Proofiness

Charles Seife's new book is an interesting discussion on the misuse of numbers. Like Darrell Huff's 1954 "How to Lie with Statistics", it helps us maintain a healthy skepticism about those who use numbers to bamboozle.

But what if people demand numbers where none are available, or even possible? What if numbers are used to make decisions that should not be made? The problems resulting from some kinds of counting and measurement is that we do so in order to sanctify abuses.

Are illegal immigrants taking American jobs? A question often analyzed with measurements and statistics. But the big questions are: Is America a country of immigrants? What makes a job "American?" What does it mean to "take" a job? Can a job be owned? These are questions of about values, not numbers.

Many poll questions expect left brain answers to left brain questions, and combine them into a left brain poll percentage. Think of how much information is destroyed along the way. Channeling the vast diversity of billions of complex humans down to a few aggregate numbers is wrong headed, verging on the obscene. Leaving out the holistic, the social, the timeless, the transcendent. Making us into narrow-minded little calculators, not human beings.

How machines make decisions

My background is measurement engineering. I worked 18 years at Tektronix, one of the best electronic instrument makers in the world. My speciality was analog to digital converters, which turn analog signals, noisy and complex and continuous in value and time, into discretely timed and quantized digital samples. An analog to digital converter might produce the following results:

What happens when the input is exactly at 0.5000 volts? Is the output 0 1 or 1 0? Sampling analog to digital converters behave like a pencil balanced on its point - they will eventually fall over, to one of the two states, but they will spend some time perched in a metastable state, perhaps with digital outputs of ½ ½, (half half) which subsequent logic could interpret as 0 0 or 1 1, both values very wrong. Sure, the output will eventually settle out to 0 1 or 1 0, but the metastability time can take longer than the time to the next sample, or the next. It never asymptotes to zero.

This is a real phenomena - if the analog to digital converter is many bits, and used to digitize sound, it can produce an audible pop. If it is used to digitize video, it can produce a white or black spot. These digitizing defects can make an image sparkle like glitter, and are called sparkle codes. I have a patent on a circuit that reduces these defects for video converters.

One co-worker insisted that he could devise an analog-to-digital converter that would eliminate, not just reduce, sparkle codes, by setting thresholds around the noisy values and detecting when they might occur, overriding the noisy result. Well, guess what? The thresholds replaced the one old sparkle threshold with two new sparkle thresholds - the two new detectors were just as noisy as the old one was, and their results propagated to the output with logical necessity. It took a while, but I eventually managed to convince him mathematically that the complete 100.000% elimination of metastability required infinite gain, or infinite speed. Otherwise, the best you can do is to preserve the unstable results in a pipeline of decision makers, keeping the high sample rate while providing more time to resolve metastability. The errors are reduced exponentially, but never to zero.

And what does THAT have to do with Proofiness and elections?

Resolving elections perfectly is equivalent to infinite analog gain. If I punch a hole, or fill in a circle, I can punch it partway or fill it partway. If I fill in none of the space in the circle, at a sufficient distance away, I've misvoted. Somewhere in between a vote and a misvote is a threshold. My ballot can be delivered at 7:59:59 and get counted, at 8:00:00 and not get counted. Somewhere in there is a threshold. Every rule regarding the validity of my vote contains a threshold on a continuous measurement.

Voting is analog. Counting votes is theoretically digital, but involves analog measurement, combined with systematic error and bias.

So elections are analog. And that means, to make perfect decisions requires infinite gain. More subtly, if a decision is decided to be flawed (a statistical "tie", for example) that decision also requires infinite gain. Usually, the decision that an election is flawed is triggered by many measurements and decisions, infinite gain required all over.

And what is the infinite gain amplifying? NOISE. The more "improvements" that are added to the decision process, the more noise gets into the output, the more often there is contention.

Further, we don't vote about things we all agree on. Parties, platforms, and candidates are about issues for which there is no overwhelming majority, no congruity of motivations. Parties and candidates address many issues, and only a thoughtless person will agree with the whole party line, or weight the priority of the issues the same as a given candidate. Only a spineless fool is "100% Bush, 0% Gore" or vice versa. And we change our minds - that is why we have them. So our vote is an analog one, and the sum of our votes has a much lower signal-to-noise ratio than the "signal" of all that we know.

So voting fails, frequently, more often than we expect it to. And we blame those failures on our political opposition, rather than our own ignorance and absurd expectations. Guess what? The opposition thinks the same way of us, and all our silly perjorative claims about them vanish when we sit down and talk politely. Of course, if we were disposed sit down and talk politely, many fewer things would be contentious, and the subject matter of elections would dwindle and they would be mostly irrelevant to our lives.

Elections are not discrete. Elections are not commutative (see Arrow's Voting Theorem). Elections do not end conflict. Elections can be the signal to start wars. They are a necessary tool, but not a perfect one.

Voting is probably the best public decision making process we have. And it is a lousy one - better decisions are made all the time, in many other venues. We should not expect too much out of voting, and we should never assume that voting is the best way to make all decisions. And we should not spend too much time looking for improvements in the process without getting a better handle on what the process is intrinsically incapable of producing.