I think about democracy a lot, and specifically about what a vote means. Today the bowels of my mind shat out an analogy to compression algorithms. It struck me that as a way of transferring information about political opinion, votes are extremely lossy. But then I wondered if I could strengthen the analogy at all, or if it was a dead end.
Are compression algorithms that are lossy rated in some way with how lossy they are? Is there a way to compare them like that, to indicate how much information was lost? Most importantly, if I wanted to independenly research the topic, where in the hell do I begin?
I think voting would probably be better compared to sets - you have a zillion voters, each of whom has their own point of view. Then you have a few candidates, each with their own POV. The voters make choices based on what candidate best represents the voter’s POV. The candidate that wins should then have (or, at least, pretend to have…) a POV that lies at the largest intersection(s) of POVs in the voter population.
As for compression algorithms, yes, you can rate some as more or less lossy, and even within one algorithm you can change a few variables within it to come up with a more- or less-lossy result.
Standard disclaimer:
Of course, having the government mirror public preferences is at best only one potential normative characteristic. One could also desire that minority rights be protected or decisions be reasonable.
Ah, flowbark, I have heard of dear Kenneth Arrow but not this other work. Interesting.
And the matter that is important to me is that information transmission be as accurate as practical; what we then do with the information is a matter of debate.
The right place to start looking at lossy compression algorithms is probably in the context of information theory, but unless you’re mathematically sophisticated that’s going to be a bit difficult to study.
Y’know, this is an interesting analogy. I think that different forms of voting lose a different amount of information per vote. In the “one person, one vote” system, you lose a lot of information from one person’s vote. But in a system like approval voting, you lose far less.
Compression probably isn’t quite the right analogy. Information theory is definitely the way to go here.
Thanks, ultrafilter. I don’t know if I am mathematically sophisticated, but it still makes for a good time browsing my encyclopedic dictionary of mathematics.
Ultrafilter is right-on. The field of applied math used to quantify compression (lossy or lossless) is called information theory. Some of us who work with information theory apply it to areas like decision structures (e.g., voting structures, corporate hierarchy, etc.). There are ways to quantify the loss in information between a direct democracy and an electoral college system. I do not know of any work talking about the information loss inherent in a single vote though, if that’s what you’re thinking about.
As Ultrafilter said, info theory can get pretty involved, depending on your specific math background. By far, the most common general purpose info theory book out there today is “Elements of information theory” by Cover & Thomas. One specific area used to study lossy compression is called rate-distorion theory. Basically, it quantifies the communication rate needed to ensure information transmission within a distortion limit. You may be able to relate this to how many votes are needed to adequately express the will of a population. This area can also get very complicated, but if you want to dive in, one of the classic references is “Rate-distortion theory: A mathematical basis for data compression” by Toby Berger. Good luck!
The latter seems to be out of print, crozell, but best if I browse the former to ensure I’m not in over my head and discouraged. This thread has proven very helpful.
I think the analogy is so stretched it is liable to snap.
First past the post majority voting is one sucky compression algorithm – all information is disgarded except for one bit (or two bits, if there were four candidates (hence the term “two-bit candidates,” which you must all be familiar with)).
Sorry, I forgot that it was out of print. It’s easy to find where I am, but I didn’t think about it being hard to get online. I would think that it’s in the library of most school with engineering departments. I’ll look around for other resources and see if there is anything else I can find for you.
I can think of a very basic approach. I’ll use the one person, one vote method as an example.
Define a random variable X to be the candidate a person votes for out of a field of n candidates. X is a discrete random variable with distribution p[sub]1[/sub], …, p[sub]n[/sub], and its information content is sum(-p[sub]i[/sub]log[sub]2/sub, 1 < i < n).
Now let’s assume that the entire range of political opinions can be represented as a set of k statements that a person can either disagree or agree with. Define a random variable Y to be the political opinions a person holds. Y has 2[sup]k[/sup] possible outcomes (let q[sub]i[/sub] be the probability of the ith one), and its information content is sum(-q[sub]i[/sub]log[sub]2/sub, 1 < i < 2[sup]k[/sup]).
The ratio of the information content of X to the information content of Y gives a simple measure of how much information is lost in the process of voting, although I don’t think you can regard it as a percentage.
Everything varies on minute subtleties.
That’s why ballots have to rotate the candidate at the top.
Say we’re talking about the recent California governor’s race.
Two questions: Should Gray Davis be recalled, and if so who should replace him?
Had those questions been reversed, the voting would certainly be different, although I have no idea which way, just have to be different. Maybe Gary Colman would know.
