BALM FOR THE TROUBLED SOUL

Since I really do not want to participate in a debate about whether Jill Stein and Ralph Nader are narcissists, and because I am so upset about what is happening in the world right now that I need for my own psychological well-being to retreat a little bit into the realm of theory, let me write something about the whole complex issue of the left right political spectrum. Those of you who are only comfortable fulminating or casting aspersions can take a short break while I talk to whatever readers out there share my interest in theory.

 

The metaphor of the left right political spectrum dates back, of course, to the time of the French Revolution when the most anti-monarchical and radical delegates to the National Assembly sat on the left side of the meeting hall and the supporters of monarchy sat on the right. The assumption, often unexamined, that underlies the image is that the issues before an assembly or electorate can be arrayed one-dimensionally in such a way that wherever one positions oneself on that array, the closer anyone else is to one’s own position in either direction the more likely one will be to agree with that person. So a moderate Democrat is more likely to agree with a liberal Democrat than with a radical Democrat and also more likely to agree with a moderate Republican than with a conservative Republican.

 

Now this is a very powerful assumption that is true only rather rarely. Just to choose a real example, when I was a young man very active in the campaign for nuclear disarmament, I made common cause with Catholic pacifists who did not at all share my views about reproductive freedom as well as with libertarian anarchists who took a position diametrically opposed to my own on the question of forced redistribution of wealth.

 

Even if the left right political spectrum is a reasonably accurate representation of the views of members of the House or Senate, it is not at all reasonable to assume that someone occupying a position in the middle of the spectrum will have broader or more accommodating views to either side than someone occupying a position much farther left or right. To be sure, because of the two-party structure of American politics, someone who occupies a middle position more likely will be found voting with members of the opposed party, but it might very well be that he or she has in fact a very narrow spread of positions with which he or she can find accommodation. It might be, and frequently is, that someone on the far left is prepared to reach much farther along the spectrum to work out a compromise than someone routinely classified as a “moderate.”

 

The left right political spectrum does have one intriguing logical characteristic, however. To explain it, I must go back to the 18^th century and the work of the great Enlightenment figure Condorcet.  Condorcet demonstrated (and perhaps discovered, I am not sure) what has come to be referred to as the paradox of majority rule. It turns out that a group of voters, each of whom has perfectly consistent preferences among three or more alternatives, may by a process of majority rule arrive at an inconsistent collective preference order.

 

To see that this is so, consider the simplest possible case, one of three voters, A, B, and C, and three alternatives, X, Y, and C. Assume that A, B, and C have the following quite consistent preferences among three alternatives:

 

A:    X > Y > Z

B:   Y > Z > X

C:   Z > X > Y

 

When the three vote for X against Y, X wins because both A and C prefer X to Y.

When the three vote for Y against Z, Y wins because both A and B prefer Y to Z.

From which it follows, if the group is to be consistent, that it must prefer X to Z.

But in fact, since both B and C prefer Z to X, majority rule requires that the group prefer Z to X.

 

This is not a trick, it is a genuine contradiction. Kenneth Arrow, in a doctoral dissertation that eventually won him the Nobel Prize for Economics, generalized this result and demonstrated that no mode of collective decision-making that meets a quite minimal and reasonable set of constraints – roughly those of majority rule and similar systems of group decision-making – can avoid this distressing contradiction.

 

Now the nifty thing – demonstrated by an Australian political scientist named Duncan Black – is that if the preferences of the individuals voting can be arrayed accurately along a single two-dimensional left right spectrum, then majority rule is guaranteed to yield a consistent choice.

 

Nerds like me really dig this sort of thing and I must confess that writing about it has soothed the savage breast.