Network Persistence and the Axis of Hierarchy: How Orderly Stratification Is Implicit in Sticky Struggles

Network Persistence and the Axis of Hierarchy

Network Persistence and the Axis of Hierarchy

How Orderly Stratification Is Implicit in Sticky Struggles

Steven Rytina

Anthem Press

An imprint of Wimbledon Publishing Company

www.anthempress.com

This edition first published in UK and USA 2020

by ANTHEM PRESS

75–76 Blackfriars Road, London SE1 8HA, UK

or PO Box 9779, London SW19 7ZG, UK

and

244 Madison Ave #116, New York, NY 10016, USA

Copyright © Steven Rytina 2020

The author asserts the moral right to be identified as the author of this work.

All rights reserved. Without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise), without the prior written permission of both the copyright owner and the above publisher of this book.

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

ISBN-13: 978-1-78527-196-0 (Hbk)

ISBN-10: 1-78527-196-2 (Hbk)

This title is also available as an e-book.

CONTENTS

List of Illustrations

Preface

Chapter One Sticky Struggles: The Unified Pattern of Social Ranks Inherent in Networks

Chapter Two Foundations of Cacophony

Chapter Three Knots of Regularity

Chapter Four Hierarchy: Inevitable but Inevitably Messy

Chapter Five The Inevitable Emergence of Stratification

Chapter Six Scaling Intergenerational Continuity: Is Occupational Inheritance Ascriptive After All?

Chapter Seven Taming the Mobility Table

Chapter Eight Is Occupational Mobility Declining in the United States?

Chapter Nine The Continuum of Class over Time: Deconstructing Imposed Class to Uncover Empirical Classes

Chapter Ten Concluding Reflections

Appendix: Why Robust Attraction Is (Effectively) Inevitable for Mobility Data

Index

ILLUSTRATIONS

Figures

6.1 Path diagrams of the role of education in intergenerational continuity of occupational rank

7.1A Fitted density of the SAT model

7.1B Fitted density of the SAT model net of marginal sizes

7.1C Fitted density of the status and autonomy components of the SAT model

7.1D Ratios of outflows based on status and autonomy components of the SAT model, comparing each category’s outflows to a reference category, other Craft

7.1E Fitted density of the status component of the SAT mode

7.2 Quantile-quantile plot of 1 degree of freedom likelihood ratio tests for asymmetry of father versus offspring location for 348 detailed occupations

7.3 Quantile-quantile plot of 1 degree of freedom likelihood ratio tests for difference of location on principle dimension versus MSEI2 for 398 detailed occupations

7.4A Fitted density net of marginals for the SSIA mobility surface

7.4B The mohawk. Fitted density for the SSIA mobility surface, net of the marginals, with uniform micro-diagonal inflation

7.4C The mohawk of uniform micro-diagonal inflation viewed from a different angle

7.5A Fitted density using SSIA for the 17 aggregated SSIA categories, net of the marginals

7.5B Fitted density using SSIA for the 17 aggregated SSIA categories, net of the marginals, with inflated micro-diagonal included in diagonal values

7.6 SSIA standardized to offspring marginal distribution

7.7 Marginal distribution of SSIA using bin width of .29 based on 18,175 cases derived from OCGII data

7.8 Proportions of sons with current occupations at or above an SSIA value for three selected fathers’ occupations

8.1 Major occupation group

8.2 Major occupation group

9.1 An illustrative cascade of class viewed over time

9.2 Decomposition of the Erikson–Goldthorpe seven category class schema

9.3 (a) England and Wales data; (b) USA-OCGII data; (c) USA-GSS data; (d) Comparison of USA with England and Wales

A1 Eigenvectors as carriers for occupational scales

Tables

2.1 A socioeconomic classification and ranking of 17 occupational categories with comparisons to other ranking systems

2.2 Summary of the results of the ranking exercise reported in Table 2.1

3.1 Sticky networks illustrated

6.1 Correlations among various rankings of detailed occupational categories

6.2 Correlations of various rankings of detailed occupational categories with average offspring SEI and average fathers’ SEI

6.3 Correlations measuring the intergenerational continuity of occupational rank

6.4 Correlations of different measures of occupational rank with respondent education

6.5 Total occupational continuity and net direct effect of father’s rank on offspring rank for different measures of rank

6.6 The correlation of offspring occupational rank with father’s occupational rank for different levels of education

7.1 Measures of fit for Hout’s SAT model and for models using subsets of the terms of the overall model

7.2 Weighted and unweighted correlations of scales with average origins, average destinations, and both combined

7.3 Outliers among tests of the hypothesis that detailed occupations are vertically dispersed across job contexts

7.4 Tests for and measures of vertical differentiation due to contrasts of job context that Blau and Duncan used to subdivide 10 coarse occupational categories into 17 categories

7.5 Selected results from estimating vertical locations contrasting job contexts within detailed occupations

7.6 Comparison of aggregations based on the Blau and Duncan 17 category scheme versus 17 equal intervals of SSIA

7.7 Statistics for various association models applied to the 17 Blau and Duncan categories table and to the 17 aggregated SSIA categories table

8.1 Correlations among assorted operationalizations of occupational rank

8.2 Correlations of various occupational scales with average origins and destinations scored by various scales

8.3 Intercorrelations among measures of occupational rank

8.4 Standardized regression coefficients and multiple correlations for regressions on SEI and OCGII-SSIC of occupational ranks estimated by SSIC applied to GSS data

8.5 Results of inferential tests of whether the mobility counterparts of occupations scored by SEI differ from SEI rank. Results from OCGII used to form a priori categories to assess replication with the GSS data

8.6 Assorted rank values for all detailed occupations with SEI > 70 (top panel) or SEI between 17 and 20 (bottom panel) and at least 30 observations in the NORC GSS, 1972–90, pooled sample

8.7 Intergenerational occupational correlations using various scales for annual and cumulative annual samples of the GSS

8.8 Percentage change in the intergenerational occupational correlation versus the .3675 found with SEI in OCGII for annual GSS samples using different occupational scales

8.9 Intergenerational occupational correlations for various scales for 1972–86 and 1987–90 subsamples of the NORC GSS with tests for no difference

8.10 Changes in the role of education as mediator of the intergenerational reproduction of occupational rank

9.1 Demonstration that standard results obtained from fitting aggregated tables may be obtained as differences of models within the expanded framework

9.2 Correlations among occupational scales

9.3 Correlations between occupational scales and averaged scale values over mobility counterparts

9.4 Intergenerational correlations assessed using alternative occupational scales

9.5 Maximum likelihood models used to detect the echo of class

9.6 Gross and net immobility for the seven Erikson–Goldthorpe–Portocarero classes

9.7 Comparison of models including demonstration of the echo of class

PREFACE

This book presents some novel takes on fundamental questions of sociology, including what the nature of the social is, how one can square the sometimes evident rigidities of social structure with the effectively universal capacity to defy or resist rules, norms, or other possible sources of social cohesion and regularity, and what the nature of social stratification is.

I will not try to anticipate the full answers here—that is the task of the text. But I do want to insert a few observations about the nature of the argument.

This book took a long time to prepare—the better part of a decade although in truth I only worked on it full time during two years of sabbatical leave. It is laughable to recall this now, but when I first anticipated the project I allocated about a month at that, the brief month of February. It didn’t quite work out.

My optimism had grounds. I had a relatively short list of notions that I aimed to cover. To me, these were clear conceptions and claims that I had entertained for some number of years. Seemingly all I had to do was write them out.

What made that much harder than I anticipated was twofold. For the most part, all of my claims were mutually linked, that is, each of the facets illuminated multiple other facets and the lights shined in either direction. In a sense, this was inevitable, for what I had in mind was a singular object, a conceptual sketch of social structure, that combined multiple complementary notions. A first consequence was that no particular order for writing them out was apparent. Second, nearly all of the claims deviated from widespread sociological reasoning generally regarded as compulsory. Nakedly stated, without the scaffold of supporting elaborations, my notions could easily be read as assorted off-beat misunderstandings contrary to what most people knew or took to be true. It was only by assembling the pieces in a careful order that did not open onto sidetracks, many of which I knew were widely taught and widely accepted, that I could hope to convey how the off-beat elements were not ignorant blunders but instead were solutions. Or at least potentially productive novelties.

A brief illustration may help. A commonplace, so deeply embedded that most practitioners probably take it for granted, is that a social network is a collection of nodes graphed as points and relations or bonds graphed as arrows or lines. When the arrows are directed, that is, pointed at one end, the result is a directed graph or di-graph.

In the following I will modestly reformulate the essence of network as a strong propensity to renew association with previous interaction partners. The counterpart is widespread resistance to rupture. In contrast to the di-graph image, often taken to be a static or fixed structure, the appeal to renewal is probabilistic, subject to waxing and, more rarely, to dissolution.

At first exposure, I suspect some will react to this as commonplace, even as a notion they’ve long entertained, at least more or less. In any case, it is not particularly hard to grasp. I will express it in a form, sticky networks, that is self-evidently true, for example, by inspection of one’s autobiography.

What is no less obvious, that is, follows by very compelling¹ logical sequence, is that such local patterns are united into a unidimensional whole that, as shall be seen, is quite obviously synonymous with social stratification. Obvious and obviously in the preceding sentence are a deliberate attempt at irony. I am fully aware that for several generations, at least, nearly all sociologists have been convinced that stratification must be conceptualized or regarded as multidimensional. That there is a coherent way of looking at the social world that by strong logic leads to the contrary result is something I aim to render as obvious but is, to be sure, likely to appear strange and unfamiliar, at least in places.

As one quick illustration, the network foundation advanced below is fully compatible with universal social construction. Everything that can occur is action subject to such latitude for free will as exists in local settings. Yet this occurs against a backdrop of a unitary axis of social hierarchy, of stratification. People can deny this, of course, much as one can deny global warming or gravity. Those who step off of tall buildings do not, of course, escape the usual consequences. Stratification is social, not material, but the force of reality is in some regards comparable.

Not least, I will show below that the principal axis of stratification is amply apparent in three of the most highly regarded data sets on occupational mobility. The axis leads to models that are empirically superior to the most prominent alternatives advanced heretofore, often by substantial measure. The axis is superior to Socio-Economic Index, to coded class, and to multidimensional mappings of the mobility surface. Among other advantages, mapping using the principal axis reduces the mobility surface to a variant on the normal distribution, in a sense rendering the very notion of the mobility table as obsolete or at least dispensable.

To repeat, many of the foundational claims and concepts in the following will appear to be hardly daunting or demanding. Quite a few are commonsensical or even self-evident on their face. Not everything is simple, however. I appeal to mathematical equations in one chapter and two appendices. The statistical analyses are sophisticated where necessary.

The empirical failure of multidimensionality is final or uncompromised. Those familiar with multidimensional methods might suspect that lesser dimensions after the first or principal axis are logically inevitable. This is true. However, the final few pages in the concluding appendix show that for all three data sets the higher dimensions are effectively indistinguishable from noise. The principal axis stands alone.

In some ways, the statistical treatments arise from the theoretical reflection with faithfulness that is unusual in sociological work. That is baked in because the case for a principal dimension has considerable affinity with important methodological tools. However, the statistical treatments do not, in the nature of the case, follow in any strict logical fashion. The empiricism is a research program. It is highly successful. It is not, I hasten to add, true in any absolute or strict sense. It is successful in unveiling a great deal of new order in data that have, arguably, been more severely scrutinized than any other in the field.

I hope the preceding reflections inform how readers try to approach this work. I would emphasize that while the material is ordered by chapters, there is much to be said for reading in different orders, for skipping about, and, yes, for skipping material not suitable to one’s taste or training. I provide a synopsis of chapters at the end of the first one. I heartily recommend referring back to this to try to grasp some of the relations among the parts. The whole is best regarded as a sort of mosaic of many colors. The pieces fit where they are placed, or so I hope. But a twist of the kaleidoscope will often reveal another arrangement that is not obviously inferior in order or regularity.

One brief historical note is in order. Some of the empirical work reported below was presented at conferences and otherwise circulated in draft. A careful reader of footnotes will discover the somewhat surprising influence this has had on subsequent work, albeit not always with adequate credit, at least in my opinion.

Like most authors, I accumulated many debts in the course of this work. I had support from the Social Science and Humanities Research Council of Canada (410-95-072: 820-2006-0003) and the National Institutes of Health (Contract Z034501) (all but the first was for network research not specific to this project but was certainly welcome nonetheless). Special thanks go to my friend and one-time McGill colleague John Sandberg for sharing and facilitating my efforts with special attention to the latter two grants. Thanks as well for John’s excellent sense of humor that almost never failed to raise my spirits.

I had the benefit of some excellent research assistance. Special mention to Zhou Yang, whose econometric expertise and deep knowledge of Gauss helped untangle snarls from which I might never have escaped. Frederick Merand provided yeoman service. Babak Fotouhi, then of the McGill Department of Electrical Engineering, deserves special honor. For his PhD qualifying exam, he undertook to recap my proof of robust attraction based on a footnote sketch I had placed in an earlier draft. He couldn’t get it to go through. His evident talent motivated me to recheck my work whereby I discovered a subtle flaw induced by my printing test correlations at 3-digit accuracy, rendering .9999 as 1.000. Once I undid the rather modest twist in the relevant vector, I happened upon the insight that made the concluding appendix possible. In preparing the appendix, I borrowed heavily and essentially from the notation Babak had devised for his attempt. I owe him a large debt.

Joan Huber and William Form were unflagging in support. They also provided exceptionally close reading of early drafts. Their exceptional hospitality was a further bonus.

The students in my seminars, on networks and stratification at McGill, and on networks and stratification at Harvard, provided many useful reactions that helped me achieve such clarity as the present version possesses. I would single out Katayoun Baghhai, Chuk Plante, and Nicole Denier who provided especially careful and rich reactions.

Axel van den Berg and Anthony Masi were great friends and remain so today. Their support was considerable and always welcome.

Bairj Donabedian was a highly useful touchstone. His imagination is beyond ready compare.

Deepest gratitude goes out to Dingxin Zhou for timely encouragement that I had a real contribution in hand. This came in one of my all too frequent spells of fear that daylight would never come my way.

Mary Waters deserves special thanks for extending an invitation to be a visiting professor at Harvard after my retirement from McGill. It seems fitting that the final polish was applied in Cambridge where it all originated. My conversations there with colleagues, such as Chris Winship, Peter Marsden, and Hiroshi Ishida, were, as ever, enormously stimulating.

Other sources of excellent conversations and, at times, much needed encouragement to persevere were John Li and Peter Bearman. Randall Collins offered very generous intellectual support and encouragement at a crucial time. I didn’t always take all the advice I was offered, but I have no doubt whatever that it vastly improved the final product.

Next to the heart of the matter, that is, to matters of the heart. Lucia Benaquisto was my soulmate for nearly the entirety of this lengthy journey. She was my best friend. She put up with my endless obsessive discussion of my daily struggles. Sadly, she passed in 2016 and did not get to see the end of the process. I am sure it would make her smile, since almost anything would do that.

Thanks as well to Joy Riskin and to Josiah. My luck in finding any new family, much less one as wonderful as you are, is beyond mortal comprehension.

1. IMHO, almost needless to add.

Chapter One

STICKY STRUGGLES: THE UNIFIED PATTERN OF SOCIAL RANKS INHERENT IN NETWORKS

Sticky struggles are a metaphor that offers a new way of approaching social stratification. Three novelties give a taste of the arguments to come.

First, in place of ladders of positions or discrete classes or other concepts, I will derive rank as an inevitable counterpart of social networks. Networks, in turn, are sticky. Once formed, ties are glue that bind people into repetitive relations. This starting assumption is a commonplace, even beyond dispute. The novelty is a formal argument that stickiness must ramify to population-wide regularity: an emergent dimension of social rank. This poses a challenge, or offers new puzzle resolutions, to central dilemmas of the nature of social structure or social order.

A second novelty follows from the emergence of rank as a counterpart of sticky networks. Nearly all received opinion holds that stratification is multidimensional. But convergence to a principal dimension follows logically from the network account. Hence, one dimension is first among equals. This theory claim has testable implications. Reanalysis of several mobility data sets yields strong support.

A third novelty is a challenge to a generation or more of empirical research. Intergenerational fluidity will be shown to be less, perhaps much less, than reported heretofore. This is a corollary of the empirical superiority of the principal dimension when pitted against previous proposals for schemes of social rank.

The central metaphor, sticky struggles, emphasizes that stratification is not plural but myriad, not several but many, almost beyond counting. In place of a tidy few dimensions, stratification is many, many locales of activity. But complexity is not intractable. Quite the opposite. The emergent ranking of a principal dimension yields order out of complexity.

Sticky struggles address head-on one of the central conundrums of stratification. Stratification has a powerful impact, but stratification can be fuzzy, even elusive, not readily reduced to specific propositions about concrete circumstances.¹ That may be, in part, because stratification is not a thing, a form, a principle, or anything else pure or simple. Stratification is more nearly a tangle.

Stratification is also a metaphor, likening social ranks to the layering observed in rock formations laid down by repeating cycles of sedimentation. The metaphor of strata may be unpacked into individuals somehow bound into stable social ranks. The metaphor of sticky struggles substitutes a new vision. The binding force of stable inequalities is entanglements in social networks.

This brings a useful shift in emphasis. Strata are permanent and unchanging. Entanglements bind but also give way. New ties replace older ones. However fast or slow, there is always some tempo of change.

Networks and entanglements replace layers with more intricate textures. Social webs consist of ties between individuals. Moreover, bonds between pairs build up over time. Overlays and combinations are inevitable. To recast stratification in network terms, as sticky struggles, is to set aside pure forms in favor of intertwining and mixtures. This is true to life. Advantage comes in many forms. The sources of stable advantages include jobs, skills, family assets, property stakes, educational credentials, and social connections. As time passes, blending occurs and many forms shape-shift into other forms. Advantages transmute among kinds. Some are subject to accumulation and decay. Sometimes, allocation is rule-governed, even approaching fairness in some degree. However, coercion, deceit, and ruthlessness play a part, perhaps, but not always, restricted to less favored locales. Stratification can be messy.

A common denominator is imperfect persistence. This is stickiness. Advantage, once gained, by means foul or fair, tends to persist. Advantage is sticky. So is disadvantage. Persistence prevails. But imperfectly. Persistence is almost everywhere subject to change, usually gradual, less often abrupt. Incumbents age while capacities wax and then, sadly, wane. Death makes turnover inevitable. But so also does struggle.

Imperfect persistence is open to revision. At least some with lesser advantages seek to rearrange outcomes more to their favor, often at the expense of past winners. Some succeed. Some fall short. Winners and losers are sorted, some up and some down.

Struggles, contests over advantage, are a second common denominator. Strips of time where social ranks are stable are punctuated by contests where rank comes up for grabs. Struggles arise because individuals pursue results where one party’s success is, in some degree, the exclusion of other parties from what all desired.

Sticky struggles are a tale of stratification where rigidity prevails yet fluidity is always a possibility. That near-paradoxical character, almost thing-like in persistence yet vulnerable to disruption, is inherited from the social bonds that cement persons into ranks. Bonds can persist for entire lifetimes, but many, even most, do not. And even the oldest bonds are subject to rupture if ever the will to do so arises.

The overall argument for sticky struggles will bring together an unusual range of concerns. Three central themes of critique introduce some of the puzzles that will be addressed in the following chapters.

First Critique: The Oddly Missing Quantity of Mobility

Intergenerational occupational mobility is a starting point. Deep problems in addressing mobility will motivate a search for new foundations. Mobility will then return as an empirical topic in the later chapters.

The first theme of critique is illustrated by a question that has gone unanswered in the extensive literature on occupational mobility. The unaddressed question is: What number best summarizes how much mobility occurs?

That no number has been put forward may seem surprising. Above all, the literature on occupational mobility is concerned with statistics, estimation, and quantity. Typical contributions include vast tabulations of numbers. Plainly, no aversion to quantification accounts for the silence. What does? I shall argue that the root cause is the inability to spell out any unified conceptual scheme that lays out exactly what will count as a definite quantity of mobility.

What instead prevails is what I term cacophony: a plurality of voices united only by an agreement to disagree. What accounts for this consensus on pluralism? A possible source is a proposition that I suspect is widely taken for granted: some conceptual outlook must be adopted before operationalization can proceed. While adoption could be justified by extended exegesis, this is optional. What is not optional is to privilege some scheme of what will count as equal and unequal in some larger scheme of inequality.

Imposed class categories are a popular option. These come in different flavors sometimes attributed to Marx or to Weber. Another option is to assume that occupations are roles somehow constrained to homogeneity of status. But choice is required. Cacophony then becomes unavoidable in response to an irresolvable dilemma. No common denominator is apparent that might unify different schemes.

The dilemma cannot be avoided because mobility refers to distance traveled over some span of time. Some concept of distance has to be adopted a priori for mobility to have any meaning. Distance requires details. Details differ across schemes. Different schemes specify ranks as numbers that are crudely comparable, but no more. Simply put, different schemes use different themes to address the same phenomena in different ways. Inconsistencies abound. Some are modest, some much less so.

The differences go beyond quantities that are incommensurable. The theoretical objects are also not translatable. Any notion that translation rules could be agreed upon, or imposed by some artful synthesis, must be dismissed as utopian.

The unresolved dilemma arises because some scheme of concepts and definitions must be adopted to create data. But concepts and definitions are not falsifiable. Empirical adjudication between competing schemes is problematic or even impossible.² The dilemma stems from incompatibilities in core accounts of primitive terms such as property or authority (Chapter 2 will explore this in detail). This diagnosis suggests an end run, a minimalist conceptual scheme. Such a scheme must prefigure or allow for stratification as a stable pattern. However, it must also allow for diversity among normative accounts, favoring none but not disallowing any either. Put another way, the minimalist scheme has to allow that any (and all) alternative accounts could hold, in some degree, in some locales, at some times, and so forth.

Such an end run offers a way forward. That is no small thing. Neither empirical evidence nor methodological virtuosity offers an alternative path. That is because the dilemma arises from clashing theoretical claims. Some are explicit, but many are tacit and presupposed. Differences in perspective that arise in such background assumptions are almost impossible to resolve, not least because disputants can (and surely would) challenge any critical account that attempted to spell out the unstated specifics.

The project includes a positive side as well as a potential remedy. Perhaps stratification is sticky because tangles, impurities, and mixtures are unavoidable. On this view, individuals are, at best, imperfect substitutes for other individuals. Substitution entails friction. However, imperfections, for example, differences between an incumbent and a field of possible substitutes, are variable. Hence, imperfect substitution raises a potential selective force over a field, in this case, of candidates. And friction might be common, even ubiquitous. Perfect substitutes might be rare or nonexistent. On this new account, zero friction, that is, perfect substitution, is recast as a limiting special case. This thesis of extensive individual differences is plausible, congenial, and not too hard to imagine. Yet this seeming commonplace contrasts with concepts like occupations or classes that assert equivalences over categories of individuals. Much that is familiar can be revisited from a new angle.

Accordingly, my strategy is to lay aside older issues of the relative merits of extant master accounts. Instead, I will spell out a least common denominator that allows alternatives to coexist as options. The key is what is left open, what is not ruled out, because cacophony is unavoidable when any scheme invokes normative universals that ban or disfavor patterns that other schemes deem essential.

This requires some delicate footwork. To be complete, any account of stable inequality has to address why people take the requisite actions to reproduce the pattern. As sociologists have recognized since the Division of Labor (Durkheim 1984), loci of stable inequality such as property, exchange, and authority ultimately rest on norms.

The trap of cacophony is hard to evade. Norms might seem unavoidable in any attempt to account for action and reproduction. Without reference to norms, it is difficult to speak of social order or social structure or of stable, ordered, inequalities. However, irreducible diversity of views rears up as soon as any analysis turns on commitments to some norms at the expense of alternatives.

This is conventional stuff, if rather removed from typical discussions of occupational stratification. Quantifying stratification requires data definitions. Whether stated up-front or buried somewhere in some fine print, every such scheme favors some account of the dominant forms of stable inequality. Such accounts are norm-laden. And such accounts clash by each ruling out at least some facets or features that other accounts deem central or essential.

But this formulation reveals a path toward a synthesis, albeit one whose feasibility will require some effort to spell out.

An initial step toward a new synthesis is the minimalist conceptual scheme, mentioned above. Such a scheme entails stratification but is strictly neutral among clashing normative accounts. This allows for a reality of mixtures, impurities, and even occasional oddities.

This relaxed account shows how stratification might persist in spite of the weakness (or absence) of features that global accounts proclaim as essential. Stratification is viewed as a patterned mess that is unlikely to conform to any essentialist account. However, this does not displace structure in favor of some fuzzy notion of fading inequalities. A tangle is none of intangible, evanescent, or vanishing into some fog of post-something-or-anotherism. As shall be seen, a tangle is the sum of many possible partial patterns that will prove more empirically potent than any pure forms. Thus, sticky struggles provide a different tack for accommodating the difficulties that clean, neat, pure accounts often face.

While this should prove of interest in its own right, it is helpful to situate it in terms of a problem that is less embedded in future argument.

Cacophony among outlooks is a deep problem. Nearer the surface, appeals to objects that are not very object-like are all too common. Key terms in stratification research oversimplify. Many imply neat divisions that nowhere exist.

Occupation provides a handy illustration. Every scheme for studying occupational stratification rests on some classification of jobs into occupations. (Most add rich further qualifications, combining occupations into class categories or assigning them to ranks on some indicator of standing.) But occupations are hardly thing-like. The jobs grouped into categories by such schemes are hardly identical. And such internal variety is almost surely uneven across categories. And so forth. At best, occupations as coded refer to fuzzy probabilistic clouds. The clouds vary in density and in overlap. Inside, each contains internally diverse collections of jobs.

Thus, any singular concept of Occupation somewhere gives ways to plural occupations. Not only does each vary internally, but they are uneven in their degree of variability.

For some, this truism may suggest the conventional need for further, future empirical research. But it also signals a theoretical lacuna. Any assertion that occupations are elements in some further master scheme, of classes or ranks of some kind, oversimplifies. Unclear, indefinite notions, referring to disparate collections that vary in internal diffuseness, provide an insecure foundation for specifying macrostructures.

The empirical chapters will include many illustrations of questionable coding details. However, awkward examples culled from elaborate exercises do not reflect any shortage of skill or expertise. The compromises and expedients that are evident on close examination are best seen as unavoidable in creating coding schemes of such complexity.

Second Critique: Social Bonds as Probabilistic, Not Binary

Putting mixtures and impurities at center stage emphasizes the central role of probability in understanding stratification. The second theme of critique leads to the same emphasis from distinct start: social networks.

An amendment to the dominant network concept brings probability to the fore. The amendment may seem quite modest but proves rich in implications.

Social networks are widely equated with graphs. Graphs are sets of points and lines that translate into crisp pictures. The background convention takes bonds as binary, either present or absent. However, the graph is an image, or perhaps a model, not a social necessity. Bonds come and go. A modest revision is to replace binary bonds by probability: the chance that pairings from the past will be renewed in the future. This gives rise to stickiness, the notion that networks exhibit inertia or resistance to change.

This shift anchors the second central critique. Social network analysis is obviously concerned with social relations. Yet as social network analysis has matured, a dominant strand, which I will label as connectionism, has come to overshadow concern for how relations are an essential context for grasping certain phenomena. This neglected strand can be termed relationism.

Connectionism focuses on questions posed by patterns of ties. To make this work, it helps to assume that relations are taken as givens (Holland 1977, 387). Ties are assumed binary, limited to present or absent. This gives rise to the familiar image of networks as the points and lines of the graph, or as the one-headed arrows of the di-graph. For many, the graph is the network, and the object of social network analysis is patterns in graphs.

While there are rich extensions, to multiple ties, more rarely to ties with valence, the dominant image by far features relations that are present or absent.

A classic that illustrates the connectionist project is Granovetter’s (1973) Strength of Weak Ties. The central claim that weak ties are potential bridges is a pattern that can only emerge in a context of numerous nodes and (therefore) numerous*(numerous−1)/2 possible sites for ties. The counterpart of bridges is gaps, much larger collections of pairs with no ties, united only by the path leading over the bridge. And the weak ties that matter are those that are bridges. The pattern, not tie strength per se, is the crux of when weak ties claim our interest.

Another illustration of connectionism is the small world problem (Milgram 1967). This has matured into a concern for physicists (Watts 1999). Newman’s (2003, 168) much-cited review article begins as follows: "I. Introduction. A network is a set of items, which we will call vertices or sometimes edges (Figure 1.1). Systems taking the form of networks, (also called ‘graphs’ in much of the mathematical literature) abound in the world. Examples include the Internet, the World Wide Web, social networks of acquaintance or other connections between individuals. The equation of network with graph, and of relation with anything present/absent," is rigorous and complete.

Another telling illustration is Coleman’s (1990). While networks are central to his analysis, his pairs of actors were always either tied or not tied. Why some were tied and others not was not addressed. In Coleman’s analyses, the network or pattern of ties was a given, part of the assumptions from which results were derived.

As these brief illustrations show, connectionism has proved very fruitful. But only an uneasy kinship relates connectionism with relationism. Relationism poses questions of conceptualizing (or reconceptualizing) social phenomena as involving coaction. The units of analysis are pairs or, more rarely, larger ensembles of coactors. Pairs engage in transactions or interactions. A central contrast is with abstracted individuals and with the logic of traits. A telling prototype is Hegel’s treatment of the master/slave dyad as mutually constitutive. More recently, Charles Tilly was persistent in insisting on relations as a starting point.

But what is a relation? The dominant recent thrust has been toward dissecting the bond as some cultural-laden loci of shared meaning (Emirbayer and Goodwin 1994, Fuhse 2009). But solving meaning is a very stiff challenge, perhaps unlikely to be resolved any time soon. My personal hunch is that shared meanings will turn out to be joint, local products that could conform to universal premises or rules but very well may not.

Marriage is a handy illustration. No doubt there are all manner of meanings, some shared, others less so, that affect the course of particular marriages. But is there some intersection of meaning(s), some least common denominator, shared by all (or most) marriages that somehow constitutes some essential unity? It seems to me all too likely that future investigations will not uncover some profound solution heretofore unnoticed.

A different line of attack has potential for quicker payoffs. One feature that sets apart married pairs from the vast number of unrealized unions is time. Married people interact a lot.

But not all do. The general characterization immediately suggests important variation. For example, during times of war, many married pairs cease to interact, sometimes for years on end. Some renew when demobilization makes it possible. Many do not.

Marital interaction rates vary among married pairs. They wax and wane for particular pairs. In some regards, this is the essence of the generality that marriages are not uniform. Each marriage is some resolution of material, social, cultural, and psychological factors.

Marital interaction rates almost never arise out of a vacuum. In societies where pairs exercise choice, most premarital pairs were already high-frequency interaction partners before any ceremony or rite of passage. Should a divorce occur, interaction rates only sometimes go to zero and sometimes remain high.

Common denominators thus unify marriage with other kinds of ties. Ties have two components. The first is history, an accumulation of time spent interacting with some partner. The second is renewal, the probability that future interaction time will be spent with the same partner.

This gives rise to a central generalization: the historical distribution of time spent with partners will tend to persist into the future. This is the basis for what I will call sticky networks.

To a point, this is so familiar as to possibly seem banal. The entire project of network analysis—reifying bonds and actors into present/absent lines between nodes—depends on the insight that networks tend to persist over time.

However, a key difference is immediate. Just as in any marriage, whether tomorrow will be a renewal or a rupture is up for grabs. So, too, for friendships, acquaintanceships, and so forth. The apparent diversity of these assorted tie-types dissolves into a shared feature by appeal to the universal common denominator of time. Time spent is the mark of a bond.

There is a close but fuzzy connection with the graph of ties. A graph can be coded by dichotomizing time spent into ones and zeros. However, the ones and the zeros are not really constants and are not really identical. Whatever criterion is used to divide bonds from non-bonds, any coded tie or non-tie is subject to possible change. Today, tomorrow, or at some future date, some bonds will fade below whatever threshold is in force, and what was coded as a one will become a zero. And vice versa. As time passes, some marriages will fade out, albeit at rates that are usually miniscule. And new ones will form. Sometimes in the wreckage of the old.

The low rate of dissolution is a strong bias in choices: days of continuity vastly outnumber days of rupture. This imbalance is easily theorized and shall be addressed below. Ruptures are inhibited by disincentives that are cumulative and tend toward high potency.

Once again, the generalization opens up an agenda of variability in details. Any bond comes with a time trail that starts out thin but then accumulates. The joint history of interaction that constitutes a bond is a sunk cost. This is a species of investment and sets the stakes at risk to should rupture occur. Very strong sentiments may be at issue. Rupture can be painful, emotionally and otherwise, because losses can be immense. Abandoning established ties entails starting over, foregoing the benefits of accumulated joint practice time.³

For many people, most of the time, rupture is far more rare than renewal. But the choice remains. Rupture is an option. Hence, renewal is fully subject to agency.⁴

To code up ties as present/absent (or as variable in intensity) remains as an analytic option. In the background, the ever-present option of renewal or rupture underscores that the graph (or di-graph) is voluntary. However, like marriages, and to hint in advance, like many jobs, rates of rupture are so modest that for many purposes the pattern of marital bonds is a social structure, implacable, involuntary, and (nearly) static.

This dual character, of impersonal regularity that is everywhere voluntary, turns on the contrast of local details and global totalities. While any who wish could readily blow up their own marriage (or closest equivalent) in short order, no individual has any measure of personal control over the larger ensemble. The vast majority of marriages will persist through tomorrow no matter what any of us do. A parallel persistence applies with nearly equal force to most individuals’ personal situations, but the similarity in words obscures a vast difference in degree of personal control.

The distinctions involved can be subtle. Time provides a very attractive analytic standard for taming such problems. Scaling is supple, smoothly extending from seconds to decades, with due treatment for every intermediate possibility. The full range is subject to precise, rich treatments of magnitudes and contrasts. Clock time is additive and biological or psychological counterparts will retain some shadow of this.

Time, like individuals, may be partitioned into mutually exclusive and jointly exhaustive collections. Time spent with Tom is time not available for Dick or Harriet, to say nothing of all the persons resident in Topeka or in Iceland. And so forth.

That last dramatic shift in scale is jarring by design, intended to underscore that counts of persons, like amounts of time, allows rigorous contrasts across a vast range.

Past or expended time can be used to construct relative frequencies. But these empirical results are formally probabilities. Extrapolation into the future is immediate as prediction, albeit imperfect, partly fallible prediction.

Eventually, it will be seen how the ensemble of such regularities entail quantitative texture.

This focus on networks as relations pushes the patterning of connections somewhat into the background. But the foregrounded issue is why networks persist, albeit subject to rupture as the far rarer possibility. A suitably general account will be offered in terms of the learning curve, that results improve with practice. As a handy generalization, both objective performances and subjective perceptions will trend up with repetition, and more surely as larger assemblies of instances are considered.

Practice with a partner is practice at something. The what of practice is ripe with autonomy. Individuals can co-practice what they will, subject to locating amenable partners. But as practice improves outcomes, disincentives of foregone possibilities favor repetition with old partners versus starting from scratch with new ones.

The mechanism to be proposed is highly general. The account is rich in further implications, many subject to empirical tests.

Thought experiments suggest further generalizations. An illustration relevant to stratification is stickiness. One of the central puzzles of social rank is accounting for why undesirable roles and outcomes are not abandoned wholesale, for example, in favor of upward mobility. The ubiquity of stickiness illuminates rigidity as chosen, to a point. Those in less desirable marriages, friendships, neighborhoods, and jobs mostly face options of making matters even worse, at least in the short term, should they abandon extant partners in favor of the new ones available to them.

Earlier, I faulted occupations as fuzzy agglomerates. A contrast with networks is immediate. Networks, in the sense just advanced, refer to specific individuals coacting for specific durations with other individuals.

It is hard to overstate how exquisitely textured this is. Most individuals interact with a very, very modest subset of all humanity. Many persist in such patterns for extensive periods. Everyone already knows this, in some sense, from casual observation of one’s own life and that of others. It is sufficiently down-to-earth that undergraduates are readily persuaded. Yet the line of thought runs contrary to a great deal of thinking that overstates the latitude open to individual choice in social life.

Third Critique: Repeating Crystals or Tangles of Locales

This sets the stage for the third major theme of critique. Many schemes laying out foundations for sociology feature abstract universals. Often these are personified and given a human face. Ego and Alter or the Individual and Society are among the most familiar. This is standard stuff and it serves too many purposes to be dispensed with easily. To give this a name, such formulae assert some sort of least common denominator, abstract elements that hold universally.

An almost inevitable counterpart is that analytic accounts of large-scale social structure invoke some sort of replicated simplicity. These are analogues to crystals—structures formed by orderly lattices of parallel units. Classes, modalities of capital, and occupations ranked into one hierarchy are all illustrations central to the topics under consideration here. Each asserts some kind of uniformity where multiple individuals are reduced to variations on a limited number of key dimensions, factors, or what have you.

If pared back far enough, any such scheme will reveal normative limits on action, privileging some ways of organizing individual life within collectivities and disprivileging others. And since such schemes are fully general, these limits are adopted as universal propositions, applicable to all without significant exception.

This is a variant on the problem earlier identified as the source of cacophony, of agreeing to disagree, with the added stipulation that disagreements are nowhere subject to empirical contest or adjudication.

Is social life so neat and regular? As noted, there are very powerful grounds for either believing it is so or, to illustrate with one of the many options, adopting some provisional version for the sake of having a foundation for pursuing empiricism or other forms of scholarship.

The project for addressing stratification while sidestepping cacophony adds another to such options. A central tenet may be boiled down to a slogan: local rules but not necessarily Global Rules.

On this new view, various universal normative proposals are admitted as local possibilities. This is relatively easy. The formulation of network reproduction is flexible enough to accommodate any plausible master proposal for social regularity. So nothing need be ruled out.

The novelty is rendering the glue for bonds between unequals in the themes of repetition and recontracting.⁵ Primitives describe binding agreements, job situations, and property/authority. The first primitive, sticky networks, provides an account of social cohesion. The second, divided labor as teamwork, brings out friction and imperfect substitution as central features of work. The third, repeated, exclusionary gatherings, incorporate time, space, and material as infrastructure for mutually exclusive access to unequal portions.

These primitives may be of some interest in their own right. They share a common form, sharply skewed probability distributions—a tall, very narrow heap of dominant outcomes and a tail of outcomes, potentially very extensive, that are not impossible but are highly improbable. In common, they highlight a Grand Induction, an ever-recurring transition where past patterns of (highly segregated, potentially specialized) coactivity translate into a future where repetition is overwhelmingly dominant.

In a bare formula, the concepts bridge the gap where history gives way to action.

However, instead of wrestling with the nearly infinite complexities of what was done and what will be done, the concepts narrow focus to something much more tractable: changing partners is exceptional. Repeating past pairings is the (overwhelmingly) dominant pattern.

The concept sketches are very spare. Yet they are also down-to-earth and readily imagined. The sketches lay out some simple commonalities about social bonds, work, and workplaces. The notions apply across a vast range, from preindustrial and rural settings to forms prevalent today. While the notions are put forward to play a particular role in an advancing argument, some may find in them hints toward grasping familiar matters in new ways.

The guiding slogan, local rules but not necessarily Global Rules, invokes an asymmetric qualifier. The network concepts are without prejudice to any and all potential universal normative propositions that limit choices, preferences, actions, or the like. None are ruled out and none are ruled in.

This avoids cacophony. No possible pattern of exterior limits, macrostructures, and so forth is deemed impossible. Analytic individuals could optimize (or something weaker) their returns with respect to some consensus on status. Work organizations could be constrained, perhaps by some selectionist pressure, to gravitate toward a common design of class differences. And so forth. The pure forms remain as analytic options that could be adopted and pursued, but the argument advances without foreclosing other options in favor of a chosen favorite.

An appealing realism is further on offer. Pure forms give way to mixtures of polar opposites. Fair means versus foul means, exclusion by design versus inclusion by default, or locales where classes’ rigidity is crystal perfect versus zones of fluid disorder.

At least one very large question remains. Most theorists of stratification spell out some stance on the overall contours of social inequality. To put a complex matter simply, the ultimate source of the propositions that result in cacophony is efforts to conceptualize the problem of stable social ranks.

The elements of a solution, albeit a novel one, will be already present. Individuals are autonomous. Each works with partners to keep ties going. Since ties are means to ends (which the individuals pursued in constructing them), incentives to conserve bonds build up over time. Individuals are therefore imperfect substitutes. And they are much better substitutes for some possibilities than for the vast majority of alternatives.

This ubiquitous inertia provides local glue that coagulates into an overall regular pattern.

Massy, tangled inertia is only uniform in nonuniformity. This is quite unlike much older theorizing about the nature of stratification (and social regularity more generally). Most classical accounts sketch a least common denominator that holds without significant exceptions. These constitute,