand in the election following a lottery audit than was the case in the prior election. Votes for female candidates shrink proportionally. Bluntly put, women do worse than they would have had the auditors never visited.

In all likelihood, elites, but not voters in general, know about the auditors’ findings in these places. Instead of acting as a clarion call to the ballot box, the audit reports take on a different meaning. To a prospective candidate wondering whether to throw his or her hat into the ring, a report detailing local corruption may illuminate how power is really managed behind the scenes—and provide a guide, or sorts, to the nature of the relationships that are required to be a successful mayor.

The average female prospective candidate is likely to have less access to these networks than the average male prospective candidate. So she is the more likely of the two to use the information in the report to downgrade her odds of beating the incumbent, and, if she does win the next election, of thereafter being seen as a successful mayor. Disheartened, she is therefore more likely than the average male prospective candidate to not stand for office after all. In other words, where there is no indigenous media, the patterns I find in the Brazilian data are in line with the feminist institutionalist argument—gendered informal institutions associated with corruption tend to act as a barrier to women in government.

So what’s the lesson here? Anti-corruption policies can have unforeseen impacts, and should therefore be situated within a broader framework to build integrity. Specifically, if you intend to set up a transparency initiative and don’t want to harm women’s descriptive representation, you need to carefully consider who is going to become informed about the minutiae of local corruption as a result of your efforts.

Anna Petherick is a final-year DPhil student at the University of Oxford. Her research seeks to characterise and explain the often invisible effects of corruption and transparency initiatives.