Towards Optimal SocioEconomic Institutional Implementation Heuristics
Abstract
This Note tries to discuss optimality issues of the design (engineering) of socioeconomic meta institutional systems that is analyse the constitutional political economy (Buchanan 1990) problems. The analysis is based mainly on semiformalized implementation theory (design of mechanisms) and optimal decision methods and simulations of empirical constitutional mechanisms. In this the main attention is paid to the aspects of political choice systems and mechanisms that are ecologically (collectivelycooperatively) implementing efficient development of socioeconomic institutional arrangements of the conventional economies. In other words, the Note is heuristically analysing normative implementation possibilities of socioeconomic institutional systems in political mechanisms in coevolution with a general constitutional governance system (Vanberg 2005). It is especially focused on the aspects of coordinated collective problem solving (“tools for collective problem solving”, Olsen 2003) and communication issues in these kinds of engineering systems and is carried out mainly heuristically in the mathematical/narrative implementationtheoretic and optimal decision making terminology.
The discussion is heavily based on the framework of recent theoretic concepts of DescartesBayesNash transferred utility implementation of the real economy as the most precise and rigorous tools in the field of New Institutional Economics. Although, so far these tools are still quite stylised for a complex analysis of the empirical mechanisms’ clusters and constructivist design for the institutional implementation. The main missing link in a standard implementation theory by now for the latter field is that at construction of the implementing mechanisms the potential role of social implementor as coordinator is not taken into consideration and costs and benefits or optimality of the mechanisms and institutions have not yet been sufficiently endogenously described in the initial social choice relations (goal correspondences). E.g., the costs connected with transferring utilities are not taken into consideration, and also some social dimensions such as credibility of the actors, bounded rationality and learning by doing and information tradeoffs (Antonelli 2005) are not sufficiently exploited.
The emergent empirical institutional systems generally may be functioning (e.g. North 1990) sequentially, gradually, repetitively, adaptively and may be active in updating information in this process of communication, and private and public use, and the coordination fields of these systems are not only limited with primal socioeconomic activities but also with constitutional activities (institutional design, organisational engineering and construction, reforms etc). In these processes, the social planners with their private information have had parallel roles as implementers of the game and also as players in the game in the role of coordinators and utility transferors. In these mechanisms, agents’ reports may be indirect aggregated indicators; agents are worried about their consequential credibility status, depending on their behaviour in the process. They are in parallel consulted and multiply coordinated horizontally by other agents in market rules and vertically by the coordinator in their activity variant choices; they may be ostracised, they may use informal communication, they learn and create new knowledge in the coordination process, they are private and public actors etc.
Compared to the standard mathematical implementation theoretic designs, the empirical mechanisms are taking more into consideration the complexities and information content of the problems, bounded rationality and credibility of agents, heavier central coordination by quotas, more side payments, and not aiming necessarily at the minimalist mechanism design with exploitation of subsidiary elements but on sufficient implement ability. And more importantly, the imitations of empirical designs show that socioeconomic mechanisms should be dealt with in complementary or covarying clusters (Pryor 2005).
Our heuristic model findings, based on the imitations of empirical institutional systems and assumption of separability of the social choice function of explicit institutional arrangements (“institutional engineering”, Olsen 2002) by agents, containing institutional variables with complementarities and combined institutional influences (e.g. Searle 2005 and Solari 2005), are that the emergent types of mechanisms have probably robust suboptimal implementation permissiveness for a very general class of socioeconomic choice functions.
The heuristic narrative schematic proof of probable optimal implementation possibilities of a cluster simulation example of these reallike mechanism models in the field of social institutional implementation is in this note based on many splendid specific but more or less scattered results achieved in axiomatic theoretical implementation theories, first of all in the following studies (some keywords added): Matsushima (1992, sidepayments, and 2003, moral preferences), Aoyagi (1998, correlated types), Aoki (2001, institutional comparative mathematical studies), Eliaz (2002, tolerance of faulty players), Serrano and Vohra (2001, virtual Bayesian implementation), Tian (2004, nonconvex technologies and implementation), Brusco (2005, twostage Bayesian games in which agents observe a common public signal after the first stage) and by the author (1978, coordination by payments, constraints and consultations in parallel, and 1969, information and risk incentive prices), etc.
The main new insights for the field are: 1) it should be necessary to complement in the mechanisms the game forms with the implementor’s coordinative activities and 2) it should be important to synthesize into mechanisms the elements of actors’ private endogenous information communications combined with truthtelling arrangements.
JEL Classification Numbers: C72, D71, D78, H41.
Acknowledgements
The author has benefited from comments by Tiiu Paas and Stefano Solari. Financial support from the Estonian Ministry of Education and Research (Project 0142086s02) is gratefully acknowledged. The remaining errors are my own.
1. Introduction
The standard mainstream implementation theoretic approach is first of all developing as a prospective powerful constructivist tool to design variation aspects for the emergent ecological socioeconomic institutional structures. But we have to consent with Smith (2005) that these kinds of constructivist approaches are far too limited to be analytical tools or selection tools of ecologically emergent complex institutional structures, at least in their standard rigorous mathematical deduction approaches and stylised choice models. To use standard implementation theoretic tools for analysis of emergent real world institutional clusters with all their relevant facts and complexities, we have to sacrifice some precision of these simplified models, e.g. to satisfy with suboptimal solutions and combine in a relaxed logicalnarrative way many separate standard implementation theoretical narrow methods and their elements. In sum, we have to retreat to heuristics, pass back the Rubicon in purity of mathematics, what we would try in this note.
The plethora of the Bayesian mainstream axiomatic theoretical literature on social choice implementation (e.g. d’Aspremont, Crémer, and GerardVaret 2004 among others) is intellectually extremely challenging: mathematically sophisticated, aspiring to demand rigorous mathematical purity in the complicated probabilistic social choice field, elegantly tackling classical measure theoretical problems and Bayesian monotonicity and nonconsequential moral preferences, etc. But from the aspect of application, this literature seems not permissive enough, being quite distant from the real life complex phenomena that are from the spontaneously evolved ecological social choice systems in real societies in the coevolvement (Wagener 2004) with the general governmental constitutional system.
From the latter aspect, above all, the main omission seems to be that in the standard implementation theories already starting to formulate imaginary social choice functions seem not to be general enough to model transparently and adequately complex social phenomena and processes from three aspects.
Firstly, not including relevant institution building reforming activities themselves (e.g. optimal institutional structure creating reform processes in a transition country that last about dozen years). Although, in recent years some efforts to remedy this omission have been made (e.g. Ennuste 2001and 2003, Acemoglu 2003, Wagener 2004 and Lainecz 2005), and even clusters (systems) of economic institutions and market structures (Pryor 2005) have been endogenized. We may call these approaches as TwoLevel implementations (real and institutional levels, constitutional level missing, we return to these qualifications in the Table below).
Secondly, it seems that the standard theories prefer choice functions with exogenous prior information (knowledge) structures where the real world approaches are certainly based on endogenous information structures: in the sequences of operations and events by solving the problem new information may come in and learning by agents and extension of the knowledge base may take place (Kalai and Ledyard 1998), and these information streams may be correlated with the earlier choices made by agents etc. These issues have been presently put to the fore especially in connection with works by Tohmé (2004), Kaminski (2004), Foster and Young (2004), Meier (2004), Chambers (2004) and Koessler (2004).
Thirdly, the social planner who has a mandate to organise the implementation or to play a role of implementor and to use for that certain optimal amounts of resources, is not considering herself in the role of coordinator of the implemented game, in the role to make the game more effective, e.g. by considering the externalities and incompleteness of the rules of the implemented game. In other words the implementation is mainly based only on the spontaneous institutional arrangements (pure implementation) and not involving complementary coordination by policy parameters (coordinated implementation, e.g. Bassetto 2005)).
And from the application point perhaps it may seem also curious that if in the standard theoretical approaches prior social information profile is the collection of agents’ prior subjective knowledge profiles, many of them are probably faulty (as a result of probably strongly bounded rationality of some agents) and may be corrected in the solution process. Then what kind of theoretical rationality it can be to base static and exact implementation mechanism design absolutely on that kind of prior information? Why should the mechanism not have changing adaptive types with recourse, changing with learning and with the stream of incoming new information and not known or not attended in the beginning of the implementation process in the adaptive evolution of the play (Myatt and Wallace 2004).
Sometimes it looks that didactically it may be better not to start the theory from defining a “function” but to start defining it as a more general “social choice operator” (e.g. as a dynamic stochastic social optimisation model, Ennuste 1978).
And, importantly, in the standard implementation theoretical approaches, deductively designed mechanisms are perhaps not enough close models of the evolutionary developed real world empirical social technologies. In the real social mechanisms, an important factor is the consequential credibility (respectability) level (probabilities) of agents as well as of the social planner (centre, implementor). In real world mechanisms, these levels may change in the communication process and the bad agent may be penalised by transfers and constraints. We miss these coordination aspects in the mainstream standard abstract mechanism design literature. In other words the empirical mechanisms seem to have evolved to combined multiple implementation approaches. These have synthesized at least two implementation approaches: by game rules and by implementors direct coordination.
Importantly also, in the real world mechanisms, there dominates a combined coordination, mainly with (side) payments and constraints. The coordinating side payments by the centre to agents mainly harmonise the longterm social priorities with the shortterm and more myopic agents’ preferences (make the problem efficient and the incentive compatible). And the parallel use of constraints may strengthen the coordination adequately to the characteristics of the initial social choice operator (Ennuste, 1978).
Nevertheless, the existing brilliant standard axiomatic theoretical implementation literature contains in many works many elements as potentially useful building blocks to start combining a more general applied social choice implementation and mechanism design methodology, perhaps not as rigorously demanding as the standard theoretical purist approach but more practically permissive. Among the latter works, the most prominent for the purpose of this approach may be the following works and keywords:
Matsushima (1992, sidepayments, and 2003, moral preferences), Aoyagi (1998, correlated types), Eliaz (2002, tolerance of faulty players), Serrano and Vohra (2001, virtual Bayesian implementation), Koessler (2004, knowledge sharing in Bayesian games), Foster and Young (2004, learning and Nash equilibrium), Meier (2004, nonexistence of universal information structures), Baliga (1999, implementor is also a layer), Ennuste (1987, combined coordination with payments and constraints) etc.
In this Note we try to investigate heuristically and schematically the implementation theoretical conditions and problems by an example of imitating empirical evolutionary types of iterative mechanism models and corresponding institutional social choice function types. In our approach we base analysis on the ThreeLevel Multiple Implementation Model the schema explained in the Table. As one theoretical basis for heuristics we take metasynthesis analysis (e.g. Gu and Tang 2005) and no that basis we decompose a softly implementing game.
Tabel
ThreeLevel SocioEconomic Coordinated Implementation Model
Real (Ordinary*) Level: Standard socioeconomic agents make equilibrium choices among potential real activities within given (exogenous) institutional and “guiding” governance (policy) constraints (market game form structures and market coordination policy parameters (governance parameters)) fixed by Institutional Level. Field of the ordinary economics (in the mainstream approach based mainly on implicit “invisible” consideration of institutional arrangements).

Institutional (Political*) Level: Institutional arrangements designing and implementing actors make sequential Bayesian equilibrium choices among structures (clusters) of market game forms and market coordination policies within metainstitutional constraints (rules and coordination) given by Meta Level. Field of e standard institutional economics and Bayesian sequential implementation theory.

Meta (Constitutional*) Level: Social Implementor synthesises best game rules and coordination policies for the Institutional Level actors within her political and knowledge constraints. Field of the constitutional economics (synthesising superior rules for collective designing better institutions).

*Parallel to implementation theoretic terms the mainstream political economy terms: look e.g. Viktor Vanberg approach (2005).
One schematic illustration mechanism and its functions in the example are characterised by many phenomena, which are as a rule deviating from the standard theoretical implementation approaches and the deviations are primarily as follows:
1) In the example, like in real world, social system implementation is not a static phenomenon but a dynamic, sequential, repetitive, gradual, adaptive stochastic process with learning and information updating, i.e. in the stochastic environment, agents’ signals, the message space and the social alternative space are transforming in time and earlier choices may be indeterministic or contingent in the foreseeable future conditionally on information refinement where the governmental commitment to the chosen institutional strategy plays a significant role (Bassetto 2005) etc.
In other words and in greater detail, the implementation process is not an one shot big bang where all the structure of social alternatives is changed at each step, but there is going on a gradual componentwise (by agents or their subgroups etc) movement in campaigns and in iterations (subgradient like), in the direction of the moving optimum, where the initial status quo state of the system and prior information is important, especially in the path dependence and in the sequencing of the movement component selection. As the social choice problems are large problems, their implementation processes take time and there may be during this time new information (e.g. new results of earlier planned research activities), sometimes informally, arriving and thus, at the end of the iteration process, the solution may be outdated already, which makes the aspiration of exact and full implementation unpractical and approximate solutions (εbest or not worse as status quo) more preferable.
2) In the real world systems, the social planner (also in the roles of implementor and central coordinator) has also her private stochastic information about the environment (world) as agents do and in her coordination work it is partially detail free (Matsushima, 2003), as part of the detailed coordination may be made by the agents in their iterative Bayesian Nashlike game, not by direct and aggregated messages.
The agents, including the centre, may have differently bounded rationality, causing faulty specifications of their private signals (Eliaz 2002, Frank 2004, Nehring 2004, Smith 2004 and Parreiras 2005), and they may distort their messaging strategically in different ways. Therefore, we have to assume agents with different social credibility levels and these commonly known levels may change in the repeated communication. To come out of this learning and communication mischief we assume that: a) the average messages weighted with credibility levels are approximately true, b) with deviating messages and not taking into consideration other agents’ messages, the agent is harming her credibility level and this will harm her position in the following steps and campaigns, and c) the central coordinator is at least partially detailfree (Matsushima 2003 and Tian 2005) and giving partially the coordination to agents to make it horizontally. Thus, the main coordination tasks of the centre could be focused on the most significant task: harmonisation of the social function and agents’ longterm interests, to coordinate all system constraint quotas for the agents and the like.
3) The coordinator is allowed to coordinate agents’ activities by prices and quotas, to consult the agents, and make side payments for the agents on the basis of their current credibility indicators such as devices for stimulating truth telling and for better learning of environmental data. The coordinator is allowed to correct the incompleteness of the parallel coordination mechanisms.
4) Each social agent has in the process a store of initial credibility (moral status) that enhances expected utility, especially considering the longrun coordination transactions. Alas, this capital may vanish in the case of distorting message information and misspecifying private environment by the agent. In the case of the certain coordinator we postulate here simplistically that politically minded distortions of the coordination data may follow with the loss of credibilty and she may be ostracised.
5) We keep in mind that the initial social choice model to be sufficiently general should include both public and private agents. The agents’ activities should have many dichotomies such as: physical and informational, with shortterm (interventionist) and longterm (investment like) impacts, socioeconomic and constitutional (reforms, selection of institutions etc) activities etc. And the outcomes of the activities should comprise both socioeconomic and constitutional (institutional), and knowledge (Acs et al. 2004) phenomena. Institutional structures should differentiate formal (organisations, laws etc), informal (moral rules, social capital etc) and instrumental (currency, education, etc) institutions. Informational outcomes of activities are coordination strategies and additional knowledge ware into private and public knowledge base (storages). Among the institutional structures there should be structures to coordinate institution building processes and the central planner herself in the alternative functions of the central coordinator.
6) We assume that our implicit example of social choice model is a discrete concave model and the rational method of optimising it (Brandimarte 2002, 123) is componentwise driven in the direction of the subgradient that is accomplished by sequencing the components in the range of steepest ascent. We propose procedures with Lagrangean relaxation (Ennuste 2001) into a game and successive approximation heuristic (rule of thumb and narrative methods) convenient for this kind of programming and games to reach suboptimal solutions and decision making (Silver 2002, Adam 2004 and Lulli and Sen 2005).
7) The initial social choice model may be approximately decomposable agentswise on the basis of virtual implementation (e.g. Serrano and Vohra, 2004) assumption.
We are trying to show schematically, on the basis of the existing Bayesian implementation theoretic approaches, that the abovedescribed example model type of an evolutionary mechanism is probably robust and powerful and practical for a rational approximate implementation of a large set of social choice general function (with endogenous information structures, constitutional activities etc) types in stochastic environments.
This note is organised as follows. Section 2 shows the schematic basic example choice model. Section 3 defines the scheme of an example of the real life social choice implementation mechanism. Section 4 gives some schematic notes for the implementation argument and summary remarks follow.
2. Basic Framework of the General Social Choice Model
Let N ={1,…, n} denote the set of agents i who participate in the public decisionmaking process as representatives of all individuals in the society. Note that N should be a proper subset of the set of individuals who are influenced by the social decision process. And we have to keep in mind that here implicitly N is taken to model a dynamic set (to avoid difficulties with too many indexes we are not explicitly giving timeperiod indexes of sets and variables). We regard social planner (in the role of coordinator, not any more in the role of implementor) also as an agent denoted here as i=1, and assume that the coordinator is interested in the implementation.
Let A denote the dynamic set of variants of the available activities (to avoid measure theoretical problems we take all sets to be finite). The taxonomy of activities is like that: socioeconomic activities (to change the socioeconomic situation such as consumption, investments into physical as well into informational wealth etc) and reforming activities (political activities to change the institutional structure etc). We assume here that this set is decomposable according to the agents A=×A_{i}, iÎN and the variants may be contingent (depend on the states of nature).
Let M_{i} denote the dynamic set of messages for each agent iÎN. Let M=×M_{i}, iÎN. Let m_{i}ÎM_{i} denote the set of message profiles and m=(m_{i}) iÎN. For the agents iÎN1 we assume M_{i}= A and for the social planner M_{1} = {A,C} where C is the set of central (vertical) coordination parameters.
We study the following incomplete information environment. Formulating the announcement message, each agent will use her subjective private beliefs ω_{i}, which have evolved in the course of the stream of private signals received by her. We model ω_{i}. Let Ω_{i} denote the set of dynamic private beliefs for agent iÎN. Let ω=(ω_{i}) iÎN denote a social belief profile. We assume that the sets of private beliefs may change in correlation with the earlier activity profiles and are agentwise overlapping. Let Ω=×Ω_{i} iÎN denote the set of social belief profiles. Let p_{i}: P → [0,1] denote a probability of Ω, according to which the signal profile is randomly determined, where P denotes the set of probability measures and p_{i}(ω /ω_{i}).
An important departure made here from the standard implementation literature is the explicit assumption that the prior private belief ω_{i} is a subjective and not necessarily entirely rational model of stochastic objective state variable denoted μ_{i}_{.}
Thus, the agent’s subjective beliefs may be different from the true objective picture of the environment that can be achieved by “rationally” bounded rationality. The agent may principally never have the exact deterministic knowledge about the stochastic state of her environment and the private information may be modelling excessively aggregated and biased understanding of the true environment for the agent. We assume that it is possible for the agent to try to improve the objectivity of her current beliefs.
Thus, even in the case of undistorted informing by the agents they may not give objective information about the real situation. As we have stated already, in the standard literature it is generally taken that ω_{i} is a deterministic variable that is easy to document in the direct messages. In a more adequate approach, we take here that ω_{i} is a dynamic model of the stochastic variable, and the messages are not direct and are the elements of the activity sets. And we assume that the individual message sets are much smaller than the individual information sets.
Another important departure we make here is that the social planner has also her private prior beliefs about the initial social choice function, about agents’ reputations etc.
The explicit stochastic and implicit dynamic tackling of the private beliefs of the agents, first of all, extremely complicates the coordinating tasks of the centre in the implementation process and, secondly, makes the centre’s case of making truthtelling transfers (Aoyagi, 1998) very weak. To come out of this we make the implementation problem less ambitious compared to the standard literature: 1) we assume the decomposable by agents social choice function, 2) we will tackle the sequential (componentwise separately by agents 2,..,n) gradual stepbystep (adaptive) implementation situation where repetitive corrections (iterations) of the variants are possible in the course of receiving new signals or eliminating errors, and 3) we are going to be content with the implementation that is sequentially agentwise moving in the right direction, i.e. the implemented version is almost surely not worse than status quo.
Our initial general social choice function (operator, e.g. containing constraints) is defined as a dynamic stochastic mapping from the dynamic objective belief set to dynamic adaptive (contingent) activity variant set. For modelling simplifications we approximate this by the relaxed (Lagrangean) general social choice function f: Ω→ A, which is defined as a mapping operator from the initial bounded rationality belief profile set, as this signal set is the only information that can be practically used.
We assume that this mapping may in a sliding way fix deterministic plans for the next planning period (year), as well as adaptive contingent plans for the succeeding periods (depending on the realisation of belief profile evolvements). We assume that the social choice function may be approximately decomposable by characteristics of agents iÎN and there exists (f_{i}) iÎN such that
f_{i}: Ω_{i}→ A_{i} for all iÎN,
and
f(ω)=(f_{i}(ω_{i})) iÎN for all ω.
Note that A_{1 }of the social planner may be interpreted as a set of variants of the structure of the centre.
3. Basic Framework of a Mechanism
A dynamic social mechanism is defined by
G=(x,c),
where
x(a)=(a_{ii}) iÎN, the report variant of a_{ii} will be chosen by agent i in the sequences of agents, gradually by a_{ –i} =fixed and in the repetitive coordination process. In the coordination process, a_{ij} is denoting the horizontal coordinating consulting proposal of agent jÎNi to agent i, where a_{ii} ,a_{ ij} ÎA_{i.}
Coordinating agent (centre) will choose the sidecoordination profile c(a,ω_{1} )=(c_{i}) iÎN1and c_{i}_{ }=(ct_{i}_{ }_{, }cc_{i})_{ }where ct_{i}: A×Ω →R is the side payment (transfer) and cc_{i} is the side constraint cc_{i}: A×Ω →A_{i}. We assume that A is smaller than Ω, meaning that the centre is partially detailfree (Matsushima, 2003) in coordination.
We assume that transfers satisfy budgetary constraints in the sense that ∑ct_{i}(a,ω)=0 iÎN1 for all (a,ω) Î (A×Ω), and the constraint components satisfy the balance condition for all system constraints b (implicitly in f) in the sense that ∑ cc_{i}(a,ω)=b iÎN1. The coordination of the centre is dealing mainly with the problems belonging to the competence of the centre (e.g. longterm planning, social system’s external constraints, convex technologies, harmonisation of individual and social risk aversions etc). We assume that in different periods the centre may change the structure of the coordination profiles (e.g. go over to smaller constraint profiles etc), meaning that the mechanism may be dynamic.
We assume the expected utility hypothesis and define a utility function for each agent iÎN by u_{i}: →R. We allow interdependent values so that each agent’s utility can depend on the other agents’ activity variants. Let u=(u_{i}) iÎN denote a utility function profile.
We take into account ethical considerations of the actors in their expected utilities (e.g. Tamura 2005) based on their credibility considerations and possible ostracisms and in this way we consider the mechanism as a consensus formation mechanism.
The utility function profile u is common knowledge among the agents:
u_{i}=vi(a_{ii}, a_{ –i} ,ω_{i})+ ct_{i} + h_{i}Δξ_{i}
where v_{i}: (A, Ω_{i}) → R, and is called direct utility, ct_{i}_{ }is central side transfer to i, and
Δξ_{i}=∑ξ_{ij}Ind(a_{ii}=a_{ij})∑ ξ_{ij}Ind(a_{ii}≠a_{ij}), where Ind(a_{ii}=a_{ij})=1 if a_{ii}=a_{ij} and 0 otherwise, and Ind(a_{ii}≠a_{ij})=1 if a_{ii}≠a_{ij} and 0 if a_{ii}= a_{ij}, and ξ_{ij} is subjective private credibility probability of the agent j for the agent i (may be a value of the Bayesian probit function) and h_{i} is the subjective respect weight of agent i, this towards all the other agents. The latter values are more or less transparent and we may assume, e.g. that if h_{i}=0 fixed by i, then the common expectation of other agents will be at the next iteration that i has no credibility (reputation) at all.
Given the set of message profiles M, a general social mechanism is defined by a Bayesian iterative process with the combination (G, Ω,p,u).
A strategy for each agent iÎN1 is defined as a function at each coordination step as:
s_{i}: A×C_{i}×Ω_{i}→A_{i}
a_{ii}, if u_{i}=v_{i}(a_{ii}, a_{–i}, ω_{i})+ct_{i}+ h_{i}Δξ_{i}>>0, a_{ii}>cc_{i}
a_{ii} if otherwise,
where a_{ii} is the status quo and a_{–i }_{ }for jÎN_{I} is fixed by i.
A strategy for each agent jÎN_{i} for recommendation of a socially desirable a_{ii}_{ }is defined at each coordination step as:
s_{j}: A×C_{ j }×Ω_{j} →A_{i}
a_{ii}_{ } if u_{j}=v_{j}(a_{ii}, a_{–i}, ω_{j})+ct_{j}+h_{j}Δξ_{j} >>0,
a_{i} if otherwise.
The general social choice function f is said to be implemented in iterative Bayesian componentwise subgradient movement if there exists a unique iteratively undominated activity plan profile a*, and this profile satisfies the condition /f (ω) –a*/ <ε, where ε is almost certainly rationally small or the condition that the planned activity profile is not worse than status quo.
4. Schematic Permissiveness Possibility Argument
We may show schematically that the proposed simulation example mechanism should be very permissive and almost surely approximately implementing the example initial social choice function that satisfies the conditions given above.
Theorem: An initial general social choice function with prior rationally objective knowledge profile μ_{i} is approximately optimally (εbest or not worse as status quo) implemented in the gradual (componentwise campaigns) iterative (repeated refreshed messages) subgradient movement by the reallike social choice mechanism.
Indeed: The above statement is almost surely true by the assumption of separability of the social choice function and combined (see Appendix) institutional influences. E.g., the utility transfers for truthtelling and environmental externalities may be applied in parallel, e.g. the summary credibility of the fiscalmonetary system may be modelled as the sum or multiplication of the credibility indexes of both institutions. Thus, the combined implementation results may be applied to overcome difficulties of strategic behaviours of the agents and enhance their rationalities, to overcome market failures due to externalities etc.
The results of Aoyagi (1998, correlated types), Matsushima (2003, moral preferences), Eliaz (2002, tolerance of faulty players), Serrano and Vohra (2001, virtual Bayesian implementation), and optimisation theory (e.g. Brandimarte 2002), Tian (nonconvexities), Fuest and Hemmelgran (2005, coordinated tax competition), Jouvet, Michel and Rotillion (2005, choice of alaternative mechanisms), Healy (2005, learning forpublic goods mechanism design), Hurkens and Vulkan (2005, edogenous private information structures), Gu and Tang (2005, metasynthesis approach to complex system modelling), Bassetto (2005, governmental commitments and equilibrium) and Ennuste (1969 and 1978, information/risk prices and combined coordination by prices and constraints) etc.
The necessary incentive compatibility condition fulfilment may be demonstrated in relation to the characteristics of the proposed mechanism (side payments, consequential credibility levels etc). Combined coordination (parallel vertical coordination plus horizontal coordination) may probably be the basis for proving the sufficiency lemmas.
The condition of additional learning about the objective nature by agents may be demonstrated by the virtue of overlapping (correlated) and changing private information sets and correlation of agents’ credibility levels with the objectivity of the agents’ reports etc.
The coordination functions should be specified in more details relevant to the proof strategy.
5. Summary Comment
This note has schematically shown a complex combined constitutional mechanism design process example that imitates the processes of real world sequential mechanisms and almost surely has robust suboptimal institutional implementing qualities for very general types of institutional social choice functions.
The main new insights are for the field are: 1) it should be necessary to complement in the mechanisms the game forms with the implementor’s coordinative activities and 2) it should be important to synthesize into mechanisms the elements of actors’ private endogenous information communications between the actors/implementor and combined with truthtelling arrangements.
Based on that the main idea of the proposed synthesized design is to sequentially and adaptively coordinate the game of information and learning of the subsidiary constitutional actors with the help of stimulating their credibility and respectability behaviour by the constitutional coordinator with relevant side payments, quotas and consultations.
In this game, the social meta (constitutional) planner will first of all take the role of implementor and will design the rules of the meta game, and then will take a role and power of coordinator of the collective decision game, mainly trying to correct the incompleteness of the design to achieve socially desirable institutional developments.
The proposed illustrative mechanism is functioning as follows. The constitutional coordinator will focus the next sequential coordination campaign of institutional arrangements on one certain selected institutional agent (or group of them). The coordinator will ask her to share her indirect private information she has about efficient steps for her activity profile with fixed shortterm plans and state contingent preliminary longterm activity plans. For that, the coordinator will give to the chosen agent some coordinating and consulting information, including side payments and constraint quotas and about new environmental parameters. These are based on the private information the centre has, containing also the agent’s credibility probabilities. The better the rate of the agent is, the more generous the coordination and vice versa. Then the coordinator will ask other agents to send to all agents messages containing their views about the plan preferred by the selected agent on the basis of their own private information. By deviating from the probable weighted average messages, they will harm their credibility rates.
Then the selected agent will tackle the efficiency of her institutional project. For that she will take into notice the credibility rates of the communicators and her own consideration rate of others etc. This all is taken by others to correct her common credibility rate in their eyes. If her new version occurs to be overwhelmingly effective over status quo, she will implement it. If the proposed project happens to be overwhelmingly negative, she will stay with the status quo variant. In the middle of both, the centre may announce repetition of the step to try again to figure out the efficiency of the proposed corrected project on the basis of refreshed information and revised credibility rates etc.
In the end, the next campaign with the other selected agent will be initiated.
Appendix
Linear Planning Techniques to Model Combined Mechanisms/Institutions’ Equations for the SocioEconomic Choice Function with Institutional Activities
Preliminary remarks
The following narrative hints for a LP institutional model (e.g. Ennuste 2003) have been set up as a simplified version to model the economic design problems of a general conceptual national social planner (among latest others, Ennuste 2001 and Wagener 2004).
This type of LP model may be useful as a modest tool in the “political market game” process of social design of the effective institutional structure and mechanisms, especially for the evaluation of the values coordinating sidepayments in the political institutional design game. In other words, this model may give some macro approaches and coordinating parameters for stimulating micro calculations in the political institutional design game to go in the right direction.
In this model we demonstrate horizontal and vertical linear combinations of institutions’ and mechanisms’ effects in the institutional inputoutput matrix rows and columns. Horizontal effects may be complementary (e.g. the implementation of institute x is possible in the condition of existence of institute y) or substitutive (e.g. certain institute of knowledge creation x may be substituted by the alternative one y or their effects may add up). In the vertical (column) combination the different institutions may have effects in different rows or dimensions (e.g. the Tian’s (2005) mechanism has the dimension of coordinating nonconvexities but is not coordinating truthtelling, the Matsushima’s (2003) mechanism has the row effect of truthtelling, so the combination of these two mechanisms combine both institutional capacities).
It is important to note that in the following we keep implicitly in mind a stochastic twostage model with adjusting variables. Not also that this stochastic approach may make as more or less equally effective quite different institutional solution structures (with different structures of here and now and wait and see variables).
Activities and Constraints
It may be convenient to set up this model as a linear planning model (Ennuste 2003) with binary integer (1; 0) decision variables of activities (agents, institutions etc), so we may call this also an optimal constraint choice model, or a design model. We may take the target function (social maximand) and constraints here as linear combinations and all structural (inputoutput) parameters estimated by experts in these combinations are taken as descriptions of probabilities (possibly with interval distributions), as we assume that the probability values are most convenient for the experts to estimate and most natural here also for the robustness considerations. The inputoutput parameters may be calibrated as stochastic parameters to allow introduction of insurance institutions and credibility considerations.
Namely: 1) e.g., the probability of prospective credibility of national economy is sufficiently adequate to model as a sum of weighted credibility indicators of activities, where the weights are based e.g., on the significances of activities, 2) the probabilities of credibility of certain activities are easy to estimate as dependent on certain institutional arrangements in the economy, and 3) in these probability estimates it is easy also to take into account the situations of prospective economic recession and crises.
It may also be important to note that if multiplicative effects of activities or arrangements are considered initially in the model, the logarithmic transformation allows us again to reduce the model to the linear form.
The coordinates of optimisation vector denote various alternative economic institutions applied by organisations of national economy and in companies. Here we differentiate between two kinds of institutions: 1) public institutions which have the impact on all economy and are implemented by governmental legislation and other organisations, and 2) individual or local nonpublic (e.g., company, municipality, etc) institutions implemented by companies and municipalities for themselves and effective only in the same company and municipality, etc.
The target function will be a linear combination of the optimisation vector. The constraint inequalities may be linear combinations of weighted probabilities of certain socioeconomic development effects (“outputs”) that should in sum be no less than certain externally given levels. Certain constraints of the model contain also institutional “inputs”: for the implementation of certain institutional arrangements there is the need for existence of certain public institutional arrangements.
Here we assume that for the sake of robustness of the design in the future, the set of constraints may have different parameter values, dependent on the realisation of the states of nature in perspective (e.g. national economy will be member of the EU or alternatively will not be member) with the given probabilities. Not that the values of parameters of the target function may vary according to the realisation of prospective events.
Complementary institutional components
Say, there is a twodimensional institutional cluster (activity structure) a=(x,y), where implementation of the probably highly credible currency board system, denoted as x=1 (x=0 means not highly credible), demands the existence of a probably highly rigorously balancing budget institution, as a complement denoted by y=1 (y=0 means not highly rigorous): gives us the constraint x+y=2.
Additive institutional functional dimensions
Let there be a twodimensional functional/result constraint vector b=(w,z), where w may be denoting the existence of the mechanism probably regulating the strategic truthtelling, and z denoting the existence of the mechanism probably correcting the learning errors. Let the technology of x be (w,0) and for y be (0,z). Now x=1 and y=1 should fulfil the constraint b.
Public knowledge creation and dissemination
We use here the concepts by Acs et al. (2003) that the knowledge (stock) is a cumulative (in time) linear combination (sum) of the respective activities (public and private). And this stock is available for the free use for all activities. The latter condition is modelled in a way that all activities have the same constraint to operate under the same knowledge stock constraint.
Understandably, in the case of Lagrangean relaxation of these constraints, the public knowledge will get the shadow prices, each different for each activity.
Tax systems
Each year there is a binary choice to build in the next year a new tax system with all connected costs taken into account, or to say with the status quo.
Target function
Could be conveniently modelled as a GrossNet National Product (GrossNet meaning here less deprecations of all assets, including institutional assets) or other National Performance function considering the costs of institution building and their exploitation.
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NonTechnical Remarks
We consider heuristically the efficiency and characteristic of the systems of implementing socioeconomic institutional clusters. We are in our programme going quite into the distance from the traditional implementation theory: the approach is not rigorously formalised, the environment is “noneconomic” Bayesian with significant amount of faulty players, the characteristics of the implementing mechanisms are not as constrained as in the traditional theories, e.g., we are not constraining our choices of mechanisms with “spontaneous” ones that are functioning without any external funds, we consider in the implementation game the possibilities of coordination by the implementor and the credibility formation of the actors in the iterative information game and possibilities of ostracisms etc. All these complexities are involved much on the expenses of loosing precision and rigour compared to the mainstream implementation approach. But we are trying by our heuristic approach to narrow the gap between the brilliant isolated mathematical results of the traditional implementation theory and the needs of the socioeconomic reform and transition theories to get some implementation result for noneconomic environments, mode adequately complex models and complicated mechanisms.
We are trying no to achieve exact solutions to the partial problems but just some approximate solutions to more general ones. Therefore we consider the traditional implementing mechanisms as decomposed solutions and try to compose these for the efficient approximate solutions of the more general implementation problems
In other words this study tries to discuss optimality issues of the design (engineering) of socioeconomic metainstitutional systems, that is analyse the constitutional political economy (Buchanan 1990) problems. The analysis is based mainly on semiformalized implementation theory (design of mechanisms) and optimal decision methods and partly simulations of empirical constitutional mechanisms. In this the main attention is paid to the aspects of political choice systems and mechanisms that are ecologically (collectivelycooperatively) implementing efficient development of socioeconomic institutional arrangements of the conventional economies. In other words, the approach is heuristically analysing normative implementation possibilities of socioeconomic institutional systems in political mechanisms in coevolution with a general constitutional governance system (Vanberg 2005). It is especially focused on the aspects of coordinated collective problem solving (“tools for collective problem solving”, Olsen 2003) and communication issues in these kinds of engineering systems and is carried out mainly heuristically in the mathematical/narrative implementationtheoretic and optimal decision making terminology.
The discussion is heavily based on the framework of recent theoretic concepts of DescartesBayesNash transferred utility implementation of the real economy as the most precise and rigorous tools in the field of New Institutional Economics. Although, so far these tools are still quite stylised for a complex analysis of the empirical mechanisms’ clusters and constructivist design for the institutional implementation. The main missing link in a standard implementation theory by now for the latter field is that at construction of the implementing mechanisms the potential role of social implementor as coordinator is not taken into consideration and costs and benefits or optimality of the mechanisms and institutions have not yet been sufficiently endogenously described in the initial social choice relations (goal correspondences). E.g., the costs connected with transferring utilities are not taken into consideration, and also some social dimensions such as credibility of the actors, bounded rationality and learning by doing and information tradeoffs (Antonelli 2005) are not sufficiently exploited.
The emergent empirical institutional systems generally may be functioning (e.g. North 1990) sequentially, gradually, repetitively, adaptively and may be active in updating information in this process of communication, and private and public use, and the coordination fields of these systems are not only limited with primal socioeconomic activities but also with constitutional activities (institutional design, organisational engineering and construction, reforms etc). In these processes, the social planners with their private information have had parallel roles as implementers of the game and also as players in the game in the role of coordinators and utility transferors. In these mechanisms, agents’ reports may be indirect aggregated indicators; agents are worried about their consequential credibility status, depending on their behaviour in the process. They are in parallel consulted and multiply coordinated horizontally by other agents in market rules and vertically by the coordinator in their activity variant choices; they may be ostracised, they may use informal communication, they learn and create new knowledge in the coordination process, they are private and public actors etc.
Compared to the standard mathematical implementation theoretic designs, the empirical mechanisms are taking more into consideration the complexities and information content of the problems, bounded rationality and credibility of agents, heavier central coordination by quotas, more side payments, and not aiming necessarily at the minimalist mechanism design with exploitation of subsidiary elements but on sufficient implement ability. And more importantly, the imitations of empirical designs show that socioeconomic mechanisms should be dealt with in complementary or covarying clusters (Pryor 2005).
Our heuristic model findings, based on the imitations of empirical institutional systems and assumption of separability of the social choice function of explicit institutional arrangements (“institutional engineering”, Olsen 2002) by agents, containing institutional variables with complementarities and combined institutional influences (e.g. Searle 2005 and Solari 2005), are that the emergent types of mechanisms have probably robust suboptimal implementation permissiveness for a very general class of socioeconomic choice functions.
The heuristic narrative schematic proof of probable optimal implementation possibilities of a cluster simulation example of these reallike mechanism models in the field of social institutional implementation is in this note based on many splendid specific but more or less scattered results achieved in axiomatic theoretical implementation theories, first of all in the following studies (some keywords added): Matsushima (1992, sidepayments, and 2003, moral preferences), Aoyagi (1998, correlated types), Aoki (2001, institutional comparative mathematical studies), Eliaz (2002, tolerance of faulty players), Serrano and Vohra (2001, virtual Bayesian implementation), Tian (2004, nonconvex technologies and implementation), Brusco (2005, twostage Bayesian games in which agents observe a common public signal after the first stage) and by the author (1978, coordination by payments, constraints and consultations in parallel, and 1969, information and risk incentive prices), etc.
This study has schematically shown a complex combined constitutional mechanism design process example that imitates the processes of real world sequential mechanisms and almost surely has robust suboptimal institutional implementing qualities for very general types of institutional social choice functions.
The main new insights are for the field are: 1) it should be necessary to complement in the mechanisms the game forms with the implementor’s coordinative activities and 2) it should be important to synthesize into mechanisms the elements of actors’ private endogenous information communications between the actors/implementor and combined with truthtelling arrangements.
Based on that the main idea of the proposed synthesized design is to sequentially and adaptively coordinate the game of information and learning of the subsidiary constitutional actors with the help of stimulating their credibility and respectability behaviour by the constitutional coordinator with relevant side payments, quotas and consultations.
In this game, the social meta (constitutional) planner will first of all take the role of implementor and will design the rules of the meta game, and then will take a role and power of coordinator of the collective decision game, mainly trying to correct the incompleteness of the design to achieve socially desirable institutional developments.
The proposed illustrative mechanism is functioning as follows. The constitutional coordinator will focus the next sequential coordination campaign of institutional arrangements on one certain selected institutional agent (or group of them). The coordinator will ask her to share her indirect private information she has about efficient steps for her activity profile with fixed shortterm plans and state contingent preliminary longterm activity plans. For that, the coordinator will give to the chosen agent some coordinating and consulting information, including side payments and constraint quotas and about new environmental parameters. These are based on the private information the centre has, containing also the agent’s credibility probabilities. The better the rate of the agent is, the more generous the coordination and vice versa. Then the coordinator will ask other agents to send to all agents messages containing their views about the plan preferred by the selected agent on the basis of their own private information. By deviating from the probable weighted average messages, they will harm their credibility rates.
Then the selected agent will tackle the efficiency of her institutional project. For that she will take into notice the credibility rates of the communicators and her own consideration rate of others etc. This all is taken by others to correct her common credibility rate in their eyes. If her new version occurs to be overwhelmingly effective over status quo, she will implement it. If the proposed project happens to be overwhelmingly negative, she will stay with the status quo variant. In the middle of both, the centre may announce repetition of the step to try again to figure out the efficiency of the proposed corrected project on the basis of refreshed information and revised credibility rates etc.
In the end, the next campaign with the other selected agent will be initiated.
The main new insights for the field are: 1) it should be necessary to complement in the institutional implementing mechanisms the iterative game forms with the implementor’s coordinative activities, 2) it should be important to synthesize into mechanisms the elements of actors’ private endogenous information communications combined with truthtelling and learning stimulating arrangements based on the credibility stock of the actors and 3) the coordination in the system should combine sidepayments and sideconstraints and informational consultations.
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