I first discovered the business significance of AND logic while participating in the redesign of my then-employer’s capital approval process. Among our findings: A $25,000 proposal required at least five approvals — the immediate manager, followed by the department head, division head, CFO and CEO. All had to agree — AND logic at its finest.

The average $2.5 million proposal, in contrast, required only three — the division head, CFO and CEO. The practical consequence? My employer had 67% more opportunities to reject simple, low-risk, high-return investments than large, risky endeavors.

All in the name of control.

Organizations grow and thrive on YES decisions. YES is how they increase revenue, decrease costs, increase speed and agility, improve quality and add excellence.

YES decisions also create risk, because every one proposes a change of some kind. Change isn’t safe. It always includes the possibility that no matter how good it looked in the PowerPoint, and how carefully everyone involved with it planned, designed, engineered and built, it might not work out.

The typical mechanism organizations use to mitigate risk is the veto. It’s requiring some number of individuals to independently decide whether the risk is worthwhile, and if any one of them doesn’t think so then the proposed change never sees the light of day.

In practice, it comes down to getting signatures. And in practice, this usually means that the process designed to mitigate risk instead becomes the process through which the organization plays favorites. You know how it works: If the proposer is, or works for, someone who is in the inner circle or is one of their proteges, then signatures become rubber stamps.

If, instead, the proposer is unknown or works for an unknown then it receives scrutiny usually reserved for the scene of a murder on CSI. And if the proposer works for someone who has annoyed anyone whose signature is required, rejection is automatic.

What’s the solution? That depends on how you define the problem.

If your company’s goal is to make its investment decisions as fairly as possible, then its governance process should look a lot like how radio stations make hiring decisions for their announcers: Applicants speak behind a screen, so that if you have a “face for radio” it won’t bias the interviewer. Similarly, a fair governance process operates on paper, and all proposals are anonymous so that nobody has a chance to play favorites.

Fairness is, however, an overrated virtue. Among its defects are its speed, which can be glacial, and its expense. In business, you’re more likely to set a different goal — to invest in the most promising proposals. Fairness might be a means to this end, but often it isn’t.

If you don’t accept this, imagine you’re evaluating two competing proposals. One comes from an associate with whom you’ve worked for more than ten years — someone you know well, like, and trust. The other comes from an outside vendor — a company that’s unknown to you.

If you ran a fair process you’d perform the exact same due diligence on both proposals. But you’ve already performed ten years of due diligence on your trusted associate, so your first step is deciding whether considering the unknown company’s proposal is worth any time and effort at all.

That, rather than the apostrophe, is the crux of the biscuit: The only difference between trust and favoritism is whether you’re among the trusted few or the anonymous many.

Here’s a nit to pick: In business, trying to invest in the most promising proposals … the best ideas … is pointless, for two reasons: Uncertainty and multidimensionality.

Uncertainty is an issue because the business justification included in every proposal is, at best, an estimate with a sizable error bar. “Best” implies a level of precision that isn’t available to you.

Multidimensionality means that every proposal has more than one justification — more than one reason for pursuing it. These different reasons have different levels of importance for different decision-makers, so “best” depends on which chair you’re sitting in.

When it comes to corporate governance, it’s best to set the bar a bit lower. Just trying to make sure every funded and scheduled proposal is worth pursuing is tough enough.

To achieve even that requires an executive team that operates as a team — whose members like and trust each other and who have a common purpose — rather than a roomful of rivals.

As CIO, you can’t make this happen. That’s the CEO’s job.

If your company doesn’t have one of these you’ll have to work toward the next best thing: Making sure as many of the decision-makers as possible like and trust you.

Adios, Cingular.

So far as I can tell, AT&T just repurchased itself from itself for a lot of money. I’m sure that can’t really be the case, though.

I just can’t handle the math.

Math can be useful. It can help us understand when circumstances we don’t like are built into the fabric of the space-time continuum. That’s particularly handy for companies that have a blame-oriented culture and are wondering whose fault it is.

For example:

Combinatorials: I’ve mentioned the formula n(n-1)/2 before. You can use it to calculate the number of pairs of objects in any collection. It explains why an entrepreneurial startup venture can operate as a “band of brothers.” Until, that is, it succeeds.

Imagine the startup consists of five old friends who know and trust each other. n(n-1)/2 means it contains 10 pairs of people. With only ten pairs, everyone can maintain trust; everyone knows what everyone else is good at, and the company operates smoothly.

So the company succeeds. Pretty soon it has 100 employees — 4,950 pairs. There’s simply no way every pair will exhibit mutual trust. Some pairs are total strangers; others consist of people who just plain don’t like each other; who see each other as rivals; or otherwise can’t work together effectively.

Surface area to volume ratio: Blow up a balloon — for simplicity, imagine it’s spherical. When it’s an inch in radius, its rubber surface covers 12.566 square inches (4*pi*radius^2) and encloses a volume of 4.189 cubic inches (4/3*pi*radius^3). Surface Area/Volume = 3.

Blow up the balloon to a five inch radius. It now has a surface area of 314.159 square inches, and encloses 523.598 cubic inches. Surface Area/Volume = 0.6.

Small balloons have a lot of surface area for each unit of volume. Big ones have very little. It’s why we’re made out of many itty bitty cells instead of being big globs of protoplasm. The quantities of oxygen and nutrients cells need (and wastes they must dispose of) depends on how much stuff they contain — their volume. Their surface area limits how fast they can exchange it all with the outside world.

If this still doesn’t make sense, compare the five-inch balloon to 125 one-inch balloons. Both enclose about 524 cubic inches. The five-inch balloon contains it in 314 square inches of rubber. The 125 one-inch balloons need about 1,570 square inches — five times the surface area.

It is because small objects have a much higher surface-area-to-volume ratio that iron dust is highly flammable while iron bars are not (nor do a prison make, not that it’s relevant).

It also explains why it is that in small entrepreneurships, every employee has a clear view of real paying customers and what they need, while in large enterprises almost nobody does. The surface area has become far too small relative to the company’s volume.

AND logic: Back when I was studying electric fish I learned to wire together simple electronic circuits. Many included AND gates. Feed nothing but 1s to an AND gate and it outputs a 1. Make any input a 0 and it outputs a 0.

AND logic extends to any number of operands. (A AND B AND C AND D) is only true if A, B, C and D are all true. If any are false, the entire proposition is false.

The executive suite is one big AND gate. In order to proceed on an idea suggested by an employee, the employee’s manager, the employee’s manager’s manager, and the CEO, CFO, COO, and CAO all have to say yes. If any say no, the entire corporation has said no.

Big companies become risk-averse, not because their individual executives are excessively timid, but because of AND logic.

Sympathetic vibrations: Pluck a string on a guitar. It vibrates. Place the guitar near another identically tuned guitar and the same string on the other guitar will vibrate, too.

It’s called a sympathetic vibration.

In business, sympathetic vibrations are why bad ideas can take on lives of their own. It works like this:

A superficially attractive idea (move our factories to China, perhaps) creates good vibes. An executive with vision but no attention to detail picks up on it and repeats it, making it louder — and therefore better-able to induce sympathetic vibrations in yet more executives. Soon, everyone repeats the idea, and it sounds just like an informed consensus.

But really, it’s just one boneheaded idea that, through the physics of sympathetic vibration, ends up filling the company.

Don’t agree? How else do you explain it?