Vital Failures and the First Pillar: The Impossibility of a Democratic Social Welfare

Vital failures are tied to two types of objections: the impos­sibility of taking people's preferences as a reference for public action, underlined by Arrow (1950, 1951), and the ‘radical' objections to the effectiveness of public action of the kind raised by Lucas (1976).

The impossibility of a democratic social welfare function prevented the identification of a term of comparison for market failures. Without such a term of comparison, in fact, market failures could not be easily defined and identified.

This section is organised as follows. The first subsection is devoted to the axiomatic demonstration of the impossibility of a democratic social welfare function, i.e. to the conclusions derived on the basis of preconceived sensible requirements for the construction of social ordering starting from multiple individual orderings. In Section 2.4.2, I discuss the procedural aspects of this construction, involving voting mechanisms.

2.4.1 The Axiomatic Impossibility

In order to overcome the partial nature of Pareto orderings, Arrow (1951) took an approach that was different from that adopted by the proponents of the compensation principle (see Chapter 1). He tried to construct a complete social order­ing axiomatically by supplementing the Pareto principle with other widely accepted axioms having the nature of both ethical norms and procedures satisfying them.

For example, let us consider a set of alternatives a, b and c and suppose that all consumers prefer a to b, but some prefer c to a and others prefer a to c; similarly, some prefer b to c and some c to b. If we apply the Pareto principle, the unanimity of individual preferences for a over b allows us to construct a social ordering of a and b; in other words, society will prefer a to b. However, the Pareto principle does not allow us to order c with respect to a and b. Arrow attempts to construct a complete ordering by employing the Pareto principle with additional conditions that enable us to order Pareto-non- comparable states as well. These additional conditions can be expressed in axiomatic form. The normative content of the axioms used by Arrow is underscored in Mueller (1989: chap. 20). The axioms also have a procedural counterpart; i.e. there are voting procedures (majority voting, for example) that satisfy the axioms, as we will see in Section 2.4.2.

Take the weak version of the Pareto principle, which states that society must prefer social state a to social state b if all its members prefer a to b. In order to extend this ordering and make it complete and ‘rational’, it seems necessary (or reasonable) to supplement the Pareto principle with the following conditions:

1. An Unrestricted Domain Condition. The ‘rule’ for con­structing a social ordering out of individual orderings must be defined for all possible sets of individual order­ings. In other words, the rule for the social ordering of individual preferences holds whatever these prefer­ences may be, as long as each system of individual preferences is not contradictory.

2. An Independence of Irrelevant Alternatives Condition. In choosing between a and b, we must only take into account individual preferences with regard to those alternatives, ignoring individual orderings of other pos­sibilities. This hypothesis is introduced in order to economise on the information necessary for social ordering, but it also enables us to exclude insincere expressions of preferences made for strategic reasons.

Following Arrow, it can be demonstrated that with this set of hypotheses, the Pareto principle enables us to obtain a complete social ordering. However, this can only happen if the preferences of one individual are ‘decisive’; that is, if the choice of one individual determines society’s choice, regardless of the preferences of the other members of society (i.e. there is a dictatorship in determining social preferences).

The practical significance of this result is of considerable importance: the members of a community who wish to con­struct a complete social ordering satisfying the conditions of unrestricted domain and independence of irrelevant alternatives, as well as the weak Pareto principle, must necessarily accept the preferences of one individual regard­less of those of the others. Under these conditions, rejection of dictatorial choices makes it impossible to define a complete ordering that overcomes the partial character of the Pareto principle while still applying the principle itself. This is the Arrow ‘impossibility theorem'.^[25]

The outcome of Arrow's attempt to construct a complete social ordering put an end - with little or nothing to show for its efforts - to the scientific programme initiated by Robbins' (1932) essay. The attempt to direct welfare economics towards the exclusive study of problems of efficiency, separated from those of equity - and, thus, of values - was a failure.

2.4.2 The Procedural Impossibility

I have reviewed the main problems that arise in the axiomatic attempt to devise a social ordering based on individual pre­ferences. The axioms normally reflect value judgments, which may be more or less acceptable. This apart, the axiomatic approach is a purely logical exercise and apparently almost entirely ignores the procedures normally used in the real world to aggregate individual preferences, i.e. forms of voting.

This subsection shows that

1. Different procedural methods are based on different value judgments;

2.

3. It is difficult to construct a social ordering in a demo­cratic society.

Voting theory therefore enables us to extend the analysis of previous sections and look at it from a different point of view. Every voting situation presupposes a set of rules of varying complexity, each of which is the product of choices that have significant effects on the results of the vote itself. One group of rules regards the choice of who can vote and the number of votes each participant will cast; this calls for the same sort of interpersonal comparisons as those used in the axiomatic construction of the social ordering and for the selection of a dictator.

A second group of rules concerns the voting proce­dures and involves establishing

1. The proposals to be put to a vote (in particular, deciding who can formulate the proposals);

2. The voting procedure proper; this can be either a binary rule (in which pairs of alternatives are voted on) or a plurality rule (in which more than two alternatives are voted on simultaneously); and

3. The order of voting, which is important in cases where not all the alternatives are voted on at once.

The influence of value judgments in determining the proce­dure for formulating proposals is clear, but we will shortly see that they are also involved in the other procedures.

A final group of rules concerns the procedure for determin­ing the outcome of the vote; for example, we can choose between unanimous or majority voting. The degree to which individual preferences are respected in social choices differs in the two cases. In the two following subsections I will concentrate on the problems connected with this last group of rules.

To sum up, there are difficulties in constructing a social ordering in a democratic regime. They regard, in particular, (1) insincere voting for strategic purposes and (2) ‘multi­peaked’ individual preferences.

Political institutions nevertheless can be arranged in such a way as to reduce or even eliminate these difficulties by skirting the conditions under which they arise. For example, strategic voting can be reduced if participation in votes on specific alternatives is voluntary, which in practice limits the vote to people interested in those (and not other) alternatives. In addition, despite the existence of multi-peaked prefer­ences (which is often a consequence of the fact that choices are multidimensional), we can still apply the median voter theorem if voting regards ‘slates' of proposals, candidates or parties. What is more, while cyclical majorities can emerge from single votes, multiple votes on different questions might avoid them (see Ingberman and Inman 1988). I will not extend my analysis of actual political institutions here because I wish to keep this part of the discussion on a more abstract level. Such an analysis in any case lies within the domain of political science. The last forty years have seen the emergence of a new approach, the public choice school and political economics, which deal with the economic study of non-market decisions or, simply, the application of econom­ics to political science, as indicated earlier.

My objective so far has been to show that

1. All the procedures in the construction of a social order­ing through voting constantly reflect value judgments about the best action to take; these judgments lead to the selection of one or another of the possible alternatives and therefore benefit one or another of the members of society.

2. There is a correspondence between the value judgments underlying the voting rules and the conditions that make the aggregation of individual preferences possible.

3. It is difficult to define a social ordering in a democratic regime. It was shown that using either unanimous or majority voting rules as an aggregation procedure for individual preferences.

a. Does not guarantee that a well-defined social pre­ference will be expressed and

b. Can lead to different results depending on the cir­cumstances (in particular, on voting procedures); social preferences therefore can be altered by voters and/or those in charge of the voting if spe­cial measures are not taken to avoid this.

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