On Freedom

A Centenary Anthology

Eileen Barker

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000678444
• Edition: 1
• Topic: Politique et relations internationales
• Subtopic: Droits de l'homme

The London School of Economics and Political Science has embraced the full range of the social sciences and its related disciplines. Contributors to this book were invited to write on the subject of freedom.

Part 1 It All Depends What We Mean By…

DOI: 10.4324/9780429338168-1

Choice or Chance?

DOI: 10.4324/9780429338168-2

D. J. Bartholomew

Social law and human choice

Samuel Johnson spoke for many in saying, ‘Sir, we know our will is free, and there’s an end on’t.’ Our own sense of personal autonomy, not to mention the varied and seemingly unpredictable choices of those around us, all point in the same direction. But it is not only among philosophers that doubts have been raised about the validity of this judgement. Some of the early social statisticians saw empirical evidence of lawfulness in the collective, if not the individual, behaviour of people. An individual may decide to vote Liberal Democrat, buy a video, become a nurse or, even, commit suicide in an apparently unpredictable manner but, when the aggregate effect of such decisions are examined, law-like patterns are found. The market shares of goods such as breakfast cereals may be remarkably stable in the short term even though customers think they are free to choose which they will buy. Such regularities are well known and have long been the foundation of the insurance business, for example.

We are used to the idea that the world is subject to physical laws which prevent us from taking liberties with gravity and electricity. Are we similarly constrained by social laws and, if so, does that undermine our belief that we have freedom to choose?

This question was brought sharply into focus towards the end of the last century by the work of the early social statisticians. Adolphe Quetelet, who was the Belgian Astronomer Royal, produced his celebrated Physique Sociale in 1869. The title clearly expresses his aim of doing for the social world what physics was already doing for the world of nature. In his book, Quetelet gave many tables displaying the regularities of social behaviour. Florence Nightingale, the ‘passionate statistician’, saw in this lawfulness the path to human betterment. A fascinating account of her thoughts on these matters will be found in Diamond and Stone (1981) who use Nightingale’s marginal notes in the two volumes of Physique Sociale which the author had presented to her. Something of the flavour of her thinking is conveyed by the this quotation from their article:

Quetelet delighted in expressing the apparent paradox of the co-existence of such free will with the ‘remarkable’ constancy of numbers of marriages, male births etc from year to year or the ‘frightful’ exactness with which the number of murders, suicides, etc reproduced themselves from year to year. Such expositions were sadly misunderstood by some who were thereby provoked to denials of the applicability of statistics to matters that involved free-will. (Diamond and Stone: 75)

They go on:

…the Prince Consort did devote a good part of his address to the 4th International Statistical Congress in London 1860 to explaining the position of his former tutor, Quetelet, and opposing ‘the fallacy that statistics lead to fatalism’. (Diamond and Stone: 75)

Florence Nightingale was able to resolve the apparent conflict to her own satisfaction, although this resolution owed nothing to the insight which an understanding of probability theory would have given her. She thought that there really was an iron necessity in the nature of things which required ‘quotas’ to be met.

She wrote:

… of the number of careless women to be crushed in a given quarter under the wheels of ill-driven cabs: were the number not made up on the last days of the Quarter, we await (not with coolness, let us hope) the inexorable law of Fate which - always supposing the state of Society not to be changed -always fills up its quota. (Diamond and Stone: 77)

Later in the same piece she added:

And in this regularity certainly which makes our hair stand on end lies in fact our best, our only hope for the future. For were the results not certain, how could we foresee them? How could we modify, change them? (Diamond and Stone: 77)

Free will, for Florence Nightingale, lay in our ability to discover those laws and to use them for the improvement of society. She, like many others since, did not appear to be aware of the paradox implicit in this position. How is our supposed freedom to use these laws to escape from the iron necessity which those same laws impose on our decision making?

Whatever the merits of the case, these early debates fairly stated the problem. Few today would go along with Florence Nightingale’s social determinism, but that is not because the facts have changed. Indeed, the variety and subtlety of today’s ‘social laws’ go well beyond those which so fascinated the pioneers. Before we go on to resolve the misunderstanding which linked statistics with fatalism, it is worth looking briefly at the nature of the statistical evidence.

Some examples

Suicides and accidents continue to provide illustrations of the regularities in social events. Young ladies no longer fall under the. wheels of ill-driven cabs, but accidents at work and in the home and on the roads and railways occur with monotonous regularity as do criminal acts. Table 1 gives two examples taken from The Annual Abstract of Statistics (1993) (Tables 10.12, p. 145 and Table 4.20, p. 86).

Table 1 Numbers of road deaths attributed to ‘other’ causes and the numbers of convictions for handling stolen goods in Northern Ireland

	‘81	‘82	‘83	‘84	‘85	‘86	‘87	‘88	‘89	‘90	‘91
Road deaths	244	238	226	240	233	277	213	260	264	237	229
Convictions	390	390	406	476	419	413	417	347	398	482	455

The numbers are not absolutely constant, but the variation over time seems haphazard. Given that the individual circumstances of each happening are unique and unrelated to one another, it seems remarkable that the totals are so nearly the same year after year. If we probe a little deeper there often seems to be a pattern in the variation itself. The amount of variation may be measured by the variance – the average of the squared deviation from the mean. It is very rare to find that the variance of such series is less than the mean; it may be roughly equal to the mean, but usually it will be larger. Somewhat perversely, we may think, there seems to be a limit on how small the variation can be.

If the number of events in each period is very small, the pattern of variation may itself be very revealing. A good example is provided by the work of Lewis Richardson on the outbreak of wars between AD 150 and 1931 (see Kendall 1961). Such outbreaks were relatively rare, there being 223 out of the 432 years in which no outbreaks occurred. Sometimes there were as many as four in a year. The complete frequency distribution is given in Table 2.

Table 2 Outbreaks of war by year

Number of outbreaks in the year	Number of years
	Observed	Poisson
0	223	216
1	142	150
2	48	52
3	15	12
4	4	2
	432	432

Is there anything special about this distribution? Its mean is 0.69 outbreaks per year and its variance is 0.76. These are reasonably close, but the significance of the pattern of frequencies emerges when it is noted that the frequencies conform closely to the terms of what is called a Poisson series; this is the name given to a sequence of numbers where the ith in the series is proportional to (mean)i divided by i x (i − l)…2xl.

Were this an isolated example it would be no more than a curiosity, but it is characteristic of many other kinds of events such as outbreaks of strikes and accidents of many kinds, all of which involve human decision making, individually or collectively. The regularities displayed can certainly be turned to practical use, but what do they tell us about the freedom or otherwise of those whose decisions lie behind them?

Another interesting distributional pattern is known as Zipf’s law, after its originator. It is closely related to the Pareto distribution, which arises in the study of income distributions and in other fields. The ‘law’ is exemplified by the example shown in Table 3 taken from Kendall (1961: 5).

Table 3 Size and rank of US steel producers

Producer	Capacity Millions of tons/year)	Rank Order	Capacity x Ranks
US Steel	38.7	1	38.7
Bethlehem	18.5	2	37.0
Republic	10.3	3	30.9
Jones & Laughlin	6.2	4	24.8
National	6.0	5	30.0
Youngstown	5.5	6	33.0
Armeo	4.9	7	34.3
Inland	4.7	8	37.6
Colorado Fuel & Iron	2.5	9	22.5
Wheeling	2.1	10	21.0

Steel producers are listed in decreasing order of size, and the point to notice is that the figures in the last column are very roughly constant, and the variation which does occur is not systematic. Again, this would not be particularly remarkable but for the fact that a similar property has been observed in many other examples as diverse as sizes of towns, sizes of religious castes, claims against insurance companies and salaries of executives. Once again there seems to be a simple pattern emerging in the aggregate which belies the complexity of the factors involved in particular cases.

If lawfulness of the kind we have described is so common – and there are many other fields to which we could have turned for evidence – the question of how free social actions really are cannot be avoided. Was Florence Nightingale right in her belief in the ‘iron necessity’ of social law?

Law and chance

The first step to understanding the nature of the regularities which we have illustrated is to see that similar ‘laws’ can arise even when we deliberately arrange matters so that there can be no constraint. As an example, suppose that we toss a coin repeatedly until the first head appears. It may take one, two, three or more tosses for this to happen. We know that a fair coin falls heads and tails equally often, so we would expect the sequence to terminate at the first toss on about half of the occasions. In those cases where we are not successful on the first toss, about half will yield a head at the second attempt. This means that on about ¼ (= ½ x ½) of occasions the first head will occur at the second toss. By extending the same argument to subsequent tosses, we deduce that a head will occur for the first time at the third toss on about ⅛th of occasions, at the fourth toss on 1/16th, and so on. In a very large number of trials, the relative frequencies of the waiting times will be given by the series

$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$8$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$16$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$32$}\right.,\dots$

Note that there is no limit on how long we may have to wait for the first head, though the chance decreases rapidly as the waiting time increases.

We might call this result the ‘geometric law of waiting time’ since the terms in this series form a geometric progression. In common with the examples given in the last section, there is a simple regularity in the aggregate behaviour of the collection of tosses. But here there can be no question of the outcome of any trial being constrained by the need to yield a geometric series because the outcome of each toss was arranged to be quite independent of all others. The geometric law is the consequence of the randomness of the tossing and not the other way round. The randomness of the individual tosses leads to the geometric pattern in the aggregate and not vice versa. The lawfulness lies in the constancy of the chance of a head and of the conditions of the tossing rather than in the frequency distribution of the outcomes. Florence Nightingale’s error in ascribing an iron necessity to the regularities displayed by Quetelet’s tables was a classic example of putting the cart before the horse.

The tendency of the argument thus far is to show that lawfulness may arise from chance rather than from some externally imposed law. In the earlier examples discussed, the outcomes were, apparently, the results of human choices, and it is not immediately clear what relevance coin tossing has in this context. Unless we can link chance with choice in some way we are not much farther forward. The nature of the difficulty and its resolu tion may be clearer if we look at the data on outbreaks of war more closely.

Suppose that on any day the outbreak of war has a very small probability of occurring. That is, although there are situations that could give rise to a conflict, one will occur only if a rather unusual set of circumstances arises. The chance of an outbreak need not be the same on every day but could vary with the season, or with economic or demographic factors. We further suppose that the occurrence of an outbreak on any one day is not influenced by other occurrences. This is hardly realistic in the modern world, but would have been more plausible in earlier centuries. Given these two conditions, it may be shown mathematically that the distribution of outbreaks per year would be expected to have the form of a Poisson series.

This result does not depend on the details of how the participants made their calculations – all that it requires is the smallness of the probability and the independence of the outbreaks. It is not, therefore, very surprising to find the Poisson law arising so frequently since its basic requirements are consistent with a wide range of decision-making processes and so it tells us virtually nothing about the factors that precipitate conflict.

Although this example clarifies the issue, it still involves a probability, which means that we find randomness at the point where we would expect to locate human choice. It is clear, therefore, that if statistical analysis is to throw any light on the nature of choice we must look more closely at individual choices and not simply view things in the aggregate.

The explanat...

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Rerum Cognoscere Causas
• Part 1 It All Depends What We Mean By…
• Part 2 More of Less Freedom?
• Part 3 Political and Economic Freedoms
• Part 4 Choices and Policy Issues
• Part 5 Techniques for Freedom?
• Contributors
• Index