How to Cope With (New) Uncertainties—A Bounded Rationality Approach

Whenever certain axioms are fulfilled decision-making under uncertainty can be modeled as if maximizing the expected utility of results of risky choices over a known state space with non-ambiguous probability weights. As opposed to this, practically coping with ever new uncertainties—new in that statistical, empirical evidence is lacking—requires a purely procedural bounded rationality approach as paradigmatically proposed here. The procedures can be evaluated and improved in view of evidence of their “objective” success or failure whereas the prescription to behave as if maximizing a subjective utility function is of no direct technological use for a boundedly rational actor.


Introduction and Overview
In theoretical contexts passing judgment can be withheld altogether until the growth of conjectural evidence-based knowledge has transformed genuine uncertainty into risk. Yet, in practical contexts even though tested nomological hypotheses that reduce uncertainty to risk are unavailable action or omission of a conceivable intervention may seem unavoidable. In matters practical this kind of urgency is the rule rather than the exception. With each ''new'' practical case new uncertainties may arise while suspending judgment may seem grossly inadequate. The demand for ''experts'', even if relying on their judgements may not be expected to lead to better outcomes than rolling dice, typically will arise in such situations. Despite the fact that statistical evidence is lacking they can at least nurture the illusion that their experience transforms uncertainty into something akin to risk. 1 Neither expert practitioners nor the disciplines that train them (in practices of ''clinical judgment'' in business, medicine, law and (social) engineering) should be blamed for their failure to find ideal ways of coping with (new) uncertainties. What deserves criticism are the many efforts to conceal ignorance and the uncertainty of decision-making that stems from it from the views of both the general public and the trained practitioners themselves by modeling uncertainty as if it were risk. Misplaced and misunderstood uses of mathematical models deserve to be criticized. Proper uses of mathematically rigourous models that describe ignorance and the limits of knowledge transparently should, however, be endorsed.
That the growth of our analytical knowledge concerning models coincides automatically with a growth of our knowledge of the world is a particularly seductive and dangerous illusion. This ''model risk'' of rigorous mathematical formulation must be acknowledged as a psychological fact. At the same time acknowledging that mathematical rigour can invite misinterpretations does not amount to subscribing to the popular but rather nonsensical view that practical relevance can be lost through more rigorous treatment. Systematically there is no trade-off between rigor and relevance. If there is relevant knowledge it can be presented clearly. 2 However, if as in case of new uncertainties, there is none, the lack of knowledge must be made rigourously transparent by our models rather than be concealed by elegant ''as if'' constructions. In short, there is never a trade off between rigour and relevance, yet rigour cannot substitute the lack of relevant knowledge either.
Endorsing the preceding remarks on the merits of rigorous presentation we start our discussion of how boundedly rational decision-makers can cope with ''new'' uncertainties with a glance at the foundational work of Blaise Pascal. This work embodies the achievements and problems not only of past but of much present decision theoretic modeling at its very founding (2). It is illustrated next how decision-theoretic standard models dress up uncertainty as if it were risk and thereby tend to lead (boundedly rational) decision-makers psychologically astray into ''overconfidence and control illusions in the face of uncertainty'' (3). As an alternative to adapting the-in our view-practically misleading externalist theoretical model of rational choice making we sketch an internalist procedural alternative. Characterizing the internal point of view of an actor we first identify a fundamental source of uncertainty arising from the specifics of interactive decisionmaking (4.1). We then sketch in rigorous externalist terms how boundedly rational actors in fact cope with uncertainties (4.2). After this we strengthen the ''technological'' aspects implicitly present in good boundedly rational practice to yield ''workable'' prescriptions for ''coping with uncertainties'' (4.3). Finally we briefly discuss how prescriptions that can be followed by an actor from her or his internal point of view might be improved by boundedly rational decision-makers after observing results of standardized procedures (4.4). In conclusion we return to the relationship of theory and practice in a world in which boundedly rational actors have to cope with ever new uncertainties to which they have to respond despite a lack of experiential evidence (5).

Modeling Uncertainty and Ignorance
Since the beginnings of decision theory in the work of Blaise Pascal (2003: § 184) scholars have tried to rein in uncertainty by treating it as if it were risk. When Pascal originally developed his innovative mathematical analyses of risk in betting these were based on hypotheses with some empirical (statistical) or theoretical support. This straightforwardly led to statistical (actuarial) models of risk. But Pascal went beyond this. His famous wager argument is arguably the most prominent case in point. It suggests that a Christian may cope with uncertainty concerning the existence of God in ways akin to the model of risk taking. Why this to the present day influential way of modeling uncertainty may be misleading can be illustrated by focusing on Pascal's ''(very) original sin''. 3

The Historical and Present Relevance of Pascal
Though among fallible human beings ''residual uncertainty'' of all knowledge claims will never be eliminated completely we need to clearly distinguish between uncertainties that became risks to the extent that we have empirical and/or theoretical information on them and uncertainties for which such information is lacking. Pascal was well aware of the distinction. He was, on the one hand, 3 When we originally wrote this paper we committed our own rather unoriginal sins. In particular we were then ignorant of Hájek's fine (2003) paper in which he is waging war on Pascal's wager. To our embarassement we must also confess that we were likewise ignorant of Alexander Herzberg's efforts to use his high powered mathematical skills in contributing to the debate (see 2011). We are satisfied with the somewhat lame excuse that we were and are interested only in a kind of stylized intellectual history of how certain forms of modeling that originated in Pascal have led boundedly rational decision-makers and their theoretical advisors astray in their efforts to find ways to cope with new uncertainties as raised by practical problems. calculating expectations concerning gambles in which frequencies or chances of outcomes were known. On the other hand, he explored ways to cope with uncertainties in one-off situations in which information concerning probability distributions was lacking (see Knight 1921) and/or event spaces were genuinely unknown.
The argument that became known as ''Pascal's wager'' is the paradigm case in point. Despite the lack of evidence concerning the theistic hypothesis that God exists Pascal tried to present an a priori decision theoretic argument meant to show that even for vanishing probabilities in favor of the hypothesis it would be practically rational to believe in God's existence. Pascal makes the assumption that if God exists and if He rewards the believers, and only them, then infinite bliss will be bestowed on those who believe while infinite desperation will accrue to those who do not believe. 4 With this premise in hand, Pascal addresses the Christian who is facing what appears to her as a matter of existential and unavoidable choice (i.e. a practical problem). The Christian cannot postpone the decision until the hereafter. At the same time all she knows in the here and now does not provide experiential (i.e. either empirical or experimental) evidence that God does (not) exist. 5 But since believing might lead to eternal bliss while non-believing might lead to hell or an eternity of no experience, Christians have-thinks Pascal-a good practical reason to believe in Him even for the smallest probability of His existence.
Somewhat more precisely, assume that all we know induces us to put a probability estimate of (1 -q) on the negation of the theistic hypothesis. As long as 1 -q \ 1, then for arbitrary low probability q [ 0 it would be subjectively preferable to decide on believing ( Table 1).
Assuming that a measure of value allowing for the appropriate algebraic operations exists the following inequality could be fulfilled for arbitrary small q and fixed Y -B if A -X becomes arbitrarily large: To make the argument valid for ''infinity'' we need to cope with the formal problem of providing a consistent measure capturing the ''overwhelming'' desirability of eternal bliss. An axiomatic account of a utility function closely paralleling the original von Neumann-Morgenstern utility conception can be provided and represent the implicitly assumed preferences in formally adequate ways. 6 Yet, what is lacking is an evidence-based rather than desire-based reason for restricting the possibility space to what Christian belief suggests.
For instance, that God will reward those who believe on insufficient grounds is uncertain. Dispositions like being credulous may be seen as vices rather than virtues-at least according to common views of what may be called the ''ethics of belief'' (see Clifford's 1974Clifford's /1879. Still a will to believe when confronted with problems perceived as unavoidable seems deeply rooted. It is not restricted to religion and metaphysics, but has a strong presence in particular in medical, business and law practice. And, it need not be maladaptive as supporting practices of theorizing. Uncertainty as well as action in the face of it may be unavoidable in particular in situations in which what we regard as inaction in one sense amounts to a choice in another sense as well. 7 No way of modeling can change this feature of the world itself. It is, to put it slightly bombastically, part of the ''conditio humana''. Yet we need to take precautions against wistful thinking and self-deception. The latently fatal role of a Pascalean approach to modeling uncertainty can be brought forward by looking at its incarnation in what has become the standard model of rational decision-making. Ever since Savage's (Savage 1954(Savage /1972) seminal work it is (ab-)used to represent uncertainty as if it were risk.

The Standard Model of Rational Decision Making
The most fundamental aspect of human practical rationality is the faculty to distinguish between what is and what is not causally influenced through interventions of a human actor. 8 This leads to a minimal characterization of rationality: An actor who is instrumentally rational tries to build-to the extent that this is viable with ''acceptable'' effort-a model of the action situation that 7 For instance withholding judgment in financial affairs is impossible since inaction with respect to financial assets is a form of action as well-after all the decision ''not to invest'' in assets amounts to an investment choice, too. 8 Gilboa (2009, 12) has dug out a beautiful quote from the-appropriate in the present context-Theologian Reinhold Niebuhr who said in a prayer ''God, give us grace to accept with serenity the things that cannot be changed, courage to change the things that should be changed, and the wisdom to distinguish the one from the other.'' Gilboa emphasizes in the final sentence of his apt comments on this quote that ''having the wisdom to distinguish between acts and states is one of the main challenges in approaching any decision problem.'' distinguishes between what is and what is not subject to her causal influence in each instance of choice. The focus on the causal structure is a crucial aspect of all rational-choice modeling. In terms of rational practice this focus corresponds to the quest for knowledge that has instrumental uses in developing ''technologies'' (recipes of how to go about problems). Technological knowledge is used in setting up decision models for planning purposes. Slightly simplifying, 9 in models of decision-making concerning purposefully rational intervention into the world we have: 1. plans, s, comprised in a set S 2. states, z, comprised in a set Z 3. results, r, comprised in a set R 4. causal knowledge, comprised in f:S Â Z ! R. 10 The standard model as represented by Table 2 below lists as rows the results f(s i , z k ) that are expected to emerge when alternative plans s i , i = 1, 2,…,m and k = 1, 2, …, l states of the world Z ¼ fz k jk ¼ 1; 2; . . .; lg ''become real''. To each of the states, z k , corresponds a column of the table listing the results that may emerge if one of the alternative plans s i is executed in state z k .
The standard model assumes knowledge of f, the set Z of states of the world and a probability distribution p on Z (which induces over f(.,.) a distribution). Rational choice behavior complies with axioms that guarantee the existence of values that can be assigned such that preferences over lotteries can be represented by expected value formation (such that relying on the assigned values does not distort the preferences over the set of all lotteries).
Though the uncertainty that arises from general ignorance and the fallibility of all human knowledge must be acknowledged, there is no systematic place for uncertainty in the standard model-except for the fact that the probability distribution may not be based on statistical or other empirical knowledge as allowed for by Savage. Still, following the lead of Pascal one might try to represent uncertainty by providing an explicit place for it within the model.

Uncertainty as Risk?
Consider the following Table 3 that appears deceptively similar to Table 2. It conceals that the underlying problem is completely different from that in Table 2: If ''state z else '' is one of which the choice-maker assumes that she may neglect it in view of her pursuits then she implicitly assumes that the neglected state will not ''relevantly'' affect her rankings even though she has no empirical information on it and/or may not have any clue how f translates it into consequences. To put it slightly otherwise, if ''something else'' as non-anticipated result after choosing one of the plans occurs, this will not affect her global ranking of plans. If she would not implicitly make that assumption and base the ranking on all states except the ''else'' state the model would be wrongly specified. It would deal with ''something'' as if it could be represented in a ''closed'' model without a reason for assuming closure.
We do not criticize standard models of decision-making for not transforming uncertainty into risk. No formal model can do this; only knowledge can. Since the models merely can represent but not create empirical information, better information must be created in the first place to transform uncertainty into risk.
To stop somewhere is a practical necessity but to present the ''else category'' as if it were on a par with what is explicitly specified according to empirical evidence is unnecessary. It is a distortion since it represents the ''untamed'' type of uncertainty-not reined in by some empirical knowledge, that is-as if it were a ''risk''. Though decision-makers can be warned of the misspecification, the representation of uncertainty as if it were risk tends to make them psychologically prone to distinguish what is and what is not evidence-based in their mental models.
A more realistic representation of decision behavior in situations of uncertainty can acknowledge the bounds of knowledge explicitly and prepare the ground for more adequate decision models and more adequate models of ''decision-support''. The models to which we turn next do not assume away uncertainty and the fact that the decision-makers have merely limited intellectual resources to cope with it. Quite to the contrary they emphasize the paramount importance of operational fact finding procedures when faced with uncertainty.

Practices of Coping with Uncertainty in Interactive Decision-Making
Simple decision models can represent decision problems in two ways: first from the external point of view of an onlooker who observes decision-maker behavior, second, as reconstructing the internal point of view of the decision-or choice-maker who intentionally does something herself to bring about effects by her action. In the first case the outside or external ''observer'' represents the situation in which Plan s m f(s m , z 1 ) f(s m , z l ) Table 3 Open space Homo Oecon (2017)  decision-makers make their decisions with the theoretical aim of describing, explaining and predicting overt action in an agent independent way. The results of this kind of research are typically meant to be communicated to fellow theorists. In the second case the decision-theorist emulates the position of a ''doer'', that is, an actor who does not predict but makes decisions (to be executed as choices) in response to the question ''what should I do?''.
Most economic models of choice making do not answer the practical question of ''what should I do?'' nor are they helpful for that purpose at all. In particular those based on revealed preference conceptions start from representing overt choices rather than commencing with the desires and beliefs generating the overt choice behavior. They often counterfactually ascribe to the choice makers the externalist theory of rationality-i.e. that they are operating ''as if'' the correct model of the situation was guiding the internal process of decision-making. 11 This is typically widely off the mark as far as processes of real decision-making from the internal point of view of the decision-maker are concerned (decision makers do not deliberate in terms of the model).
In our stylized-and, as we think in view of empirical evidence, more realisticexternalist characterization of how boundedly rational decision-makers as a matter of fact try to cope with uncertainties, in particular in interactive situations, we first sketch how and why the presence of ''other minds'' may be a and presumably often is the most important source of uncertainty (4.1). We then present-still from an external point of view-boundedly rational choice making in situations of interactive uncertainty (4.2). Refining this reconstruction leads to an exemplary prescriptive flow-chart of a decision support procedure that can be used by the decision maker herself from her internal point of view (4.3). How this procedure can conceivably be evaluated and improved in view of observable results is finally illustrated (4.4).

Other Minds as a Source of Uncertainty
From the point of view of an external observer the strategic representation of a game is defined on the Cartesian product of the strategy sets S j of the j = 1,2, …, n interacting individuals S :¼ X n j¼1 S j ¼ fðs 1 ; s 2 ; s 3 ; . . .s nÀ1 ; s n Þjs j 2 S j ; j ¼ 1; 2; . . .ng: Let S Àj be the restriction of S as emerges if the product comprises merely f1; 2; 3; . . .; ngnfjg with S ¼ fsjðs j ; s Àj Þ; s j 2 S j ; s Àj 2 S Àj g.
Obviously those who will play the game can adopt the point of view of an external observer as well for purposes of reflecting on the game and planning. They 11 Often this otherwise stunningly unrealistic assumption is justified by the argument that in competition only those who behave as if guided by full rationality would survive. This ''evolutionary'' argument, elegant as it may be, cannot tell actors what they should do from their internal point of view. In particular it is useless for developing models of decision-support that would actually tell boundedly rational actors how to go about decision-making; see for a classical statement of the evolutionary argument Alchian (1950). may even adopt the view of considering strategic options of a ''community of rational beings'' in a reasoning about knowledge approach which is different from the objective attitude that is characteristic of so-called games against nature. 12 At the same time human beings are part of nature. In this sense interactive decisionmaking in a group of human actors can conceivably be reduced to as many ''games against nature'' as there are actors; that is, if there is a set of n [ 1 decision makers j = 1, 2, 3, …, n each decision-maker, j, is facing n-1 other decision-makers with their plans. 13 Assuming that in planning rational actors distinguish between what is and what is not a causal effect of their planning (acting), each planner, j's, expectation of s Àj 2 S Àj is non-conditional on s j 2 S j (though possibly conditional on some commonly known theory of rational play). Thus, including, Z there are S Àj Â Z states of the world player j has to consider as non-conditional on her choice of plan (and/or action). Each strategy is a full plan specifying an action (''move'') for all information sets that can conceivably be reached as part of some play of the game. It is obviously viable to construct for each individual decision-maker j a table that pits him or her ''against'' f1; 2; 3; . . .; ngnfjg. According to the semantic rules of interpreting such a table the actor j chooses a plan s j 2 S j knowing that he has no control over s Àj 2 S Àj . For each strategy s j 2 S j of actor j the results that j expects to emerge according to her mental (causal) model f j form rows f j ðs j ; s Àj ; zÞ for ðs Àj ; zÞ 2 S Àj Â Z of j's decision table.
Human actors as well as their minds are ''part of nature''. This speaks in favor of forming as many separate games against nature as there are individuals treating the states of other individuals as states of nature. Plans and actions of other rational individuals are as much beyond the control of actor j as are other states of nature. Yet it is also obvious that human beings are a special part of nature which ''contains'' representations of states of nature, i.e. what is ''on other minds''. If there are shared conventions, knowledge and norms, expectations may be conditioned on such ''theories'' and converge. To the extent that the several separate games against nature become thereby correlated in commonly known ways, the uncertainty about how others shall play may be reduced. On the other hand, the familiar problem of representing mental models of other individuals in mental models of still others who again have mental models etc. emerges. Among actors with finite reasoning capacities this may and as a rule will create a complexity and context dependency akin to uncertainty rather than risk-in particular in non-repeat interaction. Moreover, lacking an initial fixed point of the modeling dynamics the several games against nature will remain separate-uncorrelated-in ways that may prevent conditioning on shared theories.
Note also that the rational actor who-qua rationality-can distinguish between what is and what is not among the causal influences of acts has no causal power to 12 On the relationship of game theoretic conceptualizations to Strawson's (1962) fundamental philosophical distinction between participant's and objective attitude see Kliemt (2009). 13 He clearly cannot perform the actions of others as his own. Likewise distinguishing between what is and what is not under the direct causal influence of the actor through his own actions thinking in terms of collective action is beside the point. fix a sequence of acts ''in one act'' unless there is an option to do just this. 14 He can plan on exerting a certain kind of influence by making a specific move but he cannot make the move beforehand. He cannot exert a causal influence until the occasion for the influence arises. The fact that, opposed to choosing a fixed program, strategies as plans have to be put into action sequentially confronts the (boundedly) rational actor with commitment problems. In particular this adds to the difficulty of foreseeing future states of the world as brought about by actions of others.
That the ignorance concerning this additional layer of uncertainty is not plausibly classified as ''risk'' can be illustrated by taking a closer look at the seemingly simple concept of mixed strategies. The assumption that mixed strategies can be chosen clearly amounts to introducing new faculties of exerting causal influences in a game. It may well be that human beings command such faculties of choosing a probability distribution over so-called pure strategies. Yet, if individuals are endowed with the faculty to choose randomizations it seems likewise natural to assume that players can do so in many ways implying that they at the planning stage are confronted with sets of probability distributions rather than with single such distributions. At the planning stage, they are faced with uncertainty in the sense of ambiguity rather than with risk in the sense of a single distribution. If they are ambiguity averse-and if they expect others to be ambiguity averse-this may change the game analysis. 15 Whether it helps to transfer the mixing from its ''location'' in the choices of actorsas in von Neumann's and Mogenstern's (1953) interpretation-into the eyes of the beholders of such actions is open (see Harsanyi 1973). According to this nowadays standard view, so-called mixed behavioral strategies are probability distributions over choices of an actor that describe not the randomness of her choices-after all, as an actor she must subjectively ''do'' something 16 -but rather the ignorance of other actors. Accordingly, if participants-not external (omniscient) onlookers-of an interaction ascribe probabilities to the behavior of other participants of an interaction they sum up their own ignorance of what others might do. This is very similar to constructing uncertainty as a residual category (as in case of Table 3 above) or as if it were an ordinary risk on which statistical evidence exists. 17 Yet, that behavior of fellow humans can seem both less or more 14 Even boundedly rational actors understand this quite well. They often use tricks like having no chocolate/cigarettes/liquor in the house to commit themselves not to give into immediate temptations. 15 In this volume Frank Riedel expands on this; see also Riedel and Sass (2014), Sass (2013)). Though it may be objected that this introduces additional options of exerting a causal influence on the game which may or may not exist. In any event, the assumptions are not too far away of what originally von Neumann assumed and are clearly worth exploring. 16 An actor who plans to choose contingent on some natural stochastic process must still choose a move ''deterministically'' after receiving a signal. In fact, if the actor could commit to let her act be chosen by rolling a die or make it contingent on some other random event from Z then this would be another choice option that the actor would choose deterministically. ''Active'' mixing of choices is a reasonable strategy only if the actor has in fact the power to commit to following the outcome of the random experiment. Otherwise he can only plan on doing so and then has subjectively the option of deviating from the planthough due to indifference has no incentive to do so. 17 It becomes doubtful whether classical game theory specifies its model of the world adequately if it renders it as Ken Binmore-also in this volume and at other places-remarked almost by definition a small world (Binmore 2009). predictable than nature but hardly the same way as ''natural'' events seems quite obvious. Institutions like for instance markets, auctions etc. can create incentives that channel individual behavior in repeat interactive situations and make it more predictable. However, in view of the fact that human actors can always decide on the basis of their own idiosyncratic models of the future human behavior seems always uncertain in some way.
Participants of interaction will perceive the strategy sets, the states of knowledge and the likelihood of actions they cannot control such that the situation should be modeled differently from the standard model. Actors may have some knowledge of some scenarios but it seems far fetched to sum this knowledge up in a single probability distribution over a state space assumed to be known.

Scenario-Based Practices of Coping with Complex Decision-Problems 18
Starting from the full set S 9 Z and common knowledge of some closed model describing all plans s j 2 S j and all s Àj 2 S Àj , seems an outrageously far-fetched assumption concerning real human decision-makers (except perhaps for some illustrative simple ''toy'' games). Therefore, it should be assumed that, depending on their idiosyncratic experiences and their memory, boundedly rational actors will focus on a rather ''small'' belief set B j S Àj Â Z since boundedly rational actors can focus merely on a few s j 2 S 0 j & S j , with exemplary scenarios s Àj ; z À Á 2 B j S Àj Â Z to form potential case solutions s j ; s Àj ; z À Á À Á . 19 Relying on the fiction of unlimited rational capacities is useless from the internal point of view of a boundedly rational decision-maker who actually needs to make choices without being in command of such faculties. She could not handle the complete information even if she had access to it. She selects scenarios ðs Àj ; zÞ 2 B j to form scenario-specific aspirations A j s Àj ; z À Á of goal achievement. It is a dynamic process of search-permanently open to further improvement-rather than the search for a solution of a ''given'' problem. Aspirations and belief sets may be revised if it turns out that they cannot be fulfilled at all or can be fulfilled to a higher degree than initially assumed. Likewise some s j 2 S 0 j may be excluded or another may be included to yield a modified set S 00 j . If the modified S 00 j emerges because an additional element is considered the mental modeling process will take place for the additional element to yield f j ðs j ; s Àj ; zÞ for ðs Àj ; zÞ 2 S Àj Â Z. Only for select s j ; s Àj ; z À Á À Á the effort of gathering evidence to construct f j ðs j ; s Àj ; zÞ is made. (Adaptations may take place also if the underlying aims, ends or values change or new information is gathered.) 18 To make clear where we stand: in our next step we shall characterize what real choice-makers who are boundedly rational as a matter of fact seem to do when confronted with uncertainty. On the basis of this slightly idealized descriptive account of what broadly speaking rational actors do we shall then present a slightly refined prescriptive suggestion of what they should do in coping with uncertainties. We finally address the issue of evaluating the procedure in terms of feedback on results. 19 Akin to the concept of ''case'' used in Gilboa and Schmeidler (2010) who also allow for selective mental models in their externalist characterization of case based decision-making.
Though an external game theoretical observer might describe playing a game in terms of maximizing the subjective expected value of a utility measure the participant of the interaction cannot meaningfully do so. His model will be so sketchy that it is better characterized in terms of uncertainty about the state spaces and ambiguity about the resulting probability distributions than in conventional terms of risk.
Properly speaking the A i (s -i , z) will be lists of dimensions of value A i k (s -i , z),k = 1,2,…l or action goals rather than a single item; i.e. , z)). The aspiration levels of the k = 1, 2, …, l action goals are scenario specific. The boundedly rational actor will generate these scenario specific levels along with the scenarios and then evaluate her options s i 2 S 0 i & S i for each scenario s Ài ; z ð Þ2B i . If an option satisfies her aspirations for all scenarios this can be a stopping point. If no s i 2 S 0 i & S i yields results that satisfy all goals of the list A i k (s -i , z),k = 1,2,…l in all scenarios considered then the actor i may adapt her aspirations (action goals) at least for some scenarios. 20 To repeat, outside ideal game theory (eductive in the sense of Binmore (1987Binmore ( / 1988 the assumption that the full set S j may be checked is unrealistic in all but in unrealistically simple cases. The mental modeling effort that creates f j ðs j ; s Àj ; zÞ for options s j 2 S 0 j and scenarios s Àj ; z À Á 2 B j will be undertaken merely selectively. For a boundedly rational actor this is necessary to economize on scarce mental resources. From the perspective of ideal externalist modeling that assumes away all such costs to form models on theoretically complete spaces this may seem unsatisfactory. Yet, from a practical point of view it has the immense advantage of openly acknowledging that a boundedly rational decision-maker has to cope with uncertainty. In all realistically complex situations of uncertainty the ''boundedness constraint'' will be binding and an instrumentally rational actor has-in view of his aims, ends or values-good reason to proceed selectively. It will be more or less a process of systematic trial and error in which the pursuit of aspirations will as a rule consist in successive search and adaptation of all aspects of decision-making and the process of mental modeling underlying it. In a theoretical context this search could in principle be open ended whereas in cases in which action must come forward (the James (1897/1956) and Pascal case of ''life options'', see above, 2) search must end at some point and action must be taken. And, it can and will be taken without treating uncertainty as risk.
Up to now the argument was conceptual. It was more to the descriptive than to the prescriptive side. The analysis of what boundedly rational actors in fact do is, however, not all we are interested in. Ultimately the aim is to improve procedures of boundedly rational decision-making rather than to reconstruct them. A reconstruction often already contains some idealization. It is stylized and in itself embodies hypotheses and (value) judgments concerning the relevance of certain aspects of what is reconstructed. Therefore such a stylized account can ''naturally'' serve as a step towards creating rules or recipes of how an actor herself should go about decision problems. To put it slightly otherwise, the externalist reconstruction of the previous two sections can assure that suggestions for prudent behavior are sufficiently close to what real human individuals can in fact do and plan from their internal point of view. On this basis then something akin to the following flowchart may sum up the search process through which an instrumentally but boundedly rational actor should go. 21

An Outline of a Decision Procedure for Coping with Uncertainties
The individual i must answer questions concerning the relationship between action goals which can be achieved by exerting causal influence directly and the aspirations that can be reached only in a deferred way by a sequence of such actions or ''moves''. Since the instrumentally rational actor is also bounded in her capacities she is not able to form a full plan for everything she might learn in a sequence of decisions. Yet, she can adopt a process (see Güth and Ploner (2017) for a detailed discussion and illustration as well as for first experimental studies) in which she would adapt her choices to information that might become available after examining and testing some acts of a sequence of acts.
To prepare the ground for learning from scenarios and interventions into the course of the world a boundedly rational actor needs to have some hypotheses concerning the evaluation of steps (moves, actions) she is making. In short, she has to select which ''variables'' are to be used in her mental modeling as short-term indicators of long-term success. We will not go over the details of this rather crucial process of finding indicators for the fulfillment of the underlying larger aspirations. We can emphasize merely that the quality of end point results will crucially depend on making the right choices on the level of ''intermediate'' variables. This as well as the preceding flow chart are in a way unsatisfactory. However, living in a large rather than a small world avoiding the ''model risks'' that arise from modeling uncertainty as if it were risk with a known distribution over a known state space, seems even less satisfactory and certainly not a plausible recipe for coping with ever new uncertainties: Such models will distract their users only from searching selectively for and testing relevant hypotheses concerning technologies of bringing about desired ends.

Evaluating the Decision Procedure for Coping with Uncertainties
Most conventional decision-theoretic approaches model behavior from the external point of view of an ''observer of choices'' rather than the internal point of view of a ''maker of choices''. As opposed to the implicitly externalist perspective underlying standard tabular representations of decision behavior the preceding flow-chart is 21 On the role of so-called bridge principles like ''ought presupposes can'', see Albert (1985); on a ''methodologically dualist'' view that separates the-in Selten's terms ''normative''-effort to explicate a concept of ideally rational intentional behavior in mathematical terms completely from the effort to empirically describe/explain real human behavior and the technological aim to develop recipes of improving it in ways that boundedly rational individuals can as a matter of fact use, see Selten (1999), 303 f. meant to be used by the decision-maker herself as guidance or prescription of how to proceed in view of uncertainty from the internal point of view as a planning and acting subject.
For those who as participants of interaction actually have to generate their own behavior the externalist stenographical representation of behavior as if maximizing a function is practically useless. After all, the choice-representing measures (utility cum probability) do not represent reasons for making choices from sets of alternatives. Which action from the internal point of view of the decision-maker should be chosen cannot be justified by utility and probability expectations that (after the fact) merely represent the choices made.
The deliberations of a choice maker must rely on evaluations of causal effects of action that are brought about for a reason. A motive must be operative from the internal point of view of the decision-maker. It is effective within his or her cognitive processes rather than representing the overt behavior resulting from such processes. In this realm rationality must be procedural. It is about the rules that generate choices; that is, it is about the procedural and not about the so-called substantive rationality of choice making.
Still, there are links between the two points of view. First of all, if a choice maker learns that her choices violate acyclicity in that she-in some indirect way or otherprefers some alternative A to B then B to C and then C to A she may want to change her internal processes of generating choices. In this sense result-oriented rationality criteria can-one level up so to say-feed back on the procedures themselves and contribute to their improvement. 22 Secondly, procedures like the one represented in the flow-chart can be tested for consistency of results-like voting procedures can be tested for creating/avoiding cycles-and success according to some measure that is relevant according to the aspirations formed (what in biology would be number of offspring would be profit, firm growth or whatever).
Applying the preceding remarks on the relation between procedure and success to the issue of how to cope with (new) uncertainties is straightforward. If the hypothesis is that procedures can best be described in flow charts, then competing flow-charts standardizing competing procedures should be tested for non-procedural success. One setting might be contests between competing procedures of forecasting. 23 These settings reduce the problem by choosing intermediate rather than ultimately relevant endpoints in that the success of planning and action on the basis of such forecasts is not taken into account. A good setting for further scrutiny could be the experimental economics laboratory provided that aspects of the flowchart are properly embedded in incentive structures. For instance, participants of an experiment can be induced to generate explicit scenarios. Likewise one can elicit aspiration levels and incentivize their explicit formulation by paying according to the aspirations if actual success is satisfying them. This can be compared to informal decision making without incentives to reason and plan according to a decision support system as characterized by the chart.
Obviously one has to be open-minded in evaluating alternative approaches. Procedures that can be represented in flow charts of the preceding kind may have superior competitors that cannot be presented by such a chart at all. We would predict, though, that the conventional representations in terms of the standard model of decision making will not lead to superior results. 24 Certainly many experiments should be run. If our basic implicit empirical hypothesis is correct all successful kinds of decision support that might be charted out should be ''prescriptive extrapolations of good practice'' as characterized here. We ''predict'' that the prescriptions derived will always incorporate the distinction between what is and what is not controlled by the decision maker, beliefs, aspirations, and action variables. The focus on causality structures (see Pearl (2000)) based on hypotheses linking plans/actions, scenarios and goal achievement should be essential across the board. As long as we are dealing with one off decisions not much more can be said about how exactly the degrees of freedom can be reined in. Yet, since the broader procedure is present in all decisions it is itself not one-off and we can gather statistical evidence on its workings that reduces the uncertainty attached to explicating the rationality concept in procedural terms. 25

Conclusion
After reflecting on procedures of case based decision-making many researchers tend to endorse some concept of inductive reasoning (see Gilboa and Schmeidler (2010)). Leaning towards the fallibilist view that in a fundamental sense to err is human and residual uncertainty will never go away we tend to reject a foundationalist role of induction-while accepting a statistical concept of corroboration. The basic view that an established human practice per se implies recipes that have some prima facie claim to technological usefulness seems reasonable to us, too. Accordingly we reconstructed the observable practices of boundedly rational decision-makers first. The technological proposal at improving practices was a kind of extrapolation based on the prevailing practices of real people. We started from where they ''are'' and from there on tried to critically reflect on our practices and to critically assess them in view of the results of such practices.
Foundational uncertainty cannot be eliminated by a priori arguments. Therefore we should act as good empiricists and try to form and test hypotheses concerning good practice. The aim is to collect evidence on what works and what does not work with the proviso that we may have to revise our views as we go along. We believe that much more piece meal research is necessary to gather evidence on how to cope better with uncertainties. All decision-making should be evidence based to the possible extent but never conceal when evidence is lacking. Formulations of decision problems as well as recipes of how to go about them should be as rigorous as possible. If mathematical language is used correctly it should make us alert of what we do not know rather than conceal it from our views. Many models of perfect rationality tend to conceal the true extent of our ignorance when presenting uncertainty as if it were risk or at least something akin to risk and therefore should be avoided in practical decision making.