Monday, September 15, 2008

Arrow's Theorem and Group Decisions

Way back in 1951, Kenneth Arrow wrote a book called Social Choice and Individual values, in which he introduced Arrow's Paradox (aka Arrow's Possibility theorem, aka Arrow's Impossibility theorem). Slightly less back in 1972, Arrow won the Nobel Prize in Economics for his work.

To oversimplify and ignorantly sum up, democratic voting doesn't work when weighing subjects against various criteria. (Blogger's note: No pretenses; I'm not capable of understanding, let alone explaining this equation with any sensibility. Check out the link for that. I'm just running with my blanket statement, and what to do with that conclusion).

If alternative analysis can't be trusted, then how can the input of multiple people help get to a decision? One thought would be to use the results of a vote to surface opinions, and use these as a springboard for more focused discussion. This isn't a silver bullet. But, will there ever be? Will algorithms ever take insights and transform them into optimal decisions? Services like Expert Choice are apparently making strides. There may be solutions on the horizon, but engaging people in discussion surrounding voting inputs also produces new insights and further benefits.

To be fair, there's always a risk in opening up results to discussion, of course.

1 comment:

Anonymous said...

Better group decisions are possible

Ever felt powerless in an election?
Ever been overruled by a majority over and over again?
Ever seen a group decision fail to pick an obviously good compromise?
Ever wondered whether democracy and majority rule are really the same thing?

Then this is for you!

True democracy is about every person having power, not just a mere majority!
Groups can make just and efficient decisions!
And it's surprisingly simple, too!
Here's how: Vote, but don't use majority rule. Use a better voting system!

Give it a try! Use this simple method for your next group decision:

Discuss the options and make sure any good compromise options have a chance of being identified as such. Then, on a ballot listing all options, each person ticks as many options as she likes, from one to all, and then underlines the one of them she likes best. Tally the ticks for each option. Then draw two ballots at random. If some option is ticked on both ballots, the winner is that such option which got the most ticks overall. Otherwise, the winner is the option underlined on the first of the two ballots.

You doubt that drawing ballots at random can be any good? Then think again: this is the only way to make it impossible for a mere majority to overrule all others and ignore their preferences! As everyone's ballot has the same chance of getting drawn, everyone has the same amount of power.

But isn't this the same as just drawing an option at random? Not at all! The better options will get more ticks and have thus the largest chance of winning.

Still, how can a good compromise arise from a process involving randomness? Think strategically: it is in the best interest of everyone to tick a good compromise, since that reduces the probability of getting a less preferred option. Therefore good compromises will very likely win! Often the system will even lead to complete consensus so that no randomness remains at all.

This system, called "D2MAC" (which stands for "Draw Two / Most Approved Compromise"), is only the simplest of a series of good voting systems that are much more just and efficient than mere majority rule...