# Corruption: a Mathematical Perspective

Occupy Math will start with a quote from the American Declaration of Independence:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed.

This part of the Declaration is saying that the reason we have rules (laws) and government institutions to enforce them is so the rights of all citizens will be respected by all other citizens. Corruption is any of a large number of practices that set aside protection of the rights of individuals to create an advantage for those engaging in the corruption. In this post, Occupy Math will make the case that corruption is obviously disadvantageous to a vast majority — possibly to everyone — using logical argumentation, one of the great branches of mathematics.

This post is not as clearly mathematical as most that appear in Occupy Math, so it may be worth noting that mathematics, in spite of all the focus on arithmetic and algebra, is primarily about the creation and manipulation of formal systems of rules. There is a reason that “math major” is one of the two best majors for getting into law school. It also means that corruption is more obvious to the mathematically inclined. With that excuse, let us continue on to the corruption!

The simplest form of corruption is taking bribes. You may take a bribe to do your job or you may take a bribe not to do your job. An official might require a payment under the table to issue a business license that the applicant has a perfect right to for no more than the official filing fee. A health inspector might ignore health code violations for a bribe. Anyone who has a regulatory or inspection role can take money instead of doing their job properly. People who have been doing this for some time start to think of the bribes as their right, a perk of their job.

It may be that some government jobs are complete wastes of time and public money, but Occupy Math has trouble viewing the job of a health inspector as one of these. If bribery can be used to bypass health regulations, there is a danger of food poisoning, rat-borne disease getting loose, or any of a number of other problems. This is the simplest form of corruption to understand and dislike and the problems caused are obvious.

Let’s move to the next level. The phrase “There ought to be a law!” exemplified the American belief that if there is a problem, it is the role of the government to address the problem by passing a law. People on the left want laws against guns. People on the right want laws against abortion. The citizens of California wanted a law against excessive property taxes and, in 1978, passed Proposition 13 — which “solved” their tax problem, but cripples their government to this day. No matter what they say, Americans believe that laws are a critical tool for running the country.

Corruption means that you cannot have laws.

If anyone with enough money can set aside a law by just bribing the enforcer, the rule of law is replaced by the rule of wealth. A cocaine dealer in Hamilton, Ontario says he paid \$20,000 a month to the Hamilton Police and was freely allowed to sell cocaine. This means a dangerous and addictive drug was informally legalized by the police, a group which enforces the law but which has no authority to change it.

It gets worse. If you are accepting bribes, then you are typically violating the law yourself. The members of the Hamilton police force did not manage to bribe the people above them who will be throwing them in jail — but if corruption goes far enough, they could. It happens in some countries. Think about this. The low level officials must bribe the higher level officials, in a chain, until the social fabric unravels. It also means that, except for the highest levels of official, most of the money ends up flowing up the chain of corruption to someone else. Selling your soul for money is bad, but in a corrupt system most people engaging in corruption end up selling their souls for a pittance, which may be even worse.

Who is hurt the most?

If the money from corruption flows up the chain of power, then those who are hurt the worst are the powerless. The poor, minorities who lack the social status needed to get away with corruption, anyone who has something a corrupt official wants. Another aspect of this is that those in charge of planning for the common good, setting tax rates, allocating resources to power and water, to health and safety have no idea what the actual costs and benefits of spending money are. When the rules are made meaningless by corruption, planning becomes far more difficult, sometimes impossible.

Bribes are addictive. Almost no-one is happy with their current income. A corrupt border guard who makes \$200 from bribes to let people cross the border would be happier if he could make \$500. A billionaire with mansions in a dozen countries lobbies for lower taxes because the millions he makes every year are just not enough. This means that corruption, if not sternly opposed, will grow. This is an example of a positive feedback loop.

Institutional Corruption

The corrupt health inspector that sets you up for a rat-dropping omelet is an obvious, almost cartoon, villain. There is another end to the spectrum of corruption. If corruption is any practice that sets aside the rights of others for personal advantage, then corruption can be woven into officialdom and the law itself. Oliver Wendell Holmes Jr., a past Associate Justice of the Supreme Court of the United States of America, observed that “Taxes are the price we pay for a civilized society”.

Taxes are problematic. Set unfairly high they incite revolt, such as in the Proposition 13 example earlier in the post. Set too low, they cannot fund critical infrastructure and services. There is also the problem of who pays the taxes. Many others have made this point, but Occupy Math will restate it. The wealthy benefit far more from tax spending than anyone else and so should pay a much higher tax as a percentage of their income. Occupy Math uses the roads to get to work and to visit family and friends. A trucking magnate uses the roads to make a huge income by moving his or her private business over public roads. This is elementary economics and obvious fact.

Here is where corruption enters. Because the United States has mistakenly decided that “money is speech”, the free speech of Americans that excites the wonder and admiration of the world has become a tool of corruption. The wealthy may, though campaign contributions that are modest in comparison to their gains, dictate tax law. The recent massive tax cut, which flowed mostly to the wealthy, is one of the most corrupt acts in history.

This tax cut grants a small group that has most of the money even more money. Cuts to health care, after school programs, environmental protection, farm safety nets, support payments for child nutrition, and a plethora of other programs are all already enacted. A vast increase in debt will also accrue. Given the mathematics of compound interest, the poor and the middle class will be paying billions in interest for decades to put money in the pockets of the rich right now.

Occupy Math does not mean to imply that the tax cut is not legitimate within the rules of government or that it is illegal. There is nothing in democracy that prevents it from acting in a corrupt fashion except the actions of its citizens. It seems likely that the next election will start the process of reversing this decision whose corrupt nature makes it entirely contrary to the common good.

Is this really math?

A economist can run numbers under all of this and make it so mathematical that it makes your teeth ache, but the mathematical high points are these. Corruption is addictive in a manner that make it grow via a positive feedback loop when not stomped out. Recognizing corruption requires an objective definition that lets you reason out if a particular act or practice is corrupt. Occupy Math offered the following: corruption sets aside protection of the rights of individuals to create an advantage for those engaging in the corruption. Try applying this definition to sketchy practices you encounter. Finally, planning is something that benefits enormously from doing the math, crunching the numbers. Corruption makes planning harder or even impossible.

Avoiding corruption is not hard if you set your mind to it. Do your job, pay your fair share cheerfully (or at least promptly), and if you see a corrupt practice or act, speak out! Silence is the greatest ally of corruption. Occupy Math apologizes if you were hoping for another post on fractals or an activity for students. We have more of those on the way, but Occupy Math’s slogan is Math is the Right of All Free People and corruption stands in opposition to our mission. Have some thoughts on this? Do not be shy, please comment or tweet!

I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statistics