Rational Choice Theory

There is a commonly made distinction between two types of scientists: risk-taking, trailblazing mavericks and detail-oriented followers. A number of recent papers have discussed the question what a desirable mixture of mavericks and followers looks like. Answering this question is most useful if a scientific community can be steered toward such a desirable mixture. One attractive route is through credit incentives: manipulating rewards so that reward-seeking scientists are likely to form the desired mixture of their own accord. Here I argue (...) that this idea is less straightforward than it may seem. Interpreting mavericks as scientists who prioritize rewards over speed and risk, I show in a deliberatively simple model that there is a fixed mixture which is not particularly likely to be desirable and which credit incentives cannot alter. I consider a way around this result, but this has some major drawbacks. I conclude that credit incentives are not as promising a way to create a desirable mixture of mavericks and followers as one might have thought. (shrink)

This paper concerns Warren Quinn’s famous “The Puzzle of the Self-Torturer.” I argue that even if we accept his assumption that practical rationality is purely instrumental such that what he ought to do is simply a function of how the relevant options compare to each other in terms of satisfying his actual preferences that doesn’t mean that every explanation as to why he shouldn’t advance to the next level must appeal to the idea that so advancing would be suboptimal in (...) terms of the satisfaction of his actual preferences. Rather, we can admit that his advancing would always be optimal, but argue that advancing isn’t always what he ought to do given that advancing sometimes fails to meet some necessary condition for being what he ought to do. For instance, something can be what he ought to do only if it’s an option for him. What’s more, something can be what he ought to do only if it’s something that he can do without responding inappropriately to his reasons—or, so, I argue. Thus, the solution to the puzzle is, I argue, to realize that, in certain circumstances, advancing is not what the self-torturer ought to do given that he can do so only by responding inappropriately to his reasons. (shrink)

Together we can achieve things that we could never do on our own. In fact, there are sheer endless opportunities for producing morally desirable outcomes together with others. Unsurprisingly, scholars have been finding the idea of collective moral obligations intriguing. Yet, there is little agreement among scholars on the nature of such obligations and on the extent to which their existence might force us to adjust existing theories of moral obligation. What interests me in this paper is the perspective of (...) the moral deliberating agent who faces a collective action problem, i.e. the type of reasoning she employs when deciding how to act. I hope to show that agents have collective obligations precisely when they are required to employ ‘we-reasoning’, a type of reasoning that differs from I-mode, best response reasoning, as I shall explain below. More precisely, two (or more) individual agents have a collective moral obligation to do x if x is an option for action that is only collectively available (more on that later) and each has sufficient reason to rank x highest out of the options available to them. (shrink)

Philosophical accounts of collective intentionality typically rely on members to form a personal intention of sorts, viewed as a mental state. This tendency is opposed by recent economic literature on team-directed reasoning, which focuses on the reasoning process leading up to the formation of the members’ intentions. Our formal analysis bridges these paradigms and criticizes the team- directed reasoning account on two counts: first, team-directed reasoning is supposed to transcend traditional game and decision theory by adopting a certain collectivistic reasoning (...) method. However, we show that team-directed reasoning yields the same action recommendations as a certain I-mode we-intention type. Accordingly, an important part of we-mode reasoning can be reduced to I-mode reasoning with certain preferences. Second, contrary to the claims of team-directed-reasoning theorists, we refute that team-directed reasoning surpasses pro-group intentions in selecting cooperatively rational solutions. That is, in some scenarios team-directed reasoning fails to guarantee successful cooperation whereas pro-group intentions succeed in doing so. We therefore propose to revise team-directed reasoning and introduce a third we-intention type, called participatory intentions. We prove that participatory intentions guarantee that a best group action is performed whenever either team-directed reasoning or pro-group intentions do. (shrink)

In the context of two recent yet distinct philosophical debates—over choice under conditions of moral uncertainty and over transformative choices—several philosophers have implicitly adopted a thesis about how to evaluate alternatives of uncertain value. The thesis says that the value a rational agent ought to attach to an alternative under the hypothesis that the value of this alternative is x, ought to be x. I argue that while in some contexts this thesis trivially holds, in the context of the two (...) debates in which the thesis has been adopted, it does not. I also discuss several implications of this failure. (shrink)

Social science employs teleological explanations which depend upon the rationality principle, according to which people exhibit instrumental rationality. Popper points out that people also exhibit critical rationality, the tendency to stand back from, and to question or criticise, their views. I explain how our critical rationality impugns the explanatory value of the rationality principle and thereby threatens the very possibility of social science. I discuss the relationship between instrumental and critical rationality and show how we can reconcile our critical rationality (...) with the possibility of social if we invokes Popper's conception of limited rationality and his indeterminism.Las ciencias sociales emplean explicaciones teleológicas que dependen del principio de racionalidad, de acuerdo con el cual las personas exhiben un tipo de racionalidad instrumental. Popper señala que, además, las personas exhiben una racionalidad crítica, que es la tendencia a distanciarse, y a cuestionar o criticar, sus distintos puntos de vista. Aquí explico cómo nuestra racionalidad crítica impugna el valor explicativo del principio de racionalidad poniendo en peligro la propia posibilidad de las ciencias sociales. Asimismo, discuto la relación entre la racionalidad instrumental y crítica, y muestro cómo podemos reconciliar nuestra racionalidad crítica con la posibilidad de las ciencias sociales si invocamos la concepción de racionalidad limitada de Popper y su indeterminismo. (shrink)

I provide a taxonomy of the various circumstances under which one might reasonably say "P and I will believe that not-P" or violate the Reflection Principle.

The expression "analytic narratives" is used to refer to a range of quite recent studies that lie on the boundaries between history, political science, and economics. These studies purport to explain specific historical events by combining the usual narrative approach of historians with the analytic tools that economists and political scientists draw from formal rational choice theories. Game theory, especially of the extensive form version, is currently prominent among these tools, but there is nothing inevitable about such a technical choice. (...) The chapter explains what analytic narratives are by reviewing the studies of the major book Analytic Narratives (1998), which are concerned with the workings of political institutions broadly speaking, as well as several cases drawn from military and security studies, which form an independent source of the analytic narratives literature. At the same time as it gradually develops a definition of analytic narratives, the chapter investigates how they fulfil one of their main purposes, which is to provide explanations of a better standing than those of traditional history. An important principle that will emerge in the course of the discussion is that narration is called upon not only to provide facts and problems, but also to contribute to the explanation itself. The chapter distinguishes between several expository schemes of analytic narratives according to the way they implement this principle. From all the arguments developed here, it seems clear that the current applications of analytic narratives do not exhaust their potential, and in particular that they deserve the attention of economic historians, if only because they are concerned with microeconomic interactions that are not currently their focus of attention. (shrink)

I argue that we can generate intransitive preference orderings for a single person on the model of Sen's Libertarian Paradox.

I argue that we can generate intransitive preference orderings for a single person on the model of Sen's Libertarian Paradox.

I illustrate the use of decision-theory and game-theory in the social sciences by means of examples from Gauthier, Tversky and Kahneman, and Bouldon.

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. (...) We discuss the implications for the winner-takes-all system in the US Electoral College. (shrink)

We come to the finding of the sociology of scientific knowledge that all rationality is local, dependent on local customs and practices, shaped by the contingencies of history. Either this claim or that of the rational choice program is wrong. One way out of this conflict would be to accept the irreconcilability of the various concepts of rationality, to reject Boudon's and Bourricaud's conclusion that these usages have a common core, and to make rationality an "empirical problem." Yet this strategy (...) involves difficulties as well. To separate "analytically" the elements or aspects of rationality and then to "discover" empirical causal relations between them seems akin to spinning gold from straw. (shrink)

When S.C. Dodd concocted the empty formulae for which he is now remembered--as the butt of Sorokin's ridicule--he imagined that he was making a first pass at formulating the laws of social science. Dodd was as serious as Jasso and perhaps a bit more sophisticated and consistent in his choice of philosophical authorities. So one might suppose that Jasso's formulae (1988), which resemble them in certain respects, are subject to the same criticisms. I will argue that Jasso’s formulae are not (...) empty, but that they are also not what Jasso represents them to be. (shrink)

(Expected) adverse effects of the ‘ICT Revolution’ on work and opportunities for individuals to use and develop their capacities give a new impetus to the debate on the societal implications of technology and raise questions regarding the ‘responsibility’ of research and innovation (RRI) and the possibility of achieving ‘inclusive and sustainable society’. However, missing in this debate is an examination of a possible conflict between the quest for ‘inclusive and sustainable society’ and conventional economic principles guiding capital allocation (including the (...) funding of research and innovation). We propose that such conflict can be resolved by re-examining the nature and purpose of capital, and by recognising mainstream economics’ utilitarian foundations as an unduly restrictive subset of a wider Aristotelian understanding of choice. (shrink)

Social science employs teleological explanations which depend upon the rationality principle, according to which people exhibit instrumental rationality. Popper points out that people also exhibit critical rationality, the tendency to stand back from, and to question or criticise, their views. I explain how our critical rationality impugns the explanatory value of the rationality principle and thereby threatens the very possibility of social science. I discuss the relationship between instrumental and critical rationality and show how we can reconcile our critical rationality (...) with the possibility of social science if we invoke Popper’s conception of limited rationality and his indeterminism. (shrink)

I propose a novel model of the human ego (which I define as the tendency to measure one’s value based on extrinsic success rather than intrinsic aptitude or ability). I further propose the conjecture that ego so defined both is a non-adaptive by-product of evolutionary pressures, and has some evolutionary value as an adaptation (protecting self-interest). I explore ramifications of this model, including how it mediates individuals’ reactions to perceived and actual limits of their power, their ability to cope with (...) risk and uncertainty, and how this model may interpolate between rational choice models and cognitive psychology. I develop numerous examples and applications, including poverty traps, to demonstrate the model’s predictive power to elucidate a broad range of social phenomena. -/- [December 2018: Updated version to submit for publication. Expanded Sections 4 and 5.1, revised Section 5.7] -/- . (shrink)

In this article we explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that this is empirically (...) true: i.e. that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance with this pattern in the 18th century and how it recurred in the 1950s when Allais made his case against the neo-Bernoullians. (shrink)

Economic theory may explain the behavior of animals. Its application to animals is not straightforward, however.

The choice of a social decision rule for a federal assembly affects the welfare distribution within the federation. But which decision rules can be recommended on welfarist grounds? In this paper, we focus on two welfarist desiderata, viz. (i) maximizing the expected utility of the whole federation and (ii) equalizing the expected utilities of people from different states in the federation. We consider the European Union as an example, set up a probabilistic model of decision making and explore how different (...) decision rules fare with regard to the desiderata. We start with a default model, where the interests, and therefore the votes of the different states are not correlated. This default model is then abandoned in favor of models with correlations. We perform computer simulations and find that decision rules with a low acceptance threshold do generally better in terms of desideratum (i), whereas the rules presented in the Accession Treaty and in the (still unratified) Constitution of the European Union tend to do better in terms of desideratum (ii). The ranking obtained regarding desideratum (i) is fairly stable across different correlation patterns. (shrink)

What, normatively speaking, are the grounds of rational choice? This paper defends ‘comparativism’, the view that a comparative fact grounds rational choice. It examines three of the most serious challenges to comparativism: 1) that sometimes what grounds rational choice is an exclusionary-type relation among alternatives; 2) that an absolute fact such as that it’s your duty or conforms to the Categorial Imperative grounds rational choice; and 3) that rational choice between incomparables is possible, and in particular, all that is needed (...) for the possibility of rational choice is that one alternative is not worse than the others. Each challenge is questioned. If comparativism is correct, then no matter what normative theory you favor, your answer to the question, ‘What makes my choice rational?’ must be comparative in form. In this way, comparativism provides a framework for normative theorizing. (shrink)

Rational choice analytic narratives claim to take seriously the way real actors form their beliefs. I argue that a commonly applied formal technique perfect Bayesian equilibrium inadequately accounts for realistic beliefs, unnecessarily impoverishing analytic narratives. I propose an equilibrium concept drawn from cognitive psychology support theory equilibrium that provides an accurate account of beliefs within a formal analytic narrative approach. I ground both the critique and the alternative in a discussion of ethnic mobilization in Yugoslavia. The result is a behaviorally (...) informed analytic narrative that offers a more accurate account of the role of real including bizarre beliefs in strategic interaction. (shrink)

*This is the first draft of this book* -/- What you value and the extent to which you value it changes over the course of your life. A person might currently greatly value pursuing philosophy, and value spending time in nature much less; but, having watched their parents as they have grown older, and noting that they are very much like their parents, that person might have good reason to think that they will value the pursuit of philosophy much less (...) when they are sixty, and value spending time in nature much more. Given that we make our decisions on the basis of what we believe about the world and what we value in the world, the fact that the latter may change throughout our lives poses a problem for decision-making — in particular, for making decisions whose consequences will start to be felt or continue to be felt later in our lives. To which values should I appeal when making such a decision? My current values? My future values at the time when the decision will have its most significant effect? My past values? Some amalgamation of them all — past, present, and future — perhaps with some of them given more weight than others? (If so, how are the weightings assigned?) Or such an amalgamation only of a few of them? (If so, which ones?) In this book, I aim to provide a comprehensive account of rational decision-making for agents who recognise that their values will change over time and whose decisions will affect those future times. Included in the analysis will be not only agents who recognise that their values will inevitably change in certain ways, but also those who recognise that some of their decisions will lead to consequences that will change their values — thus, in effect, they will choose to change their values. (shrink)

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, Harman (...) 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions. (shrink)

Rationality in decision making is commonly assessed by comparing choice performance against normative standards. We argue that such a performance-centered approach blurs the distinction between rational choice and adaptive behavior. Instead, rational choice should be assessed with regard to the way individuals make analytic decisions. We suggest that analytic decisions can be made in two different modes in which control processes are directed at different levels. In a RUN mode, thought is directed at controlling the operation of a decision strategy. (...) In the JUMP mode, the individual analyses the interpretation of the decision situation as well as the appropriateness of alternative strategies. We suggest that a decision should be considered “rational” when an individual is able to switch between these modes and balance their interaction. (shrink)

I consider two puzzles in which an agent undergoes a sequence of decision problems. In both cases it is possible to respond rationally to any given problem yet it is impossible to respond rationally to every problem in the sequence, even though the choices are independent. In particular, although it might be a requirement of rationality that one must respond in a certain way at each point in the sequence, it seems it cannot be a requirement to respond as such (...) at every point for that would be to require the impossible. (shrink)

By introducing elements of phenomenological philosophy to the analysis of human needs in economics; from Sartrean postulates as well as the nature and essence of individual’s needs, has been revealed a theorethical framework that serves to ponder human being’s existential behavior by means of their phenomenologic social choices and welfare. Defining a planning agent under strong assumptions of rationality and projective efficacious capabilities, the Arrow’s theorem has been proved for the economic agent aware of its finitude in this world.

The paper revisits the rationality principle from the particular perspective of the unity of social sciences. It has been argued that the principle was the unique law of the social sciences and that accordingly there are no deep differences between them (Popper). It has also been argued that the rationality principle was specific to economics as opposed to the other social sciences, especially sociology (Pareto). The paper rejects these opposite views on the grounds that the rationality principle is strictly metaphysical (...) and does not have the logical force required to deliver interesting deductions. Explanation in the social sciences takes place at a level of specialization that is always higher than that of the principle itself. However, what is peculiar about economics is that it specializes the explanatory rational schemes to a degree unparalleled in history and sociology. As a consequence, there is a backward-and-forward move between specific and general formulations of rationality that takes place in economics and has no analogue in the other social sciences. (shrink)

This French paper is a preliminary version of P. Mongin, "Does Optimization Imply Rationality?", Synthese, 124, 2000, p. 73-111, to which readers are referred to.

The present book makes a particularly engaging case for a whole range of policy implications of behavioural economics. The rhetoric is highly compelling, and their approach is already having a significant impact. However, while the wider audience for whom the book is written may not be interested in the justification of the underlying principles, it is precisely the cracks in the foundations that pose the greatest threat to the project. For example, if Thaler and Sunstein are to have any chance (...) of their 'libertarian paternalism' meriting ‘libertarian’ credentials, it is essential that the re-engineering of choice architecture not be guided by any particular political or moral agenda. Their claim here is that what makes a nudge beneficial is not that it steers people in the direction of behaviour that is objectively ‘good’ but rather in the direction of behaviour that they won’t regret. That said, there are a number of points where it is hard to shake the suspicion that Thaler and Sunstein help themselves rather conveniently to the idea that, if a person’s choices are largely a function of various framing effects, say, then overriding those choices violates no autonomy, since there was no autonomy there to be violated. -/- In this review, I raise four concerns not adequately addressed in the book. -/- (1) Thaler and Sunstein are misleading in their use of the term ‘paternalism’, which is standardly defined as a matter of interfering with a competent person’s choices out of a motivation to improve that person’s welfare. As Thaler and Sunstein use the term, however, it becomes equivalent to beneficence: when the government acts to improve people’s welfare by influencing choices in any way, according to them, it is engaging in paternalism. -/- (2) Their appeal to the resistibility of nudges is a centrepiece of the account and particularly of its claim to be ‘libertarian’, but given what they themselves write about how effective nudges are and how poor we are at even noticing the influences to which we are subject, it is entirely unclear why we should expect nudges to be easily resisted. -/- (3) Thaler and Sunstein generally align themselves with the perspective of planners who half-pose the presumptuously rhetorical question, ‘Who would really mind?’ But the question is not just whether people would object, if they were consulted. People also care about whether they are consulted and whether they understand the influences to which they are subject. Thaler and Sunstein advise choice architects against being secretive about nudges, but this espousal of principle, in a late chapter responding to objections, is not borne out by the discussion in the rest of the book, which focuses almost exclusively and rather effusively on the possibilities for channelling individuals’ choice-behaviour toward better outcomes. -/- (4) Thaler and Sunstein tend to downplay alternative approaches to improving decision making that are perfectly compatible with the behavioural economics and social psychology discussed by Thaler and Sunstein, but less paternalistic. For example, there is a growing body of research on how to construct contexts of interpersonal deliberation to generate stable solutions to collective action problems, by improving people’s collective decision-making capacities, rather than subjecting them to nudges. More generally, one comes up with very different recommendations if one thinks of the problems to which nudges are supposed to be a solution not as a matter of human failings per se, but rather as a socially and historically contingent misfit between the decision-making capacities that particular policies and institutions require of individuals and the capacities that people actually have. Conceived in the latter way – in terms of what I have elsewhere dubbed ‘autonomy gaps’, it becomes an open question whether what is called for is a choice architecture that makes it easier to avoid regrettable decisions or, rather, various measures to improve individuals’ decision-making capacities, say, through education, ‘buddy’ arrangements, decision-making heuristics, etc. (shrink)

A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. Applications (...) to decision making under conditions of risk and uncertainty are provided. (shrink)

This paper proposes a new theory of rational choice, Expected Comparative Utility (ECU) Theory. It is first argued that for any decision option, a, and any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility of a in G – that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this principle, it is then argued, roughly (...) speaking, that an agent should rank her decision options (in terms of how choiceworthy they are) according to their expected comparative utility. For any decision option, a, the expected comparative utility of a is the probability-weighted average of the comparative utilities of a across the different states of the world. It is lastly demonstrated that in a number of decision cases, ECU Theory delivers different verdicts from those of standard decision theory. (shrink)

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

We generalize Harsanyi's social aggregation theorem. We allow the population to be infi nite, and merely assume that individual and social preferences are given by strongly independent preorders on a convex set of arbitrary dimension. Thus we assume neither completeness nor any form of continuity. Under Pareto indifference, the conclusion of Harsanyi's theorem nevertheless holds almost entirely unchanged when utility values are taken to be vectors in a product of lexicographic function spaces. The addition of weak or strong Pareto has (...) essentially the same implications in the general case as it does in Harsanyi's original setting. (shrink)

This paper discusses a challenge for Comparativists about belief, who hold that numerical degree of belief (in particular, subjective probability) is a useful fiction, unlike comparative belief, which they regard as real. The challenge is to make sense of claims like ‘I am twice as confident in A as in B’ in terms of comparative belief only. After showing that at least some Comparativists can meet this challenge, I discuss implications for Zynda’s [2000] and Stefánsson’s [2017] defences of Comparativism.

Real-world economies are open-ended dynamic systems consisting of heterogeneous interacting participants. Human participants are decision-makers who strategically take into account the past actions and potential future actions of other participants. All participants are forced to be locally constructive, meaning their actions at any given time must be based on their local states; and participant actions at any given time affect future local states. Taken together, these essential properties imply real-world economies are locally-constructive sequential games. This paper discusses a modeling approach, (...) Agent-based Computational Economics, that permits researchers to study economic systems from this point of view. ACE modeling principles and objectives are first concisely presented and explained. The remainder of the paper then highlights challenging issues and edgier explorations that ACE researchers are currently pursuing. (shrink)

Mass atrocities are commonly explained in terms of changes in legal or moral norms. This paper examines the role that changes in social norms can play in precipitating or prolonging mass atrocities. I focus specifically on manipulative transformations of social norms. I first distinguish between the manipulative introduction and the manipulative activation of social norms. I then explain how both forms of manipulation can contribute to mass atrocities. Finally, extending a line of thought first suggested by Hannah Arendt, I present (...) a case study of the manipulative introduction and activation of language rules amongst the Nazis during World War Two. (shrink)

Contemporary discussions of the positive relation between rational choice and moral theory are a special case of a much older tradition that seeks to show that mutual agreement upon certain moral rules works to the mutual advantage, or in the interests, of those who so agree. I make a few remarks about the history of discussions of the connection between morality and self-interest, after which I argue that the modern theory of rational choice can be naturally understood as a continuation (...) of this older tradition. I then go on to argue for a controversial three-fold thesis: (1) that grounding a theory of morality in terms of rational self-interest is the only epistemologically respectable way to proceed with the justification of moral principles; (2) that despite this, most of the contemporary explorations of rational choice foundations for moral principles do not work—that the models of rational choice to which they appeal yield less than the substantial results that they are intended to yield; but (3) that if one rethinks just what it means to be rational, one can find in fact a promising way to connect the two—specifically through the development of a theory of genuinely cooperative activity. (shrink)