Collective coherence?☆

Collective coherence?<

Geoffrey Brennan*

Research School of Social Sciences, The Australian National University, Canberra ACT 0200,Australia

Accepted 5 July 2000

1. Introduction

Within the rational actor tradition, at least as it is generally applied in economics andthe various associated applications of the economic method in political and socialanalysis, rationality is axiomatically an attribute of individuals. Whether or notgroupsof individuals are “rational” or can properly be thought of as being rational in the samesense, is at best a contingent matter. In fact, a great deal of rational actor analysis dealsprecisely with this issue. Within rational actorpolitical theory specifically, considerableattention has been focused on two particular aspects. The first relates to the possibilitythat individually rational action might produce collective results that are inimical to theachievement of the individuals’ goals. The prisoners’ dilemma is the most familiar, aswell as the neatest, articulation of this possibility. The second aspect concerns thequestion of whether any procedure for aggregating individuals’ preference/values cangenerate a satisfactory “aggregate preference.” This aggregation question is the focus ofArrow’s famous “impossibility theorem” and the substantial literature in “social choice”analysis that Arrow’s theorem has spawned.

At least in the most common expositions, both of these aspects appear to connect to thenature of individuals’preferences.In the prisoners’ dilemma case, for example, if theparticipants weigh the aggregate interest appropriately heavily in their preferences, theyseem likely to choose to act in each others’ interests and the characteristic “dilemma” seemscorrespondingly less likely to arise. In this sense, at least in the more standard applications,

< An earlier version of this paper is to be published in Guido Pincione and Horacio Spector (Eds.),Rights,equality and liberty. Dordrecht: Kluwer, 2000.

* Tel.: 161-612-62-49-3411; fax:161-612-62-47-8522.E-mail address:[email protected] (G. Brennan).

International Review of Law and Economics 21 (2001) 197–211

0144-8188/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved.PII: S0144-8188(01)00056-4

the prisoner’s dilemma seems to depend on the assumption of predominant self-interest.1

Equally, if individuals’ preference/values have appropriate properties (as captured, forexample, in the Plott (1967) conditions), then the Arrow problem disappears—as does theprospect of global cycling under majority rule [see McKelvey (1979)]. The fact that theprisoner’s dilemma and the Arrow theorem can be avoided by appropriate restrictions onagents’ “preferences” may encourage the conjecture that the sorts of collective actionproblems with which normative analysis in rational actor analysis has traditionally beenpreoccupied, are an artifact of the motivational assumptions used. In particular, it might bethought that if only one could persuade economists to jettison their implausibly extremepresumptions of individual egoism, most of the alleged “problems” of collective actionwould disappear.

In this paper, I want to raise doubts about any such conjecture. I want to focus attentionon the rationality of collectivebeliefs in a setting in which conflicts among individuals’interests are explicitly ruled out. The points I shall make are analytically simple and, onceseen, obvious. Yet they seem to me to be potentially important, both in broadening the scopeof collective action concerns and in formulating those concerns in a way that might attractattention from political theorists whose presumptions and style of argument are distant fromthe economistic tradition.

Let me put my object here in a slightly different way. Those who see themselves asadopting the ‘forum’ as distinct from the ‘market’ conception of politics—to use Jon Elster’snice categorization [see Elster (1986)]—seem often enough to treat the concerns of those inthe ‘market’ tradition as irrelevant to their own concerns. After all, rational actor politicaltheorists are often at pains to distinguish themselves from those who conceive of politics asa quest for “the good, the true, and the beautiful” [see, for example, Buchanan (1986)] andit may be tempting for those whodo conceive politics in such terms to think that a‘preference-based’ account of political process has nothing of interest to say to them. Theargument in this paper is meant to address those so tempted. In particular, I want to addressthose who are disposed to a conception of politics in which political debateis conceived asa quest for the truth, in which political agents are taken to be motivated to secure that truth(perhaps under appropriately idealized conditions of “ideal speech”) and where the central

1 This remark raises an issue concerning the definition of the prisoner’s dilemma. The payoffs for the playersassociated with the various outcomes can be variously understood—as objective magnitudes [such as years inprison, to take the classic case]; or as subjective valuations of those outcomes. The former are identifiable featuresof the interaction; the latter are the subjective features which determine the participants’ behavior. Typically,economists are inclined to collapse the two by the assumption that each player acts so as to maximize privateobjective return—for example, minimize the number of own years in prison. But if there are altruistic connectionsbetween agents, then there is some mapping between objective and subjective payoffs and it is possible that aninteraction that has the objective structure of a prisoner’s dilemma will not have that logical structure at thesubjective level—and vice versa. Clearly, it is a purely terminological matter whether the prisoners’ dilemma isdefined in objective or subjective terms. If, as here, the definition used is in terms of objective payoffs, thenaltruism or collective sentiment of various kinds seems to offer a possible escape from the dilemma. And casescan indeed be found where that escape-route works. However, this is not to claim that the pd cannot arise underaltruistic motivations. Nor is it to deny that in certain contexts, it may be better to define the prisoner’s dilemmain terms of its underlying behavioral structure than in terms of objective payoffs.

198 G. Brennan / International Review of Law and Economics 21 (2001) 197–211

object of institutional design is to secure an appropriate discursive environment within whichthis truth can be pursued. I want to show first, that Arrow-like problems can arise under nottoo implausible conditions within this “forum” environment, and secondly, that arrangementsthat might encourage a shift from market-style to forum-style politics may alter outcomes ina direction that is undesirable.

2. Rationality

In the “thin” theory of rationality now more or less standard in economic analysis, anagent is rational if his actions are such as to best promote his objectives, given his beliefs.This notion derives from Hume via Davidson, where the primary notions are “belief,”“desire,” and “action,” and where rationality refers to the relation between action and desire,subject to belief. Within economic applications, the main analytic focus is on the (assumed)structure of preference/desire: beliefs typically play a background role, where indeed theyplay any role at all. It is, though, taken as given that beliefs are “coherent,” by which I meanobedient to the laws of logic. So, for example, ifa, b andc are propositions such that

a ∧ bN c (1)

then belief thata is true and thatb is true compels belief thatc is true. At least on the faceof things, failure to adhere to the simple requirements of logical coherence in one’s beliefstructure would seem to disqualify any agent from the ascription of rationality. [In fact, itmay well be that this simple requirement is too strong—for reasons that I shall entertainbriefly at the end of this paper. However, those reasons do not weaken the force of theargument to be developed here and it is simpler to develop that argument within the standardlogical scheme.] On this basis, we can proceed as if a necessary condition for rationality isthat the belief structure of a rational agent accepts logical entailments—and we shall, exceptwhere otherwise stated, assume that that test is met fully at the individual level.

It is, however, (almost immediately) self-evident that collectives can routinely fail that testunder any decision-rule short of unanimity. That is, a group can (under the given rule forgroup belief) “believe”a and “believe”b, but not believec, wherea, b andc have (and areuniversally accepted to have) the logical connection shown in (1). The object of this paperis to support this simple proposition and discuss some of its implications.

3. A simple example

You are a member of the board of a company. As a conscientious member, your objective,like that of the other board-members, is to maximize company profits. In that sense, there isno conflict between board-members’interestsat stake in the board’s decisions. The issuebefore the board is whether to embark on some new venture. Whether that new venture willbe profitable or not depends, we suppose, on two and only two considerations: whethercompetitors will enter the new market within two years; and whether there will be strike

199G. Brennan / International Review of Law and Economics 21 (2001) 197–211

action over that two-year period by a relevant union. All board-members are agreed that ifthere is no entry (propositiona) and if there is no strike (propositionb), then the firm shouldproceed (propositionc)—but only if there is no entry and no strike. Simply put,

a ∧ bN c.

There is however some measure of disagreement among the board.Youhappen to believebotha andb: the union has been quiescent recently, and none of the obvious competitors isanything like as far along in the development of the product line as your firm is. So you thinkthe firm should proceed. But one of your colleagues (denote him Y) believes that some rivalcompanywill enter. He is a Chicago-trained economist and is inclined to the view that ifentry were a good idea, someone else would be likely to have thought so too. The otherboard-member, Z, agrees with you that competitors are unlikely to enter: she believesa. Butshe is always twitchy about the unions, and reckons that a strike is more likely than not. Shedisbelievesb.

Consider on this basis the beliefs of the “majority.” Clearly, a majority believesa; and amajority believesb. If the “majority” is coherent, then it must believec. But a majority doesnot believec. Both Y and Z will be against proceeding. So simple majority rule overactionwill produce a decision against entry, despite the fact that the majority’sreasonsare in favorof entry. The simple explanation is that, though a majority believesa and a majority believesb and a majority believes ‘not c’, it is not the same set of persons who compose the majorityin each case.

4. A legal example: justice or doctrine?

If the foregoing example is unpersuasive, consider the following ‘case’—familiar as anexample of this phenomenon to at least some legal academics. [See in particular, LewisKornhauser (1992), Kornhauser & Sager (1993) and, more recently, Chapman (1997)] Abench of three judges must decide a breach of contract suit. There are two questions at issuein this suit: was there a genuine contract (propositiona)? and if so, was there a breach(propositionb)? If and only if both, then one should find for the plaintiff—the defendant isliable (propositionc). The structure of belief is as follows:

Mr Justice X believes there was a contract, and a breach.Mr Justice Y believes that, if there had been a contract there would have been a breach,but that there was, in fact, no contract.Mr Justice Z believes that there was indeed a contract, but that there was no breach.

There is a majority view on the bench for the defendant—both Y and Z will find againstthe plaintiff. But there is no majority view onreasonsfor the judgment. Perhaps finding forthe defendant is the just outcome; but one cannot come up with reasons that satisfy amajority. In this sense, justice and doctrine are at odds (hence the title of this section). If onefollows the majorityreasons,one gets a minorityoutcome,and vice versa.

For one who believes in the significance of coherent doctrine [Chapman (1997) seems to


be in that camp, for example], it is important to follow the logic of the collective reasons.Moreover, one can ensure that this logicis followed, by appropriate structuring of thedecision-making process. Specifically, suppose the court is required to judge on the questionsseparately. Then a majority decision will find that thereis a contract; and then, at the nextstage, that therewasa breach; and thereby find for the plaintiff. But this decision will leavetwo of the three judges believing that justice has not really been done—though they will, ofcourse, believe that justice has not been done for different reasons.

There are, it seems to me, three possible responses to this situation. On the one hand, onemight insist that the idea of rationality carries with it the idea that decisions should bedrivenby reasons, and hence the majority’s reasons should decide the case. (This seems to beChapman’s view, for example). On the other hand, one might argue that the critical issue hereis to get the “right decision” and that the judges’ collective judgment on the proper outcomeshould prevail. Or as a third possibility, one might be agnostic on the right outcome and seethe moral of the story to be that the very notion ofgrouprationality is incoherent in general,or at least deeply problematic in lots of plausible cases. Under either of the first twointerpretations, one will have views about the proper procedures for the court’s decision-making processes. Under the latter interpretation, one will be agnostic about that aspect aswell.

5. The general formulation: the distribution of belief

It is easy to see what critical feature these examples share. This feature can be neatlydepicted in terms of a “matrix of belief” as shown in Fig. 1. The entries in the matrix showthe numbers of persons who believea, banda ∧ b; rows reflect beliefs in propositiona, andcolumns beliefs in propositionb.

The individuals whose beliefs are represented in this matrix are all entirely rational in thesense that each individual holds coherent beliefs. The row and column “totals” show theaggregate pattern of beliefs with respect tob anda respectively. Accordingly,b is held trueby a 2:1 majority; and so isa. But a ∧ b (that is,c) fails by a 1:2 majority.

Of course, the same aggregate pattern of belief ina andb could arise without any logicalinconsistency. This would happen if the Matrix of Belief took the form indicated in Fig. 2—that is, if those who believeda also happened to believeb.

Fig. 1.


The essential difference between Figs. 1 and 2 is that, whereas in 1 the reasons forbelieving;c (“;” designates “not”) are distributed across different persons (one believes;a, another;b), in Fig. 2 those negative reasons happen to be concentrated in the sameperson. Is there any reason to think that one or other distribution of (dis)belief is somehowmore authoritative than the other? I am inclined to think not. After all,a and b areindependent propositions (inboth examples): reasons for believing;a are not in generalreasons for believing;b. It could be an essentially random matter whethera ∧ b getsmajority support or not. If that is so, then we have as much reason to rejectc when the patternof support illustrated in Fig. 2 prevails as when that illustrated in Fig. 1 prevails. There seemto be no good grounds for thinking that the reasons for;c oughtto be concentrated in oneperson (or set of persons). Given the general principle of reliance on individual judgments,it seems to me that the pattern in Fig. 1 provides us with reasons for rejecting c that arecertainly no less compelling than our reasons for acceptinga and b. We seem to beconfronted here with a simple paradox.2 Or if not a paradox, then at least a puzzle. At thevery least, there is an issue here that needs to be acknowledged—namely, that the coherenceof collective beliefs is problematic.

6. Decision rules and logical structures

The matrix of belief formulation should make it evident that collective irrationality of thiskind is not a function of the decision rule—except in the limiting case of unanimity.Suppose, for example, that the decision rule in a particular setting (let it be a jury trial)requires a majority of eleven out of twelve in order for the collective judgment to beauthoritative. Suppose further that the case before the court is a murder case. The accused isguilty if and only if he both had the intention (propositiona) and actually did the deed(propositionb). It may be that ten persons believe botha andb, but that one believes;a and

2 In fact, I shall indicate below reasons derived from an analogy with an individualized version of a similarproblem, that suggest that we ought to rejectc, notwithstanding the support for the underlying reasons. However,I am not entirely persuaded that appeal to this analogy should be decisive.

Fig. 2.


one (other) believes;b. The weight of belief is such that a relevant supermajority cannot befound to sustain conviction, even though the jury “believes” both intention and causalefficacy according to the relevant 11:1 test. The corresponding matrix of belief is shown inFig. 3.

Of course, in the limiting case of unanimity, the properties of individual belief must carryover to the properties of collective belief: it is only possible for all to believea andb if eachdoes. And if all believea andb, they will all believec as well. But short of the knife-edgeunanimity case, more inclusive decision rules do not obviate the problem.

It should also be noted that, though all our examples so far have proceeded on the basisof a dual requirement (the logical “∧”), there is no loss of generality in taking that case.3

Consider instead the range of situations in which the logical connection at issue is:

a ∨ bN c

It is straight-forward in this setting to develop examples in which the outcome receivesmajority endorsement while a majority rejects both of the reasons for that outcome. Forexample, suppose in a meeting of the Cabinet in some distant potentate, the issue is whetherto declare war on a neighboring state. There are two relevant considerations, either of whichwould (on the basis, we suppose, of an entirely agreed conception of the public interest)justify doing so. The first of these considerations is that if war is not declared, the domesticArmy will attempt a coup—which may be successful and would in any event causewidespread bloodshed. The second is that the neighboring state will attackus and have theadvantages both of surprise and of conducting the war on our territory, with the attendantdestruction borne disproportionately by our citizenry thereby. Of the ten-person Cabinet,three believea will occur; three others believeb will occur. The remaining four believeneither will occur. No-one believes botha andb. There is then a seven to three majority whodisbelieve each possibility. But there is a six to four majority in favor of war. Again, amajority rejects each reason for war; but a majority equally accepts that war is desirable onthe basis of these reasons. (The relevant matrix of belief is shown in Fig. 4.)

3 Indeed, this follows directly from the equivalence of [a ∧ b] and ;[;a ∨ ;b]. Kornhauser (1992) alsomakes this point.

Fig. 3.


I conclude from these examples that the “paradox” of collective belief is not a matter ofa particular instance of logical entailment, only of the possibility of differing majoritycomposition. And the paradox depends not on properties of simple plurality, but can arisewith any ‘supermajority’ short of complete unanimity.

7. A mouse; but is it Arrow’s mouse?

There is a question as to whether the possibility of collective incoherence in belief is not(just?) an instance of Arrow’s impossibility theorem in disguise. After all, although theArrow theorem is articulated in terms of rival valuations of social states, and gestures atdifferences in individuals’ preferences or values as being the source of the “collectiveirrationality” problem, it would presumably be possible to interpret the objects of decision ascollectiveactionsand the source of differences to lie in different beliefs about the conse-quences of those actions (and precisely not conflicts among individual values or interests).Under such an interpretation, we ought to expect incoherence of collective beliefs to ariseroutinely in the way that intransitivities in collective orderings do. In particular, it is possibleto formulate our ‘paradox of belief’ in terms of the familiar ‘cycle’ over social states, by theexpedient of treating the relevant propositions,a, b, and c, as beliefs about the ethicalsuperiority of different social states. Let the states in question be denoted S1, S2 and S3.

Let a be the proposition: S2 is better than S1;and letb be the proposition: S3 is better than S2.The propositionc is then: S3 is better than S1.

Suppose there are three agents, X, Y and Z. Suppose that the structure of belief is asfollows. Agents X and Y (but not Z) believea; and X and Z (but not Y) believeb. Then withthe matrix of belief in Fig. 5, we can certainly generate the outcome that a majority does notsupportc. Specifically, Z and Y do not supportc : Z because he does not believea, and Ybecause he does not believeb. There is no appeal here to the differentinterestsof agents X,Y and Z. What distinguishes them is not their different interests but their different beliefsabout what states of the world would be ‘best’ according to some commonly held ‘real’ valuescale.

Fig. 4.


Logically,

a ∧ bf c

However, no such logical implication is entailed by majoritarian belief. Note that wecannot conclude that Z and Y willreject c: this example is not one where [a ∧ b] is logicallyequivalent toc [in particular,c does not implya or b]. The conclusion in this example is aslightly weaker one—namely, that majority belief ofa andb does not, as pure logic woulddo, requiremajority belief ofc. However, to generate the case where a majority believes;cwould require that X believe that the social states should be ranked [S3 . S2 . S1]; and Ybelieve that the social states be ranked [S2 . S1 . S3]; and that Z believe that the socialstates be ranked [S1 . S3 . S2]—exactly that constellation of rankings that generates thefamiliar intransitivity result.

However, to say the collective incoherence in belief structure can be formulated togenerate collective intransitivity of a more familiar kind (at least of a kind more familiar ineconomist circles) is not to say that the two are mere versions of the same problem; or thatthere is nothing to be gained by the ‘belief’ formulation. Although it seems likely that, atsome structural level, paradoxes of collective values and paradoxes of collective belief owetheir origin to similar features, I have not attempted here to indicate precisely what analoguesto the various Arrow conditions would make sense in the domain of beliefs4 or, moregenerally, to demonstrate conclusively that there is an impossibility theorem on hand exactlyanalogous to Arrow’s. I simply gesture at what I see as an obvious connection.

8. Or perhaps Condorcet’s mouse?

In some ways, the nature of the context envisaged here is probably closer to Condorcetthan to Arrow.5 Specifically, Condorcet seems to take a realist view of the public interest,believes that people will vote according to their perception of that public interest, and

4 For an attempt along such lines see C. List & P. Pettit (forthcoming). See also Pettit (2001).5 This is an impression gleaned from reading the McLean/Hewitt (1994) edition of Condorcet writings.

Fig. 5.


believes that on average voters are more likely to be right than wrong in their assessment ofit. Condorcet’s famous jury theorems are built on these presumptions. Those theoremsconstitute a defense of institutions that involve larger numbers of independent decision-makers. The central idea in those theorems is that the larger the number of such decision-makers the smaller the probability that the majority decision will be the wrong one. If theprobability that a randomly selected agent is right in choosing among two options [as Iinterpret it here, two propositions] is greater than 50% then the probability that the majorityof a sample ofn is wrong goes to zero asn becomes indefinitely large. If Condorcet’s concernwith isolating Condorcet winners in complicated cases is seen through the lens of his jurytheorem rather than as an independent area of enquiry, then the issue of majoritarian cyclesis to be interpreted as an issue in a forum/belief conception of politics rather than in themarket/preference conception which modern public choice scholarship has brought to Con-dorcet interpretation.

On this reading, the critical object of the whole Condorcet project is the development ofa kind of democratic theory of truth. A necessary element in that argument is that the averageindividual is more likely to be right than wrong on any proposition—that the parameterp isindeed greater than1⁄2. It is this premise that allows Condorcet to induce likely truth valuefrom the extent of support. What follows, however, from the existence of a majoritarianirrationality problem of the kind examined here, is that this premise cannot be right, ingeneral. For suppose it were true. Then majority support gives us decisive reason to believea and b. And enlarging the size of the decision-making body will make it asymptoticallycertain that propositions a and b are endorsed. But exactly the same reasoning gives usequivalent grounds for rejecting [a ∧ b] (5c). Furthermore, even if majoritarian irrationalitydoes notarise—that is, even if the pattern of beliefs happens to follow that in Fig. 2 ratherthan Fig. 1—the fact that Fig. 1mightarise, that it cannot be ruled out by logic, suggests thatCondorcet’s epistemological system is strictly incoherent. Whether or not the threat ofinconsistencies of the type isolated here is sufficient to undermine the Condorcetian approachand indeed just how deeply that threat bites is a matter that needs more extended discussion.I shall hint below at some of the considerations that seem likely to bear in such a discussionbut will not engage a more extended analysis here.6

9. Institutional restriction and agenda manipulation

As we noted in Section 3 in connection with the legal example, paradoxes of the kindunder discussion can be resolved in one direction or the other by institutional rearrangement.In the legal example, the outcome of the decision-making process will be driven bymajority-held reasonsif decision on the component parts of the judgment is requiredseparately. More generally, those institutional arrangements that support reliance on the

6 It should perhaps be noted here that the recent spate of papers on jury theorems [for example, Austen-Smith& Banks (1996) and Fedderson & Pesendorfer (1998)] are directed at different aspects of the jury-theorem logicthan those on which we focus here.


provision of coherent argument—what we might think of as the institutions of specificallydeliberativemodes of decision-making—will serve to support logical entailment againstsubstantive judgment [that is,a andb andhence c,as against;c in the initial example]. Thisfact means that institutional choice constitutes a possible source of agenda manipulation,somewhat similar in effect to the kind of agenda manipulation familiar from the majoritycycling literature [McKelvey (1979) for example].

A simple example may be helpful here. Suppose, for the sake of argument, that you area conservative reactionary—you wantall proposals to fail. There are two sorts of policies:those that depend on a number of independent factors being simultaneously in play (the “∧”case); and those that depend on any one of a number of independent factors being in play (the“∨” case). In the first (∧) case, you will want to support an action posture. You will want tomove to the vote, and background the reasons. In the second (∨) case, you will want to insistthat the collective decision-making process be guided by “reasons,” and let the outcomefollow from those reasons. In the first case, you will seek an immediately “political” solution.In the second, you will want to have the matter referred to a Committee of Enquiry, toproduce a “considered Report” to the government/parliament.

Of course, all this would be reversed if you were an activist—if you wanted all proposalsto proceed. Or perhaps you will not be an activist or a reactionary in general—only onparticular issues. On each issue, you will first discern whether it best fits the “∧” or “ ∨” case,and then recommend either a vote or a logical discussion accordingly. The important pointto emphasize here—what is, in one sense, perhaps the most important implication of theparadox of collective belief—is that the processes of “rational discussion” are not neutral inthis respect. That is, directing attention to reasons and invoking processes in which the forceof reasons is more likely to hold sway affects in itself the likelihood of majority support—quite independent of any effects of ‘discursive’ processes on the individuals’ views.

It may be, of course, that discussion and argument does lead individuals to change theirminds about matters, on the basis of evidence against, or a discovered incoherence in, theirinitial positions. Indeed, it seems likely that this will be so; and discursive processes are oftenrationalized on such grounds. Whether or not this is so, unless discussion produces genuineconsensus, its effects in directing decision-processes towards consideration of reasons ratherthan outcomes will have systematic independent effects.

Of course, discussion may encourage consensus for other than well-grounded epistemicreasons. The idea that discussion encourages participants to filter their arguments through arhetorical constraint that suppresses purely private interests is familiar from the arguments ofideal-speech theorists [Habermas most notably]. In a similar vein, discussion might makepersons inhibited about expressing minority views, for fear of the disesteem of the majority.Or people might just think, Condorcet-like, that the predominant opinion is more likely to beright and suppress their own judgments in favor of majority-held views. Discussion can, inthese latter ways, impel a move towards consensus by virtue of its social rather than itsevidentiary dynamic. And this move towards consensus may even have some value in termsof the perceived legitimacy of the decision made. But whatever the influence of suchsocialeffects in producing consensus, their consequences for collective decisions will dependcritically on which particular issues the discussion focuses on—whether on the substantiveissue or the underlying reasons. And it is to be emphasized that discussion itself is likely to


have an effect on this issue of focus:reasonsare more likely to be salient in the discursivecontext and this will bias outcomes towards or against support according to whether therelevant reasons are of the ‘botha andb ’ kind or of the ‘eithera or b ’ kind. In short, theinstitutions of discursive democracy inject an independent and, as far as I can see, entirelyimplicit (because hitherto unnoticed) bias into collective decision-making: such institutionsare non-neutral in the face of paradoxes of collective belief of the kind that we have hereaddressed.

Consider, for example, a comparison between the processes of parliamentary and directdemocracy. In parliamentary democracy, with strong parties, governments are encouraged todevelop coherent rationalizations of the policy packages they advance. That coherencerequirement constrains those parties to consider and to declare their reasons for action.Reasons weigh in a manner that they do not in direct democratic processes where voterssimply offer a judgment on the outcome—with no requirement at all that the reasons ofdifferent voters need be the same or logically coherent in the aggregate. Parliamentaryprocesses in this sense encourage reason-driven outcomes—that is, in favor ofc in theoriginal example—while direct democracy encourages outcome-driven outcomes—that is,againstc in the original example. To this point, I have remained agnostic as to whichorientation is to be preferred—if either. My object has been rather to isolate the differenceat stake; and to emphasize the simple and obvious point that coherence of beliefs is not ingeneral an attribute of collectivities. There is no escape from majoritarian cycling problemsavailable through a rejection of the preference account of political process in favor of a‘realist/belief’ account.7

10. Individual rationality?

The collective action problems familiar from the rational actor literature focus on thepossibility that collective entities may be irrational even though individuals are not. Or morestrongly that rationality can, in general, be a meaningful propertyonly of persons and that totalk of collective rationality or irrationality is inappropriate usage. Here, at any event, I havefollowed the well-tried tradition ofassumingindividual rationality and then exploringwhether aggregates can be “rational” on that basis.

7 Obviously, one need not take the same view in all cases. One might reckon that, in any general class of cases,there are attributes of that class that favor one procedure over the others. One might, for example, think that thereis a range of cases where people are better placed to make judgments about reasons, and others in which they arebetter placed to make judgments about outcomes; such criteria might then be used to settle whether decisionsshould be reason-driven or outcome-driven. I suspect, however, that such meta-rules serve to suppress theparadox without fully resolving it. One way of conceptualizing the idea of being ‘better placed’ to makejudgments at one level rather than another is to privilege majorities at the level at which choosers are supposedto be better placed. Suppose then that a majority of a given size counts for more at the level of reasons than atthe level of outcomes, reflecting one’s priors that judgment on reasons in a particular case are likely to be superior.Nevertheless, in a community of 101 ‘voters’, 51 may believe a and 51 believe b and yet c may fail by a voteof 100 to 1. In short, the idea that people are epistemically privileged at one level over the other complicates thepicture but does not fully answer the paradox.


But sometimes the collective result can have an individual analogue—or, at least, theexamination of the collective case alerts us to ways in which individual rationality might goastray. There is, moreover, the possibility that the examination of individual analogues mightgive us some ideas about how to think about the collective irrationalities here exposed andconceivably suggest insights about which of the possible solutions to the paradox can be bestsupported. I want to pursue that possibility here briefly at the close.

One natural thought is that, just as the Condorcetian preoccupation is with the probabilitythat certain propositions are true (based in Condorcet’s case on the extent of popularsupport), so we might explore the logic of individual rationality in cases where individualbelief is constructed probabilistically. Consider in the spirit of, say, Mark Kaplan (1981), thesituation in which “belief” in propositiona is represented by a degree of confidence in thetruth of a greater than some threshold parameterp*, wherep is conceived as the probabilitythat a is true. Then it is perfectly coherent to say that I believea and that I believeb wheneither of those propositions is considered in isolation, but that I don’t believea ∧ b. Supposethat I thinka is true with probability 81% and thatb is true with probability 81% (wherep*is 80%, say); then the probability that both are true, if they are independent propositions, isonly 65.6%—not sufficient to sustain belief. In this particular example, the force of standardlogic is restricted to the negative claim that belief ina andb is notsufficientfor belief in a∧ b. It is not the case here that I believe a, b and;(a ∧ b): there is a clear distinction in thisenvironment between not believingx and believing;x. But strong paradoxes are on offer.We can, with enough independent propositions, construct cases in which I believea,b,. . .and so forth, and believe;(a,b,. . . etc.).8 What is instructive in most such cases, though, isthat the ‘paradox’ is rationally resolvable. We are simply capturing the fact that doubts ofdifferent types compound when the truth of a compound proposition is at stake; so thegrounds for believing;(a,b,. . . etc.) seem presumptively compelling.

The connection between this individual case and the collective ‘paradoxes’ should beclear. What is invited is that we should simply think of the degree of popular support as aproxy forp. Thinking about the belief structure of the collective in this way suggests that theright conclusion in the paradoxical cases is to go with the final judgment on the jointproposition a ∧ b, and ignore the judgment on the independent ‘reasons’,a and b, asinsufficient. Obversely, the truth conditions for the ‘either-or’ case are diminished:a ∨ b canbe ‘true’ (i.e.,p* is greater than 80%) when neithera nor b is ‘true’ in the same sense [thatis, by appeal to the same probability test].

It would, however, be a mistake to think that this analogy [with the individual case framed

8 In the case of simple majority rule, where p* is effectively 50%, the strong contradiction can arise even forthe simplest structure of reasons; that is, the majority that believesa, and believesb, can also believe;(a ∧ b).Does this fact conceivably provide some support for those who argue for supramajoritarian decision rules (as forexample Buchanan & Tullock (1962) do)? Clearly, the higher isp* the less likely strong contradictions are toemerge; but they cannot be ruled out. All one requires is an appropriately large number of supporting conditionsto be fulfilled. So, for example, with p* at 80% one can get a strong contradiction only if there are eight necessaryconditions. In any event, the distinction between “not believe” and “believe not,” though clearly relevant heredoes not dispose of the paradox possibility in either strong or weak form—and even in the weak form the paradoxappears troubling.


around a metric of strength of belief] disposes entirely of the paradoxical element in thecollective case. For one is still left with the point made in section V concerning thedistribution of disbelief. It seems to me to remain a distinctly disturbing feature of thecollective case that collective belief hinges on the precisedistributionof negative reasons—that if it happens that the propositions “not a” and “not b” are believed by thesameminorityof persons, then the resultant action will be different from that which would emerge if thedistribution of disbelief were distributed otherwise—aggregate disbelief in the underlyingreasons for action (a andb) unchanged. That said, the probabilistic-truth analogy does seemto favor an action-based rather than a reasons-based orientation in collective decision-making; and this consideration suggests an argument against specifically deliberative/dis-cursive processes.

The main object of this paper, however, is not so much to evaluate deliberative/discursiveinstitutions. It is rather to emphasize the special complications associated with moving fromindividual rationality to ‘collective rationality’, when ‘rationality’ is understood in terms ofthe coherence of belief rather than the connection between action and preference. My generalpoint is that such complications arise more or less analogously whether one holds apreference-based or a belief-based conception of collective decision-making. In this sense,problems of collective irrationality do not depend on the particular preference-based formu-lation normally adopted in rational actor theory: they cannot, for example, be set aside by thesimple expedient of asserting a belief in the “forum” rather than the “market” conception ofpolitical processes.

Acknowledgments

I am grateful to James Buchanan, Bob Cooter, Richard Holton, Lewis Kornhauser, PhilipPettit and Don Regan for valuable comments. All remaining errors are my own responsi-bility.

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