In the interest of completeness…
In, “A Paradox in the Theory of Democracyâ€, Richard Wollheim explains his paradox using a hypothetical example. He says:
“Let us imagine a citizen who feeds his choice for, say, A, into the democratic machine. On the present interpretation, he is to be regarded as thereby expressing his opinion that A ought to be enacted. And now let us further suppose that the machine into which this and other choices have been fed comes up with its own choice, and its choice is for B. How can the citizen accept the machine’s choice, which involves his thinking that B ought to be enacted when, as we already know, he is of the declared opinion, that A ought to be enacted? […] For if a man expresses a choice for A and the machine expresses a choice for B, then the man, if he is to be a sound democratic, seems to be committed to the belief that A ought to be the case and to the belief that B ought to be the case. […] If this is so, then the difficulty that I have described would seem to constitute a paradox in the very heart of democracy.â€
This is the essence of the paradox, but there are few questions that arise. What is the nature of the ‘democratic machine’ that decides the voting output? And what is the ‘present interpretation’ that Wollheim is referring to?
The ‘democratic machine’ is a hypothetical machine used by Wollheim to determine the results of his hypothetical votes, based on democratic theory. The machine is ‘programmed’ to take into account the values and precepts of democracy and, given a set of individual votes on different policies, churns out the ‘best’ policy. This automatically raises some more questions! Whose votes are put into the machine? And what does the ‘best’ policy mean?
Wollheim answers these questions in his article, starting with some definitions of Democracy. He differentiates between what he calls the ‘Democracy of Antiquity’ (he attributes the invention of Democracy to the Greek, Cleisthenes) and the ‘Democracy of the modern world’. The Democracy of Antiquity is defined by Wollheim with reference to other forms of government with a parallel structure; Aristocracy, rule of the best; Oligarchy, rule of the few; Plutocracy, rule of the rich; And Ochlocracy, rule of the mob. Democracy, then, is the rule of the ‘demos’. In Greek times, the ‘demos’ were a specific group of people just like the ‘best’ the ‘few’ and the ‘rich’. They were the populace, or in other words, the poor people. In all of these cases, the government was controlled by a determinate group of people. In contrast, the modern day Democracy defines the ‘demos’ as the people as a whole so that government is made up of a cross-section of the population as opposed to a specific group. To put it more concisely Wollheim says,
“…In both cases Democracy is the rule of the people; but in the classical theory the people is identified with a section or part of the population, whereas in modern theory the people is identified with the population as a whole.â€
So which does Wollheim choose for his ‘democratic machine’? The problems that arise from having the whole population as the governing body is two-fold; size and diversity. It would be physically impossible to get the entire population to come together to decide legislation and even if they did, the diversity would prevent them from coming to any sort of uniform agreement.
Wollheim argues that returning to the Greek conditions, which would include down-sizing the population which would in turn lead to uniformity, is not preferable. He says “the restriction upon population is Utopian: and the ‘true’ or ‘real’ uniformity that it advocates is worthlessâ€. However, he also acknowledges the problems relating to the modern democratic process. He manages to circumnavigate these issues by redefining the term “rule of the peopleâ€. He says,
“If modern theory insists that in a democracy the people in the sense of the whole population, not just a section of the population, should rule, it also insists that the people should rule in the sense not of devising or initiating legislation but of choosing or controlling it. And the significance of this is that it permits a people to rule despite its size and diversity.â€
We are now a little closer to understanding the nature of Wollheim’s ‘democratic machine’ since we know that the whole population will vote and that they will choose between policies rather than devising them. However, before we can fully understand the ‘machine’ and subsequently, the paradox, we must know the process by which the ‘machine’ chooses the ‘best’ policy. Wollheim acknowledges this saying, â€â€¦For legislation to be said to be by the people, it must stand in some positive relation to what the individual citizens would like legislation to be like. How is this relation to be characterised?â€
It is common practise for democratic legislation to be decided by a majority rule so that it ‘concurs with what the majority of the population would like’ and ‘it is enacted because of this concurrence’. Wollheim argues that majority rule, both absolute and simple majority, are inadequate processes for deciding legislation. He gives an example to illustrate his point.
“Let us suppose that there are three policies from which the population must choose: A, B, C. Forty per cent choose A., 35 per cent choose B, and 25 per cent choose C. On the simple majority principle A is selected. However, those who choose B prefer C to A, and those who choose C prefer B to A. In the light of this information, it is far from clear that A is the right selection if democratic rule is to be observed. For 60 per cent prefer both B and C to A.â€
Wollheim’s objection to absolute majority rule is that when there is a big range of policies to choose from, no absolute majority is reached. In our example, how would one apply the absolute majority principle since not one of the three policies has an absolute majority? It not always clear, says Wollheim, which policy should be enacted if we only take into account the first choice of the citizens in a population. He argues that the system must consider the whole ‘preference-schedule’ of the individual citizens, i.e. an individual’s position on a certain issue or policy is more complicated than one vote and a true democratic system should reflect that.
Having recognised that his ‘democratic machine’ must include some lower level consideration of individual’s needs, Wollheim suggests that his machine uses a system which, ‘would allow us to derive what might be called the “democratic choice†from the ordered choices of preference-schedules of the individual citizens’. In this way, it would be a more representative majority rule, than that of absolute or simple majority. This ‘function’, as Wollheim calls it, is the key to his ‘democratic machine’; ‘a method or rule for going from individual choices to some specific legislation such that we can justifiably call the enactment of that legislation an instance of democratic rule’.
After putting forward this ‘function’ of democracy, Wollheim then acknowledges that, in his “Social Choice and Individual Valuesâ€, Kenneth Arrow proves that it is ‘impossible to construct a function that satisfies certain intuitive criteria’ and more specifically that this Impossibility Theorem applies to Wollheim’s suggested function. Surprisingly, Wollheim does not attempt to refute this proof and instead chooses to ignore it with the intention to assume that ‘the problem of aggregation has been solved’. This may be important when discussing how to resolve the paradox but it is clear that Wollheim does not believe it to be a foundation on which the paradox rests.
Returning to our original questions, we now understand the nature of Wollheim’s ‘democratic machine’ more fully. The ‘ruling people’ is comprised of the entire population and not a specific section and the process, which determines the outcome of the vote, is based on Wollheim’s function that calculates a majority opinion based on preference-scheduled individual choices. This means that any citizen committed to Democracy will also be committed to the choices made by Wollheim’s machine. Yet it is still not clear what is meant by “the present interpretation†of a democratic voter.
Wollheim suggests two possible definitions of a voting citizen, both of which he believes are plausible, yet the paradox only arises with one of them. The first defines a voter one who makes choices as expressions of want while the second categorises the voter as one who is expressing an evaluation. In the first case, the voter would declare, “I want policy A to be enacted†whereas the latter voter would declare, “Policy A ought be enactedâ€. In the original example, when talking about ‘the present interpretation’, Wollheim is referring to the ‘evaluation voter’. Elaborating on the definition he says,
“…When the citizen chooses a certain policy or prefers one policy to another, he is expressing not a want but an evaluation. He chooses A or prefers A to B, because he thinks A is the best policy, is the policy that ought to be enacted […] not because he wants A more or needs it more than B.â€
The other definition will be tackled later when trying to resolve the paradox but for now it is only important to understand the definition of a voter that Wollheim is using in the original example. Let us now revisit Wollheim’s Paradox!
Wollheim asks us to imagine a democratic citizen who chooses to vote for policy A. Using his definition, the citizen believes that policy A ought to be enacted. As it turns out, the ‘democratic machine’, which has processed the entire populations votes, has made its own choice, that of policy B. By virtue of being a democrat, the citizen is committed to accepting the choice of Democracy (i.e. the democratic machine) as well. To put it even more formally, policy B is the equivalent of NOT policy A. Therefore, our democratic citizen believes that policy A ought be enacted as well as believing that NOT policy A ought to be enacted. Herein lie the contradiction and the paradox.
How is it to be resolved?
Wollheim suggest four ways in which the paradox might be broken. Firstly is by denying that the citizen is committed to the belief that A ought to be enacted. Secondly is by denying that the citizen is committed to the belief that the machine’s choice (i.e. policy B) ought to be enacted. Wollheim argues for and against both these ideas yet is ultimately not convinced by either. His third way is to accept the paradox and ‘consign it to the flames’, but Wollheim ‘doubts that any of us are prepared to regard Democracy as inconsistent’. His final way, to which he dedicates the rest of his article, is to argue that there is no contradiction and that our definitions of a voter and a democrat are in fact compatible with each other. He admits that his argument for this is rather sketchy, but first we turn to his two plausible yet ‘ultimately unacceptable’ arguments.
The first argument rests on the idea that the citizen’s evaluation is not complete until the machine has administered its ‘choice’. Before the machine gives its verdict, the citizen may be committed to policy A. This would be an interim commitment to policy A. Once the machine’s verdict has been cast, the citizen now has extra information available to him that could affect his evaluation. The preference for policy A is hypothetical and it may or may not change given the verdict of the machine. Wollheim states it as, “I think that A ought to be enacted, provided that other people, or enough other people, are of the same opinionâ€. It is only after the people have spoken that the citizen can make his final evaluation, which in light of the machine’s choice, he now changes to B. The citizen is now able to commit himself to policy B without fear of contradiction since he was only committed to A up until the moment when he had reason to believe that B ought to be enacted, i.e. as soon as the machine had expressed its choices. “The man, in other words, withdraws his support from A and gives it to B,†says Wollheim.
As has been said, Wollheim believes this argument is plausible to some extent but not enough. He says it’s not correct to define people’s input into the machine as interim or hypothetical since that is not the way that people vote. He uses the example of a man who votes Liberal, who knows full well that only a small minority of the population will vote for. We may disagree with his behaviour, says Wollheim, but we do not consider his actions irrational. It is a perfectly legitimate and principled way to vote. However, according to the interim definition the man is saying “I want a Liberal policy to be enacted if enough other people are of my opinion’ even though he knows that there will not be enough people of his opinion. This clearly does seem irrational and for this reason it would suggest that Wollheim is right in arguing that this new ‘interim’ definition is incorrect because it just isn’t the reality of how all people vote.
Another reason Wollheim rejects this redefinition is because it suggests that the citizen’s decisions on policy are not simply based on which policy he prefers but also on what policies other people prefer:
“The citizen who votes for A cannot, without further qualification, be understood as expressing a view that A ought be enacted if enough other people think so: because he may well be of the opinion that whether A ought to be enacted or not is in some sense or other independent or what other people think.â€
He goes on to say that democracy actually requires us to make our choices independent of others; otherwise the determinate results are unrepresentative and meaningless.
“Indeed, it would seem that democracy not merely allows but positively demands that our political preferences have a certain consistency to them and they do not fluctuate with the preferences of others. In other words, when the machine’s choice has been declared and we have given our adherence to it, there is a sense in which we still do and should stand by our original choice.â€
Wollheim admits he does not know why we should have this sense of principles. It seems that in practice, a voter will stay committed to the policy they voted and will not be affected by the outcome of the vote.
In a final attempt to argue against this denial of a constant commitment to the belief that policy A ought to be enacted, Wollheim first supposes that we allow that the citizen’s choices are really hypothetical. Even if they were, says Wollheim, why does this give their final evaluations more authority? Since when does the fact that other people agree with you give your belief any more weight? Why is this a privileged condition? Wollheim rejects this argument because it does not properly encapsulate the definition of democracy. There is no reason why “other people agree with me†should have any special prestige when deciding matters of policy. He says, “if the vote for A is interpreted as ‘A ought to be enacted if enough people are of the same opinion’, and the voter is prepared to switch to support B if enough people are of that opinion, it is obvious that ‘A’ as it appeared in his original vote was a variable, not constant.†One would agree that believing policy X ought to be enacted, where X is majority opinion, is very different to believing policy A ought to be enacted, where A is a specific policy. As it stands then, it seems that we are still committed consistently to the belief that “policy A ought to be enactedâ€.
The next commitment to come under attack is the commitment to the belief that policy B ought to be enacted (i.e. the policy that the machine has chosen democratically). Democracy, according to the argument, is government by compromise. In which case the democratic machine would choose a policy that it would be ‘wise or prudent to follow, not a policy that the citizen ought to follow’. The subtle difference is to do with authority. In the previous definition, the policy that the machine chose would be authoritative and everyone would have to follow it regardless of how they voted. In this, perhaps ‘weaker’ definition, the machine merely says what it thinks is the best policy based on the population’s input without mandating anyone to follow it. “The functioning of the democratic machine,†says Wollheim, “influences one’s behaviour, actual and potential: what it does not do is increase one’s obligationsâ€.
Wollheim’s objection to this argument is that, although plausible, it lacks conviction. He argues that if there is no obligation on the voter then people will start to support given policies for tactical and prudential reasons. He gives an example,
“Suppose that our choice is for A and that of the machine is for B. Then if our support for B were purely tactical or prudential, we should surely be content if the B government were somehow outwitted and they found themselves, contrary to their own inclinations but with the continued support of their electors, putting through policy A.â€
It seems that this sort of regime would render the idea of Democracy meaningless. If it is possible for government to enforce a policy, which the people did not vote for, then what authority does the vote have in the first place?
Wollheim goes on to differentiate between the true believer in Democracy and the one who follows democratic results for purely prudential or tactical reasons. Both have a disposition to accept democratic results yet the distinguishing feature, says Wollheim, is the reason that each has for his acceptance. “The genuine believe in Democracy is disposed to accept the successive choices of the democratic machine because he believes that what the democratic machine chooses ought to be enactedâ€. If this is the case, it seems that our ‘weak’ function of the democratic machine cannot be used and the paradox still stands.
Wollheim’s final attempt to break the paradox begins with a self-admittance that the argument is ‘sketchy’ and that his support for it as an argument is ‘disappointing’. However, in the interests of completeness, it shall be discussed here.
The initial premise is to suggest that there is in fact no contradiction between the statements ‘A ought to be enacted’ and ‘B ought to be enacted’. Wollheim argues that compatibility comes from realising that the statement in each case is being used in a different way. Once we understand their separate meanings and subsequently the context in their respective statements, we shall see how they are compatible.
Wollheim puts forward the distinction between direct and oblique moral principles. Examples of direct moral principles, given by Wollheim, would be; Murder is wrong, Birth control is permissible, while examples of oblique moral principles would be; What is commanded by the sovereign ought to be done, or What is willed by the people is right. It is Wollheim’s belief regarding the two seemingly incompatible statements above is that one is derived from a direct moral principle while the other is derived from an oblique one. From this point on, the argument becomes vague. Wollheim doesn’t say which statement is the direct one and which is the oblique. The only support he gives for his hypothesis is in the form of counter-arguing what people might say about his claim. The argument on the whole seems unconvincing and unsupported and Wollheim himself admits that.
When discussing the definition of a voting citizen, Wollheim put forward two definitions and strongly advocated one over the other. He claimed that when people voted, they were voting based on their evaluations rather than on their wants or desires. However, is this necessarily true? If we understand a voter as voting on their desires (i.e. “I want policy A to be enacted) then the paradox is no longer apparent. A voter can still desire policy A even if they believe that policy B should be enacted. In this case, the voter has consulted his principles (his belief in the principle of democracy) once the vote has been cast and has not again consulted his desires. “All he needs to be certain of is that his principles and wants, thought they may lead in different directions, are not actually inconsistentâ€.
Wollheim wasn’t happy with this definition of a voter but perhaps it offers us a way out of the paradox without accepting that Democracy is inherently inconsistent. A pragmatist may argue that it doesn’t matter if Democracy is inconsistent or not, the more important issue is whether a society can run effectively on such a system, even if it’s not the ideal system. As Winston Churchill famously said, “No one pretends that democracy is perfect or all-wise. Indeed, it has been said that democracy is the worst form of government except all those other forms that have been tried from time to time."