single case probabilities and the social world: the application of popper’s propensity...

Journal for the Theory of Social Behaviour 29:20021–8308

Single Case Probabilities and the Social World:The Application of Popper’s PropensityInterpretation

MALCOLM WILLIAMS

INTRODUCTION

Whatever one’s position on what counts as the ‘social’, there is perhaps minimalagreement that it is the aggregate outcome of individual characteristics oractions.1 The naturalistic social scientist will usually describe these phenomenain terms which suggest that they have a ‘real’ existence, that is they are held,minimally, to have properties, which at least allows the measurement of theirexistence.2 In empirical social science, specifically the social survey, theseproperties, though treated as ‘real’, are explained or predicted (in terms of theirrelationships or effects) probabilistically. Thus, for example, the emergence ofcertain cultural characteristics in a society can be explained as a probabilisticoutcome of individual actions or characteristics. Conversely whether a givenindividual will be a bearer of these characteristics can also be expressedprobabilistically.

On one hand we have aggregates, which we treat as having real propertiesand on the other we have individuals, likewise regarded as having real attributesand capable of real actions, yet the relationship between the two might bedescribed as an occult one. Indeed the foregoing restates the old problem ofagency and structure in social science. How do agents create the social worldand how does the former effect the latter? The difficulty is then, that whilst wetalk of the reality of social and individual phenomena, we can posit only a virtual

mechanism to connect them.For the most part this is a problem only in the social sciences, in so far as

whilst the relationship between individual and aggregate phenomena can oftenonly be specified probabilistically in the physical world, this limitation is rarelyconsidered problematic. For example Browmian motion describes the irregularmovement of minute particles of matter when suspended in a liquid. Whilst the

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188 Malcolm Williams

movement of any given particle cannot be known, when the liquid is heated theparticles move faster, when it is cooled they move more slowly. Aggregatemovement can be known and the movement of any given particle could bedescribed probabilistically. Unfortunately, because the ‘particles’ in this case areconscious human agents, when the social scientist treats the intervening processesas a statistical ‘black box’ this is so often seen as a measure of the failure ofsocial science, rather than resulting from the character of these processesthemselves. As Scriven points out, in this respect, the social sciences are moreharshly judged than physics:

We know what happens to falling bodies in a vacuum, but when it comes to the way bodiesbehave when we drop them in air, we are not able to say very precisely what they will do.And when it comes to the question of how a particular leaf falls from a particular tree on aparticular autumn day, we are almost helpless. This is true, but nobody feels that it is veryimportant to be able to predict the behavior of a leaf. If this were the kind of crucial problemin physics then it would be the case that physics would always be a subject of a veryunsatisfactory kind. (Scriven, 1964: 171.)

Whilst the difficulty of the problem, in social science, is not underestimated,it may become a little more tractable if we consider it in light of the interpretationof the assumptions about probability underlying social explanation and prediction.In this paper I will contrast the standard (frequency) interpretation of probabilitywith an alternative propensity interpretation, due to Karl Popper (1957; 1959;1983) and argue that the latter, somewhat modified, can lead to a methodologicalstrategy that might help us better understand the relationship between individualand aggregate phenomena.

Popper’s view of probability (he refers specifically to physical occurrences) canbe summarised as: that it measures the objective relational properties of theworld (1957:70), that individual events have a propensity to occur and that theseare real states of the world. Popper’s work in this area reached fruition in thelatter part of his career, though it has always been controversial and in respectof its original formulation, to solve an observational puzzle in quantum physics,it is seen by most commentators to have been only a partial success (O’Hear1980: 134–5). Indeed in this paper I will concede to his critics that hisinterpretation is flawed as it stands and requires some modification to work, amodification I introduce specifically in respect of its application in investigationsof the social world.3

Unfortunately Popper himself never worked through some of the key methodo-logical difficulties inherent in his proposed propensity interpretation and theinterpreter must second guess what conclusions he may have reached, specificallyin respect of the adaptation of the propensity interpretation to probabilistic dataof the social world. However whatever the methodological speculation, there isno doubt that he believed that the metaphysical import of his work went farbeyond experimental situations he described in respect of the natural sciences.

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Popper’s Propensity Interpretation 189

In his later work he extends the idea of what he terms ‘situational dependence’of probability from physics, to biological evolution (Popper and Eccles, 1977:26–8). Later still, in a paper originally published in 1990, he further extendsthis to include human social life (Popper, 1995: 17).

Despite his commitment to a metaphysical position that encompassed thesocial world, attempts to utilise Popper’s view of probability as a means ofmethodological elaboration in social science are necessarily speculative andpossibly even antipathetic to Popper’s own views. What is offered here, is then,by way of a ‘bold conjecture’ that uses Popper’s original work to suggest apossible investigative programme. The first part of the paper outlines thefrequency interpretation of probability along with Popper’s alternative and someof the criticisms of the latter. In the second part I will outline, by way of asimple example how (what Popper calls) dispositional properties are realised inthe social world and suggest how the propensity interpretation might underlie amethod by which we might study the contribution of single cases to aggregates.

THE FREQUENCY THEORY OF PROBABILITY

The frequency theory of probability is the standard, or statistical theory used tomeasure the relative frequency of an event A in a sequence defined by conditionsB. Thus the objective probability4 of an event A occurring is conditional uponB and can be symbolised as p (A/B). Take the very simple case of a standardsix sided dice. In this case event A might be the frequency of the dice comingup as a six. The odds of the dice coming up as six are, of course, 1:6 andstatistically these odds are determined by the fact that there are five other equalpossibilities of other numbers being thrown. Though there may be lengthysequences of other numbers, in the long run the relative frequency of a six beingthrown is 1:6. Conditions B, in this case, would be taken to be the characteristicsof the dice itself and no more is usually said, but as Von Mises (1951: 15)recognised, the physical characteristics of the dice are in fact dispositions. In amore realistic setting the standardised conditions of an experiment will generateanalogous distributions, but likewise it is the conditions of the experiment whichcreate the relative (and limiting) frequencies. The physical situation in whichthe frequency is generated brings about the realisation of the dispositionalproperties (B) that determine A.

Since Von Mises’ observation it is well recognised that a frequency distributionis not simply a statistical fact, but has other ontological properties. Nevertheless,whilst noting this, he specifically denied that anything further could be saidabout such dispositions (Von Mises, 1951: 11). His definition of probability isthat it is a limiting frequency and is therefore an operational definition of thetheoretical concept of probability in terms of the observational one of frequency(Gillies, 1995: 109).



POPPER’S PROPENSITY THEORY OF PROBABILITY

Popper, however, took a different view maintaining that if a frequency isgenerated by dispositional properties then those properties must reside in thesingle cases of which the frequency is composed (Popper, 1983: 349). Todemonstrate this he asks us to consider a long sequence of dice throws with aloaded dice in which it is established that the relative frequency of throwing asix is 1:4 (1959: 31–2). If we now intersperse a few throws with an homogeneousand symmetrical dice we would have to say that the frequency of throwing asix with a correct dice is 1:6, yet these throws are members of a sequence witha known statistical frequency of 1:4. In each case the physical disposition of thedice would produce a propensity to 1:4 and 1:6 respectively. The frequentist,according to Popper (1959: 32–3) would claim a statistical equivalence here,whereby the (almost complete) run of 1:4 and the very short run of 1:6 couldbe similarly expressed. The sequence of throws with the correct dice is denotedas c and that of 1:4 as b. This can be expressed then as p(a, c) 5 1:6 andp(a, b) 5 1:4, but of course the few throws of c belong also to b, but must beexpressed as p/a, bc) 5 1:6. This however, is not justified by the frequencytheory, because the latter depends on an infinite (or at least very long run) toproduce the relative frequency and bc does not provide that run, because c

consisted only of 3 throws and the frequency could not be established. Poppermaintains that b is an actual sequence and c a virtual one, moreover thefrequentist must introduce a modification, which is that any admissible sequencemust be

characterised by a set of generating conditions[. . .]whose repeated realisation produces the elementsof the sequence. (Popper 1959: 34 [emphasis in original].)

The frequency interpretation takes probability as relative to a sequence whichis assumed, but of course frequencies are produced only through repetitions,which indicates that what is repeated (single throws of the die) must generatethe sequence. This must mean, Popper maintains, that a singular event has aprobability that arises from the same generating conditions that produced thesequence. Thus a single event has a probability, even though it may occur onlyonce, for its probability is a property of the generating conditions.

Popper’s argument has one last component, which might be characterised asa realist argument for the properties of single cases and their generatingconditions. The dispositional properties that produce the sequence, must residein the single events. Now the single events must themselves have two properties:a) that they have the propensity to be realised; b) that the properties are real,not virtual.



a) Single events are themselves not determined, unless they have a probabilityof 1, in which case there is logical necessity, rather than probability (Popper1983: 356–7), but are the product of the generating conditions and will haveonly a probability of occurrence. Nevertheless, unless the occurrence of theevent is a logical impossibility (a probability of 0), they will have some kind ofprobability of occurrence, even if this is very small.

b) The reality of propensities exists in their dispositional properties. They arenot properties inherent (to say) the dice, but are relational properties of theexperimental arrangement itself. That is the realisation (or what Mellor 1971:Chapter 4) called the ‘showing’ of the propensities can only come about as aresult of a particular set of interactions. We can, for example, talk of commonsalt as having the dispositional property of dissolving in water, but this can onlycome about when salt is added to water. It is possible to imagine a world wherethis dispositional property is never realised or ‘shown’. Popper (1959: 37) likensthese relational properties to Newtonian forces.

OBJECTIONS TO POPPER’S INTERPRETATION

Most of the objections to Popper’s interpretation of probability lay emphasis onthe statistical or logical problems it entails. Thus some critics have rejected itout of hand on this basis, rather than trying to evaluate it as a metaphysicalprogramme. Exceptionally Stokes (1998: 112) equivocally accepts its importancein such a programme, whilst Mellor (1971)5 develops his own alternative (whichdoesn’t really solve the problems raised in respect of Popper’s version) andGillies (1995) who retains the propensity interpretation and links it to a personalistprobability for single cases. My strategy here is to affirm the importance of themetaphysical basis to Popper’s claim (as do Stokes, Mellor and Gillies), but agreethat first objection from O’Hear below can only be countered by an appeal tothe metaphysical nature of Popper’s project (presumably unappealing forO’Hear). His second objection, I believe, arises from an unfortunate use of theconcept of ‘force’ by Popper. I therefore think this does not hold. Finally Iaccept that an objection from Howson and Urbach does indeed find its mark,but I maintain that the criticism is a methodological one which does not applyto my own reformulation.

O’Hear’s first objection: O’Hear (1980: 138) maintains that there is nothing tostop a frequentist accepting what Popper says (arguably said already by VonMises) and remaining a frequentist. This is because although propensity advertisesitself as being capable of demonstrating single case probabilities it can only dothis in relation to their probabilistic antecedents. It speaks of ‘reality’, but deliversmore probability. Why is it that a frequentist could not simply agree that somelaws are probabilistic? Surely then, O’Hear maintains (op. cit.: 139), it becomes



hard to see how the propensity theory explains anymore about undeterminedevents than the frequency theory.

As Popper presents his interpretation one has to concede that O’Hear makesa fair methodological point, but metaphysically there is clear blue water betweenPopper and the frequentists. Though his propensity interpretation is oftenregarded simply as a modification in statistical theory, it is part of a broaderrealist attempt to account for natural indeterminacy (see his 1983). The differencebetween ‘frequentism’ and Popper’s view is that the former has a metaphysicalbasis in a Laplacian determinism, or in the case of Von Mises, operationalism(Gillies 1995: 109), whereas Popper’s advocacy of the propensity interpretationmarked his conversion from determinism in his Logic of Scientific Discovery(1959a [original 1934]) to, what might be described as a ‘realist indeterminism’.Indeed his latter position prefigures and is underscored by the later work of thetheorists of complexity and emergence (see Nicolis and Prigogine 1989; Reedand Harvey 1992; Eve et al. 1997).

O’Hear’s Second Objection: O’Hear (1980: 136) secondly claims that if a propensityis a real force (comparable to Newtonian forces) then it will prevail by necessity.If there is a propensity of 2 in 3 for a coin to come up tails and it come upheads, what happened to the propensity to tails? If propensities were likeNewtonian forces then heads would always prevail.

Popper’s comparison with Newtonian ‘forces’ is unfortunate, for althoughthese are good examples of relational properties, they do entail a necessary,rather than probabilistic relationship. Nevertheless this objection misses the pointof the argument about propensity, namely that it is in the relational propertieshas a propensity to occur, but this does not entail a necessity (otherwise itwouldn’t be called a propensity). In a coin weighted to 2 in 3 tails the propensityrealised or unrealised remains this, but the circumstancs in which the coin istossed may or may not lead to its realisation.

Howson and Urbach’s Objection: (Howson & Urbach, 1989: 223). I believe this tobe a more telling objection. In the sequence of dice throws, Popper offers byway of evidence for his theory, he asks us to consider a series of throws of aloaded dice interspersed with a few throws of a fair one. His argument that bothmust belong to a hybrid sequence, but the inclusion of the fair throws leads toan unjustified conclusion about their probability, because the frequency theoryrequires a long run of throws to produce the relative frequency and this is notavailable. Whilst Popper may be correct in this assumption, any given throw inthe hybrid sequence (assuming the experimenter doesn’t know whether thethrows are with the fair or loaded dice) must be an instance of each sequenceyielding the single case probability of both 1:4 and 1:6 and thus a contradic-tion arises.

Although Popper ascribes probabilities to single cases, their value can onlybe derived by appealing to their relative frequency (Popper, 1995: 11) in asequence. His assumption is that in the long run statistics show a tendency



toward stability (op. cit.: 12). But in a hybrid sequence, of the kind he describes,the few throws of the unweighted die would not be visible. Indeed each casemay apparently contribute to the stable frequencies obtained from throws of theweighted dice, or they may not. Conversely (because there would be interveningfactors in the long sequence weighted at 1:4) many of the throws of the weighteddice would not contribute the stability of the frequency.

Although this objection is a serious one, the issue at stake is one ofmeasurement, not of principle. Popper’s argument is firstly for a propensityinterpretation of probability and this argument is not harmed by the objection.However in a repeated experiment, measurement of the single case probabilitiesis dependent upon the relative frequency of occurrence and we simply don’tknow whether the propensities realised in the single cases, in the distribution,were the same. Nevertheless whilst the repetition of the experiments will notresolve this difficulty, an analysis of the single case themselves could, in principleat least, reveal the antecedent probabilities. This is precisely the strategyI am advocating in the application of a propensity interpretation ofprobability, in the study of the social world. Before I set out this modification Ineed to say something about the character of open systems and specificallysocial systems.

OPEN SYSTEMS AND INDETERMINISM

Popper claims that we can know the objective probability of a single case andthe strategy for knowing this is the repeated experiment. Notwithstanding thefinal objection above, this poses methodological difficulties for the social scientistbecause of the open character of the social world. However the metaphysicalbasis to Popper’s views must entertain the notion of the existence of thepropensity for events to occur in open systems. Indeed open systems by theirvery nature are the outcome of the relational properties of other elements. Thusin systems with any ‘open’ character at all, the propensity of single events andtheir generating conditions is also dynamic (this is implied by (a) and (b) above).That is, what happens over time will change the generating conditions and thusthe propensity for an event (A) to occur. This is illustrated in a simple scenariosuggested by Sapperstein (1995).

Suppose a circular table is laid for dinner with four plates set around thecircumference of the table and midway between each plate there is a wine glass.The first person to sit down is in the position of being able to choose whethershe will use the glass to the left, or to the right. If she chooses the right then somust her fellow diners. Meanwhile other diners are milling around waiting tobe seated at other similarly laid tables. Some will prefer a left handed wineglass, others a right, yet others will be indifferent, but the first person to chooseon each table will determine the side each of the others on her table will take



their wine. In this way those with left preference, those with a right preferenceand those with no preference become distributed through the room. Now furthersuppose on some arbitrary whim it is decided to serve left handed diners fromone pot of food and right handed from another. The ‘left hand’ pot containscontaminated food and those diners suffer food poisoning. Even if we had knownleft and right handed preference we could not have predicted deterministicallywhich diners would be poisoned.

The stages of the scenario from diners waiting to be seated to the subsequentfood poisoning could be represented as A ⇒ B ⇒ C ⇒ D ⇒ E, where E isthose persons suffering from food poisoning. Something like a Markov chainexists here whereby the state of a future system is effected only by its immediatepast. So E is produced by D, but not directly by C. We cannot thereforedetermine the state E from any point other than D, even though we canprobabilistically predict E from A if we know two things (1) the total number ofdiners and (2) the total number of portions of poisoned food. If there are 20portions and 100 diners then the odds of any given person being in E are 1:5.This of course assumes that all those given poisoned food will eat it andsubsequently suffer the effects. The dispositional properties realised are (princip-ally) the toxic properties of the food and human susceptibility to toxins presentin food.

Two interesting observations can be made from this (admittedly somewhatartificial example). Firstly that at any point between A and E (inclusively) therewould be earlier antecedent and quite different, probabilities external to thesetting described. For example, the left handedness of particular diners mayhave physiological, or psychological origins, the fact that the food was poisonedat all may have been the result of cost cutting, laziness, conditions in the kitchenetc. The entry of any externally originating factors seems to produce anindeterminacy in the system originating in an apparently infinite number ofpossibilities that exist outside of that system. Our lack of knowledge of whathappens between A and E, is then, either the result of the indeterminatecharacter of the social and physical world (or if it is determined, such situationsare computationally irreducible).6

Secondly although a given number of people were poisoned, each poisoningwas independent of the other. That is to say when one person is poisoned, thisin itself does not determine whether another is poisoned. Nevertheless the factof their poisoning was the outcome of the realisation of the same propensitiesat point E. The fact of the poisoning of each individual was a dispositionalproperty of diverse antecedent conditions, but from a given point in time thepropensity of some to be poisoned increased, whilst the propensity of othersdecreased. Furthermore one could say that there is a realisation of propensitiesat a number of points from A to E and the fact of the poisoning is simply theone that we as observers have privileged.



THE ANALYSIS OF PROPENSITIES IN THE SOCIAL WORLD

The foregoing demonstrates how the dispositional properties of situations arerealised, but how we can come to know the contribtion of the single cases tothe aggregate?

Popper, as I have noted advocated the strategy of repeated experiments inorder to determine the relational properties of the experimental setting. Hedescribes the strategy thus:

provided we can, as in the case of dicing, repeat the situation that produces the probabilisticevents in question; or provided the events in question repeat themselves, without ourinterference. Provided the numbers of such repetitions is sufficiently large, we can use statisticsas a method of weighing the possibilities, and measuring their weights. (Popper 1195:11.)

Though he doesn’t tell us in detail what this might entail, one supposes that theexperimenter would aim to build a model in which the relative weights of thefactors in the experimental arrangement could be calculated. If these wereexpressed as probabilities they would range from 0 (no influence) to 1 (necessity).

Assuming antecedent conditions exterior to the experiment had very lowprobabilities (that is they did not introduce too much ‘noise’), the experimenterwould finally be in a position to calculate the ‘weight of weighted possibilities’(Popper, 1959: 36–7) as contributing to the outcome, thus according to Popperdemonstrating ‘the fact that these sequences are defined by the manner in whichtheir elements are generated – that is by the experimental conditions’ (1959:37). This strategy, is of course, a theoretical one, though possibly realisable in avery simple experimental set up. A crucial factor, however, is that the frequencydistribution must have a known limit, that is the possible outcomes (such as thatof a dice throw) are known.

Popper maintains that the propensities for events to be realised are theproperty of the experimental set up itself. Now whilst social scientists do useexperiments and we would treat these as (relatively) closed systems, mostmeasurement of the social world is by way of survey research. Arguably, in asurvey, one is aping the experimental set up by creating mutually exclusivecategories, so permitting deductive inference. Variables take on the valuesassigned by the researcher. Thus the outcome possibilities are artificially ‘fixed’by the researcher. The ‘fixing’ itself takes place at a number of pointsduring the research, from the decision to measure X as opposed to Y, theoperationalisation of variables into measures and the treatment of those variablesin the subsequent analyses. The act and the nature of the measurement arecontributory factors in the result we achieve. That is not to suggest that somethingreal in the environment is not being measured, but as Bhaskar says of experiments‘scientists co-ordinate, or are causally co-responsible for, a pattern of events



(1989: 15). A frequency distribution is, as I have noted, a distribution ofindependent events, which though sharing the same or similar antecedents arenot dependent upon each other, their association represents an interventionpoint in ‘reality’. The choice of intervention at any given point in time andspace is then, the equivalent of a set of experimental conditions. R is not onlymade up of independent events (single cases), but these events have an ontologicalstatus different to that of R, which must be seen both as a virtual sequence andan actual sequence. It is the virtual sequence of a statistical conclusion, but anactual sequence of real events which are only given meaning when they becomepart of R.

The frequency interpretation thus treats each case of R(R1,R2,R3. . .n) as virtual

cases. A survey result would lead us to say, for example, that a US citizen isnearly three times as likely to attend church each week as a UK citizen, but ofcourse a further analysis would show that church attendance is associated withother variables (e.g. age, sex, location, education etc.). A simple strategy toreplicate ‘repeated experiments’ might be to retain the same dependent andindependent variables, but conduct the same survey with different samples in apopulation, or on several populations similar in known and key respects.

The difference, however, between simple experiments in physics and chemistryand surveys in the social world is that in the former the performance of singlecases in a sequence will be located in far fewer antecedent conditions than singlecases in the social world. Though the relationship between mass, symmetry,temperature etc. in a dice throw may be hard to measure, each of these variablescan be accounted for in classical laws. This is not the case in the variablesidentified by a survey researcher. These may well have different ontologicalstatuses. Consider the following:

Ethnicity: One’s ethnicity can be both a physical property (such as colouretc.), or a social construction. Different ethnicities may have different properties.

Migration: Migration is a statement about the physical movement from oneplace to another, but its antecedents in individual cases might be partly, orwholly, subjective.

Overcrowded Housing: Though what counts as overcrowding is a socialconstruction, certain densities of persons can give rise to important environmentalfactors such as ill health.

Poor Nutrition: Similarly what counts as poor nutrition will vary, certain dietswill have health consequences.

These variables can combine to produce regularities in the world that, quitedifferent from those implied by the variables on their own. Byrne (1998: 38)gives a nice illustration of this in Bradbury’s study of the incidence and causeof tuberculosis on Tyneside, England, in the 1930s. TB is ‘caused’ by the TBbacillus, but of course not everyone who is exposed to the bacillus developstuberculosis. The ‘cause’ of some catching the disease and others not was thecomplex interaction of poor housing, overcrowding and poor feeding (especially



the insufficient consumption of milk) and being Irish! Exposure breeds resistanceand as Byrne points out, the Irish had two generations fewer of urban industrialselection behind them. Any of the characteristics was a sufficient condition, butnone were necessary conditions. The incidence of TB was real enough, but whowould get TB was a dispositional property of complex interactions in theenvironment.

Quite apart from the methodological difficulty of repeating such studies (as onemight with an attitude survey for example), the complexity of antecedent variablesis clearly a much bigger methodological issue than can be dealt with by a simpleadaptation of Popper’s strategy of interpreting the single cases. The difficulty ofobjectively arriving at the odds of Mrs McGuire getting TB, will be dependent ona number of antecedent factors. Indeed this is similar to problems raised byAyer (1963: 188–208) and Howson & Urbah (1989: 221) in respect of Popper’sinterpretation more generally. The latter’s solution is to introduce subjective prob-abilities here – a move quite antipathetic to Popper’s intention. However theremay be another way of resolving the difficulty and that is to meet it head on andbegin from the single cases. Of course in individual analysis we cannot assess thestatistical likelihood of the variable upon the outcome, but if the same analysis isconducted with a number of agents, a model might be constructed in whichprobability estimates can be derived for each contributing variable.

Suppose that we could go back in time to conduct research on the incidenceof TB on Tyneside in the 1930s. A logistic regression model indicates that muchof the variance is accounted for by fitting the term ‘Irish’. We conduct the sameanalyses of several other independent samples of people and each time the mostsignificant variable is ‘Irish’. A trivial fact is that being Irish is the most importantfactor in getting TB. We could now look for interaction terms, in order toestablish other ‘causal’ relationships. Though a feasible strategy, another strategymight be to treat each case of an Irish person with TB as the realisation of apropensity – as a real event. This then leads to a different kind of analysis, theanalysis of antecedent probabilities in each case. The assignment of these is thenconditional upon other known antecedent probabilities, such as incidence of TBin the family, length of time between embarkation and contracting TB, personsper room etc. The analysis of data and construction of models becomes case,not variable, driven, with each case weighted, the weights having been derivedfrom the antecedent variables. The resulting sequence of single cases, is then,the weight of the weighted possibilities.

This strategy, used as micro level analysis, or to build simulation models, isnot methodologically particularly innovatory and is similar to the iconographicmodelling of strange attractors suggested by Byrne (1997). What is new anddifferent in this approach is that the relational properties themselves are treatedas the realisation of earlier nested propensities, not as the outcome of determinedcausal processes. The methodological approach is not itself a ‘propensity’approach, but permits a propensity interpretation.



A perhaps critical observation one could make here, is that, each anlaysedpropensity (expressed as a probability) is itself nested in earlier ones. This canonly be a criticism if one believes the world is deterministic and our goal (if notan achievable one) is to establish those determinants. But the consequence ofregarding events as having a propensity to occur, is that it emphasises theindeterminism of the world, that though each single case is a fact about the realworld, things could have been otherwise. In the Sapperstein example if westarted with a single agent who had been poisoned and worked back throughthe ‘causal’ chain, we would see that each link has only a necessary link withthe previous one. Each link is the realisation of a propensity and unlike adeterministic analysis, an analysis of propensities seeks only to know the relationalproperties of a given event, they are always nested in earlier propensities and‘rock bottom’ cannot be attained. Nevertheless prior to a realisation we couldspeak of a greater or lesser propensity for an event to be realised. For examplebeing right or left handed did not determine whether or not one got poisoned,but a left handed agent would have a greater propensity to be poisoned (becauseleft handed diners were served first and if she sat down first she would thendetermine the ‘handedness’ of the table). Propensities are, as Popper claimed,relational properties, because they are only realised in conjunction with otherpropensities.

CONCLUSION

Popper’s argument (originally advanced in 1957) can, in light of developmentsin chaos and complexity theory, be said to have come of age, at least as ametaphysical programme. Thus whether or not one believes Popper to be rightmethodologically, it is rather easier to concede that metaphysically he was onto something. The attractiveness of this approach to the social scientist is thatit suggests a method of analysis that can demonstrate the contribution of singlecases (often individual agent characteristics to aggregates). In this paper I havetried to set out some general features of what this programme might ential. Iconcede that technically there is nothing especially innovative about the approach(but then there wasn’t with Popper’s original either) other than the statisticalmodelling technology available to us now would permit the translation of sucha proposed methodological programme into a technical possibility (see forexample Smith & Stevens, 1997).

Popper’s own views on the propensity interpretation of probability have beensubject to criticism, some of which seems to be inescapably right, but this doesnot justify abandoning the programme altogether and especially in light of newinsights in complexity theory. Unlike the aforementioned Mellor or Gillies, Ihave not attempted to suggest a more general resolution of these problems, buthave, in the spirit of a ‘bold conjecture’ suggested how we might treat single



cases as having objective antecedent probabilities. If I am right, or possibly amodification (or even different version of what I suggest) is right, then it shouldbe feasible to specify the objective link between individuals and aggregates inspecific social systems.

The inability of social science (qua science) to do this in the past has handedthe best card to the anti-naturalists, who have quite reasonably argued thattreating aggregate probabilities as ‘real’ things is illegitimate when we considersuch sequences consist only of the theoretical entities posited by social scientists.These entities are unrelated to the contingent, intentional character of individualagents (this argument takes various different forms, but see Denzin, 1983;Lamiell, 1987; Taylor, 1994). I do not suggest that what I propose offers a fulland complete answer to the difficulties encapsulated in such arguments, but Ithink that the propensity interpretation, where the propensity for certain eventsor characteristics to be realised, is treated as dynamic over time, goes some wayto meeting this objection. In explicitly abandoning determinism it does not ruleout the possibility of contingency arising from intentional action. Indeed, thoughhe does not expand upon this, it was certainly Popper’s view that not only dopropensities exist in the social world but they might be changed by the intentionalaction of agents, as the following demonstrates:

Now, in our real changing world, the situation and, with it, the possibilities, and thuspropensities, change all the time. They certainly may change if we, or any other organisms,prefer one possibility to another; or if we discover a possibility where we have not seen onebefore. Our very understanding of the world changes the conditions of the changing world;and so do our wishes, our preferences, our motivations, our hopes, our phantasies, ourhypotheses, our theories. (1995: 17 [emphasis in original].)

An important point made by naturalists is despite the contingent character ofintentional action, regularity is apparent everywhere in the social world. Whilstit can be conceded that intentional behaviour entails the logical possibility ofcomplete variability, it does not follow that agent actions in given circumstanceswill display such variability. Complete variability would imply complete socialdisorder – a counter intuitive notion. Thus in principle the task of establishingthe nature of statistical stability and thus individual propensities to produce thebehaviour that gives rise to that stability is not an impossible project. Indeed ifwe accept that aggregates (logically) must be made up of single events, attributableto individual agents, then not to explain those aggregates would continue toleave a gap in our knowledge.Malcolm Williams

Department of Sociology

University of Plymouth

Plymouth

Devon PL4 8AA

UK



NOTES

1 This is meant in the sense that one might subscribe to either methodological holism,methodological individualism, or even a version of structuration theory. I do not thinkthe following is antipathetic to any of these.

2 Whilst there is an implicit commitment to a realist theory of the social world in thispaper, of the kind suggested by Popper, this point does not turn on the need for a fullblown realists ontology. Indeed agreement about the possibility of measuring sense datais all that is required here. Sometimes, however, these properties might be more ‘fixed’,or readily measured than others. Contrast, for example, the properties of a school withthose of a social class.

3 I see no reason why what is proposed here could not be used in the measurementof some open systems in the non social world. However I think, perhaps unusually, thisis one situation where the social scientist can claim some methodological advantage overthe natural scientist. Because the ‘single cases’ are often individual agents and agents canknowingly reconstruct antecedent events, there is an advantage over (say) a particle inBrownian motion, the history of which cannot be traced unless it has been observedover time.

4 Popper himself was greatly opposed to the introduction of subjective (Bayesian)probability (1959a, Chapter 9; 1983, Part II, Chapter 1), because he needed an objectivetheory for his interpretation of quantum mechanics, specifically Heisenberg’s claim thatthe experimenter brings about the observed result (O’Hear, 1980: 134–5). IronicallyPopper’s views seem to have more utility outside of quantum physics (where they werenever taken very seriously) in that something like propensities seems to be required if theintention is to espouse both realism and indeterminism. A realist ontology requires thatwe can postulate real events, probability cannot just be a function of our degrees of belief.

5 Mellor makes a distinction between the ascription of dispositional properties toexperimental situations and to the object (such as a dice) itself, claiming that dispositionsare ‘permanent entities which are re-identified through apparent change as unchangingbearers of changing properties (1971: 63). His reasoning for this change is that theascription of such properties to the whole set up, is that it makes pointless any attemptto ascribe properties to something that is said to be present, whether or not it is displayed.An objection to Mellor’s modification is that ‘permanent entities’ do not permit of theirhaving changing probabilities over time, or indeed some things do not exist at all untila particular point in time, yet emerge as a result of other relational properties. Eventhough they do not exist at time t1, a probability of their existence may be postulated attime t2, but between those times the propensity for the existence of such an event tocome about may change. The invention of new therapy, for example, might significantlyreduce the death risk of a sick person (see Bartley’s footnote in Popper, 1983: 282).

6 Computational irreducibility is a notion employed in complexity theory meaningthat to produce accurate predictions would require the fabrication of a computer morecomplex than the system it aimed to predict (see Firth, 1991). Ultimately the universemay be determined, but the anthropocentric nature of its perception renders it asindeterminate, as Popper himself argues (1950: 177–33) in claiming that there are alwaysGodelian sentences that will require a deductive system outside of themselves todemonstrate the validity of certain truth claims of such sentences.

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