Murali’s Democratic Impossibility Theorem

Ladies and Gentlemen this being the latest in a round of posts on democracy, is going to be long. I also promise that it will be bizarre. I would like to talk about two features of democracies, which each,, in themselves are essential, but create a particular strange problem when found together. These two features are

1. Universal suffrage
2. People sticking to their guns in the face of widespread political disagreement.

The reason why the two together are problematic will be shown by the end of the post. However, as a preliminary I will want to show why the two are essential for democracy. Firstly, I do not think that at this day and age, we would want to call a system which lacks universal suffrage a democracy (whatever else happened in Athens 2000 years ago). Also, if everyone moderated their judgements with respect to political preferences, then there would seem little reason to go to the polls. There are other problems that crop up that will be more explicitly spelt out later.

This criticism is aimed at epistemic defences of democracy. What are such defences? They are defences of democracy or any other regime in terms of the correct-ness of the policy such regimes produce. Of course, for democracy to be defended in a non-trivial way, we must exclude cases where the fact that a majority prefers a policy makes it the right one.

Given that we are talking about an epistemic defence of democracy, let me introduce Condorcet’s Jury theorem. Very generally, any defence of a political system with some form of voting must adhere to the constraints laid out by Condorcet’s theorem. Now what does Condorcet’s theorem say? Basically, it says that given a large enough population of voters who are completely epistemically independent from each other, all that is needed to guarantee correct policy for any individual voter to be on average just slightly more likely than not to get things right. The less epistemic independence we have, the more accurate voters have to be on average in order guarantee correctness of policy. Things that compromise independence are political parties, public deliberation etc. Of course, if any deliberative or party structures manage to compensate for the decrease in independence with better quality of information and reasoning, all will still be to the good. Regardless, few people are willing to maintain that we cannot do better. Also increasing public deliberation is not necessarily an option. Teson and Pincione’s work shows that people prefer false intuitive explanations over true counterintuitive ones. That’s why people wonder how productivity increasing labour-saving technological gains can be a good thing (even for the worst off) or why if global warming is true, it’s getting colder in Seattle.

Now, given Condorcet’s theorem one can improve the quality of governance by denying some people the vote. And given Condorcet’s theorem we could do better than democracy by denying some people the vote. I am not going to argue about whom to deny the vote to. In order to defend democracy along Condorcet lines, we must therefore presume that there is some social epistemic reason we cannot throw in a smaller net. i.e. there is some reason why we cannot epistemically privilege some voters over others. What this means that there is some sense in which all the voters in a democracy are epistemic peers.

Rather than going through all the alternatives in trying to find out what sense of peerhood could be implicit, I will just point to one that I think is most probable. This also I think happens to be one of the weakest if not the weakest notion of peerhood we could invoke. Let me lay it out:
Not everyone is an expert. Some people are experts in more subjects than others. Some people are just complete dunces. However, it is impossible to tell who is an expert and who is not. So, each person treats the other neither as an epistemic inferior or superior. This also allows that there may be expert knowledge and that it may be usefully aggregated by voting. This also falls more along the lines of traditional criticisms of rule by experts.

Is this however, really the case? Even if we cannot point out who would be the best expert, we could maybe cast a moderately wide net and capture, professionals, academics, others who are educated above a certain level. We could set political knowledge tests set up and marked by the individual political parties. We may miss out some far flung bits of information, but we would weed out a lot more misinformation. Bet perhaps, this is too difficult to implement and subject to abuse. However, if even this notion of peerhood is too strong, then an epistemic defence of democracy doesn’t really have any legs to stand on.

Let us suppose that at least this notion of peerhood is prima-facie viable. If we are epistemic peers in this loose sense, does it follow that we are to moderate judgement under widespread disagreement?

Now, when it is just one on one, while some philosophers argue that epistemic peers should withhold judgement under peer disagreement, I don’t need such an extreme result for my thesis. People whom you regard as your peers can still be wrong and can still make stupid mistakes and be unreasonable every now and then. However, if they do it too often, then you demote them from peerhood. The fact that they disagree with you becomes less and less of a reason for you to revise your beliefs.

Disagreement about a proposition P doesn’t say anything directly about whether P is true or not. However, peer disagreement about P (especially when both have the same evidence) is itself evidence that the evidence E for P is not as strong as you originally thought. It need not be dispositive though. That’s why when you have one peer disagreeing with you, that’s not sufficient reason to revise your beliefs all the time. But the weaker your primary evidence actually is, the more reason you have to revise your beliefs under disagreement. However, when lots of people who you think are just as good as you at getting it right don’t think your evidence is strong enough to support your position, then you have to revise your position or explain how they could all be wrong and still remain your peers. This would be true even if there were lots of people who agreed with you as well. If lots of peers disagreed with you and you were the sole dissenter or near enough, then you may very well have to change your mind completely. If roughly as many peers agreed with you as disagreed with you, you only need to meet the opposition half way.

There are some situations when even widespread disagreement need not affect you. That is when you think that you have an absolutely strong knock down argument/evidence that would convince them if you shared it with them. Another is where the people disagreeing with you are your epistemic inferiors. They are just not as good as you at assessing the evidence. Their disagreement with you is only significant to the extent that you think that they might have assessed the evidence correctly. Epistemic peers cannot agree to disagree without being somewhat permissive epistemically. i.e. you believe something about P in spite of knowing that there are more rational doxastic attitudes to hold towards P given evidence E.

Now, lets get back to the political situation. Of course, voters do not have access to a common pool of evidence. But let’s look at the evidence that you have for your strongly held political beliefs. Do you think your evidence is so strong that no reasonable argument could be made against it? If not, why do you hold it so strongly? If yes, what is the political belief and what is the evidence you have for it? Is the argument something we’ve all heard before? If it’s something we’ve (your fellow voters) all heard before and lots of us still disagree with you, then surely you must consider us particularly bad at assessing evidence. Maybe you’ve even got a nice explanation for the reasons why we are all wrong. So, given that you do think that we are relatively terrible at getting political issues right surely policy would have been better (according to you) if we had not voted. (unless of course we are already a fringe minority)

So Here’s the theorem. Basically I’ve described a dilemma and democracy is damned either way. If we demote some others from peerhood, it means that we can improve policy outcomes by getting them to not vote. If we don’t demote them from peerhood, we should moderate our judgements until we agree with each other. However, if we do moderate our judgements, then we’ve got a whole different set of problems.

Voting to change policy doesn’t make sense (unless you’re a Kantian and I doubt many if any of you are) because the chance that your vote will be decisive is miniscule. So, voting expressively is probably your biggest reason to vote. However, you only vote expressively if firstly there is some strongly held belief that you want to express. However, when you have moderated your beliefs as a result of widespread peer disagreement, you don’t have any strong beliefs you need to express by voting. The second condition that would make you want to vote expressively is if people disagreed with you. You would want to express solidarity with your tribe against the other tribe. However, if there was no political disagreement because everyone moderated their beliefs, what is there to express. Everyone already agrees anyway.

There is also another problem for democracy with everyone moderating their beliefs until they reached an agreement. Remember that the Condorcet theorem required a higher ratio of information to misinformation if people became more epistemically dependent on each other. Given complete agreement about political issues, they are completely dependent and democracies will require extremely high quality of information in order to function.

So, democracy which is tainted by poor reasoning among its voters cannot survive their epistemic improvement.
As a solution, I would recommend charter cities, seasteading or more realistically, the gradual delegation of actual governance to efficient technocrats (not beaurocrats)

Note: If you think that this is all well and good but that not only is there more to political institutions than getting public policy right, those other features also take absolute precedence over policy correctness, then I would genuinely like to know what those features are and why we should care about them. The instability of democracy even or maybe especially under idealised conditions is going to pose a difficulty for anyone trying to justify democracy as an ideal.

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11 thoughts on “Murali’s Democratic Impossibility Theorem

  1. The Downian paradox of voting (i.e., the argument that it is not economically rational to vote to change policy, because the probability of being the marginal voter is small) is a nontrivial concept; while ‘expressive’ theories are one argument, small degrees of altruism or lottery-type risk preferences and so on can all generate high turnout equilibria. The literature is massive and expressive voting doesn’t seem at all obvious.

    The information-concentration argument regrettably applies to a variety of other social-choice mechanisms besides voting, including market pricing (given costly portfolio assessment, it is rational for everyone to ‘bet the market’ if market prices are efficient, but if everyone bets the market then market prices are likely to cease to be efficient). The leap to the conclusion of technocracy or competitive seasteading seems… implausible, given basic Hayekian knowledge problems on one hand and the basic need to monopolize the use of force in the other.

  2. small degrees of altruism or lottery-type risk preferences and so on can all generate high turnout equilibria. The literature is massive and expressive voting doesn’t seem at all obvious

    Hmm. If you dont mind could you direct me to a few papers. The way I understand it the probability that I will cast a deciding vote is so small even in small countries with close elections to be of the order of 10^-130.

    Its not even clear how altruism will get me to vote. Altruism can get me to do things at personal cost but which is of benefit to others. Voting when I have little to no chance of casting a deciding vote is still going to be as problematic whether I caare about the public good or personal good.

    The only alternative to expressive voting is if people saw themselves as Kantians and cared about not making an exception for themselves. i.e. people saw that if everyone said that they would not vote because of the cost/benefit ratio, no one would. (its not even clear if it is therefore unacceptable) However, thn the reason for not voting would bbe undermined. This is a fairly abstract reason. It is not clear if this has any effect on most people’s decision structure.

    (given costly portfolio assessment, it is rational for everyone to ‘bet the market’ if market prices are efficient, but if everyone bets the market then market prices are likely to cease to be efficient

    Errm… Why?

  3. In order to defend democracy along Condorcet lines, we must therefore presume that there is some social epistemic reason we cannot throw in a smaller net. i.e. there is some reason why we cannot epistemically privilege some voters over others.

    Perhaps we should just pull a random sample of the population and let them vote.  Done right, it should be 95-98% accurate.

     

    The only alternative to expressive voting is if people saw themselves as Kantians

    Well, there’s always the possibility that people are just irrational.  (Or is that just a synonym for being Kantian?)

    • Well, there’s always the possibility that people are just irrational.  (Or is that just a synonym for being Kantian?)

      The Kantian understanding of morality is that morality is about acting on universalisable principles.

      If, the maxim “I will not vote because my vote has a miniscule chance of being decisive” is not universalisable because it is self defeating (under universalisation) in some way, then it is not moral. It would take a full paper to adequately deal whether any similar maxim is universalisable or not. All I am saying is that the only possibility when it comes to rationally choosing to vote to change policy is if we had a Kantian understanding of morality. And even then it would not be definitive. It may be that the maxim is universalisable.

      I doubt many people are Kantians (although they should be) in the sense I described above.

  4. Murali,

    Your argument seems to rely on their being “right” and “wrong” choices.  I would argue that doesn’t hold very often.  If we’re voting on whether AGW is happening or not, that might be the case, but if we’re voting on alternative policies it’s not the case.  In fact if our choice is between two candidates where Mr. X doesn’t believe in global warming and would do nothing about it, and Mr. Q does believe it’s happening and would do something about it, it’s still not with certainty the “right” decision to vote for Q, because it’s possible that the something he would do would be worse than doing nothing.  So only in cases where we have specified in very explicit detail the outcomes of voting one way or the other can we possibly say that there is a “right” decision. And very few elections operate on that basis.

    In fact most elections operate on the basis of competing values, where there is objective determination of which value is “right.”  I’m a staunch free trader and I firmly believe protectionists are wrong…but I also recognize that although they’re misguided in understanding the benefits of free trade, they are also operating off a competing value basis–caring more about the stability of jobs for the working class than about cheap consumer goods.  On what basis can I claim my value is the “right” one to choose (other than the fact that I’m just that much wiser than anyone else)?

    There’s a reason Condorcet’s theorem is called the “jury theorem.”  When juries are deliberating over guilt or innocence, there is a wrong and right answer.  (Well, we can imagine cases where it’s not that cut-and-dried, but I’ll leave that esoterica alone for now.)  What applies to juries is not always applicable to the selection of public policy, and rarely applicable to the selection of political candidates.

    Not that any of what I’ve just said really helps the case for democracy.

    • Your argument seems to rely on their being “right” and “wrong” choices.  I would argue that doesn’t hold very often.

      In those cases, the second part of my dilemma kicks in. If there is no clear right and wrong, we shouldnt be believing in our political positions so strongly. i.e. if there is no clear right and wrong, everyone should be similarly agnostic about what to do about global warming.

      I don’t require that the correct answer be obvious or readily available (although conceptually speaking there should be such an answer even though it may in be almost impossible to find out what it is) All I require is that there is one doxastic attitutde which is uniquely the best doxastic attitude to take given a belief. If we should believe that doing nothing is better with a credence of 0.55 given the evidence we have, then that is how much credence we should afford. (I understand that I break ith orthodox bayesians on this. But I think they’re just wrong on this one question. And no, I dont necessarily hold orthodox bayesians in general to be my epistemic peers)

      • Fallibilism, Mr. Murali.  Charles Sanders Peirce [d. 1914] might be the only genuinely great American philosopher.  He also invented “pragmatism,” but when a lesser light, the pop-philosopher William James hijacked it, CS Peirce was obliged to rename his “pragmaticism.”

        Just as later pop theorists Dewey and Popper hijacked fallibilism.   Peirce [pronounced “purse”] also pioneered semiotics and I read a few years ago about some Vietnamese dudes turning his work as a logician into a computer circuit.

        I don’t pretend to understand even a fraction of this great mind, but I fancy that I can tell a great thinker from his epigones.  Everytime I read you, I think your road leads in his direction, if you set your horizon a bit farther out.

        Best regards, Mr. M.  Keep it up.

         

  5. While you have a sound theoretical case Murali, but that is not sufficient to impeach democracy in practice.  The real question is: can we design a rule to restrict the franchise that can survive the flaws of real political institutions?  I can’t see a way to make the answer yes.
  6. I’m probably betraying my profound ignorance here, but despite the logistics used in your post, does not Western civilization’s existence and success refute it?

    Much of your reasoning seems to depend on voters getting things right or wrong, as if every decision had such a clearly divisible set of outcomes.  Therefore it almost seems like testing your reasoning is dependent upon having very rigid, idealogical criteria.  (e.g.: You might assume that a tax rate of 17% is “right,” and any higher or lower is “wrong,” rather than assuming that 17% is just one choice of many that will have both positive an negative outcomes.)

    • You might assume that a tax rate of 17% is “right,” and any higher or lower is “wrong,” rather than assuming that 17% is just one choice of many that will have both positive an negative outcomes.)

      Thanks Tod, see my reply to Prof Hanley above. If alternatives have lots of reasonable arguments going for them, then clearly, the evidence we have is not remotely dispositive. We should be suspending judgement. If we have suspended judgement about all this stuff why the hell are we voting?

  7. After you start taking more than half of the fruits of my labor, as an American I start getting way pissed off.  I am the 99%.  Or the 53%, whathaveyou.

    Any taxation scheme over 33%, and you better start justifying it to me in a fishing hurry.  Over 50%, and you better not just collect the trash, you should take it down to the can whenever the wife tells me I gotta do it.

    Those are back-of-the-envelope calculations, mind you.  But I want value, dammit, not just a bill for somebody studying gay penguins.  I’ll study ’em—you take out the damn trash.

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