For several years, I had a long-running argument with my father about the question of government. For very deeply-held reasons on both sides, he viewed anything that was a participatory government as being a sign of “demonocracy” or some other anarchical threat to his well-being, and I viewed authoritarian government in the same threatening means. Given the depth of importance of the question to both of us, there was never any solution to the difficulty, merely a consistent elaboration of the case and the arguments that we would use to support our position. I have long felt sad, especially after the death of my father, that we had an argument for so long that completely avoided the real issues at stake. It would not have really mattered to either of us, I suppose, about the reality of the case, which would be that a godly and powerful leader would be better than a corrupt oligarchy or democracy, or that a godly people is to be preferred by far over the corrupt authoritarian leaders that are all over our world and its institutions, if the deeper issues themselves could not be addressed.
Nevertheless, be that as it may, it should be at least somewhat clear to my readers that I have an interest in exploring the often strange and unexpected consequences of mathematical logic . In that light, today I was viewing a lecture in a course I am taking on introductions to mathematical philosophy (a subject, I suppose, that few of my readers would be interested in), and the course, which deals with paradoxes and unusual results, explored a very unusual theory that gives a theoretical basis to the legitimacy of democracy or other participatory regimes. Of particular interest to me was Condorcet’s jury theorem, which states that if a group wishes to decide a matter by majority vote and each member has a probability greater than 0.5 of making the correct decision (or even if the average probability of the entire body of voters has a probability of greater than 0.5), then the greater the pool of voters in making a decision, the greater the odds that decision will be a correct one .
To be sure, this particular theorem has its complications. For one, we may lack confidence in the probability of other people making a decision at better than a coin flip probability, which would mean that we are conceding the failure of any efforts at moral, economic, and political education on account of those who are responsible for such instruction (namely parents, religious leaders, and teachers). After all, if the probability of people making a correct either/or decision is less than 0.5, than increasing the size of the group voting will decrease the probability of a correct decision very dramatically. We might therefore note that this particular theorem not only gives a theoretical justification for democracy, but also points out that a republic is only safe in the hands of a moral society. That mathematics should verify the beliefs of the Founding Fathers of the American Republic ought to give us at least some pause as to their unsophistication in the question of complicated matters, as is commonly thought by the corrupt intellectual heirs of Woodrow Wilson.
After all, it is precisely the greater moral and intellectual probity of a corrupt and cossetted political elite as opposed to the populace that itself is in dispute. Given the self-interest that elites have in supporting sub-optimal solutions that will benefit themselves and their cronies, holding trust in even relatively uneducated and unsophisticated people to be able to choose according to their own self-interest is a vastly safer behavior than trusting either corrupt bureaucrats or their crony capitalistic or militaristic supporters. This is true even where the voters themselves are not independent, so long as the chances are better than a coin flip that groups of people will make a better decision than the flip of a coin. What this means, as a practical rule, is that any time we can trust that someone is going to be right more often than not in making decisions, it is to our benefit to include this person and their insights in decision-making procedures. The more likely they are to be right, the more our decision-making will be improved by involving them in it. This particular theorem ought to be easy enough to understand and imply, and yet trust appears to be the issue at stake in terms of many political matters, whether in institutions or in terms of societies at large. In fact, this particular theorem also provides justification for setting the voting age or allowing participation at the point when the decision-making capacity of people has reached a critical level (namely 0.5). In some matters, like matters of the heart, this may take a long while to reach.
A more significant limitation, and one more difficult to wrestle with, is that the wisdom of crowds, such as it is, does not necessarily work all at once. When we divide such large decisions into step-wise either/or choices, we must face the fact that making the best decision would require path-dependence, which means that there are circumstances by which a gradual decision could be stopped short of the ultimate goal because of problems along the way. This appears to be a common problem in the transition between corrupt authoritarian regimes in places like Thailand (to give but one particularly obvious example) and a functioning participatory democracy. The fear of loss of control on the part of corrupt elites and the lack of trust in the capacity of ordinary people for rule means that such gradual moves towards greater participation and the gains in decision-making that result from greater freedom, assuming that a populace is even slightly biased towards the virtuous and the wise (which ought not to be that great of a level to reach for a society or institution), is likely to be arrested by a coup of some type before it completes.
This suggests that the real barrier to greater freedom and greater participation has nothing to do with the mathematics. Rather, the issue at stake is a straightforward lack of faith in the capacity of others (or perhaps even ourselves, as was the case with my father, who was not a man who appeared to trust his own wisdom or virtue). So long as we lack faith that we or others are more wise than foolish or more virtuous than sinful, we will lack faith in their ability to choose in matters of interest to them. Ultimately, though, if we are believers in the safety of a multitude of counsel, then we ought not to fear that the adding of relatively wise and decent voices will derail the wisdom of our decisions. Rather, it will only sharpen the wisdom and accuracy of our decisions, so long as we are able to act in faith and in trust, and show the proper respect for the capacity of our fellow men and women (and sometimes even children) in making our decisions wiser and more accurate through their input and involvement. The only thing we have to lose is our arrogance, our fear, and our prejudice.
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