Cross-impact balances: A system-theoretical approach to cross-impact analysis

Cross-Impact methods are standard tools of the scenario technique. They provide a number of structured processes for the deduction of plausible developments of the future in the form of rough scenarios and are based on expert judgments about systemic interactions. Cross-Impact methods are mostly used for analytical tasks which do not allow the use of theory-based computational models due to their disciplinary heterogeneity and the relevance of “soft” system knowledge, but on the other hand are too complex for a purely argumentative systems analysis. The essentials of a new Cross-Impact approach (Cross-Impact Balance Analysis, CIB) are outlined; it is of high methodological flexibility and is especially suitable for the use in expert discourses due to its transparent analytical logic. Due to its mathematical qualities it is also particularly well suited for the analytical integration of calculable system parts. An application of CIB to a project on the generation of electricity and climate protection is described. For a theoretical foundation of the CIB method relations to systems theory, especially to the theory of dynamic systems, are discussed. This explicates that CIB scenarios correspond to the solutions of slowly time-varying pair-force systems.     

A note on one-shot public mediated talk

Lehrer and Sorin (1997, Games Econ. Behav. 20, 131–148) use a one-shot public mediated talk model to show that, given any probability distribution on the outcomes of a finite normal-form game, there exists a public mediated talk mechanism that simulates that distribution, provided the probabilities on outcomes are rational numbers. It is shown here that a minor amendment of the very same model allows a much stronger conclusion: any distribution on the outcomes, whether the probabilities are rational numbers or not, can be obtained as the outcome of a one-shot public mediated talk mechanism.     

Subjective probabilities on “small” domains

The Savagian choice-theoretic construction of subjective probability does not apply to preferences, like those in the Ellsberg Paradox, that reflect a distinction between risk and ambiguity. We formulate two representation results—one for expected utility, the other for probabilistic sophistication—that derive subjective probabilities but only on a “small” domain of risky events. Risky events can be either specified exogenously or in terms of choice behavior; in the latter case, both the values and the domain of probability are subjective. The analysis identifies a mathematical structure—called a mosaic—that is intuitive for both exogenous and behavioral specifications of risky events. This structure is weaker than an algebra or even a λ-system.     

A recursion relation for the probability of the paradox of voting

For alternatives x_i, i = 1,…, m, giving rise to m! linear preference orderings of which one is selected independently by each of N voters, a recursion relation is developed which expresses the probability that x_i is the Condorcet winner when there are N voters in terms of the probability of this event when there are N ? 1 voters. Hence the probabilities of the paradox of voting when N is odd, and of Condorcet indecision when N is even may be obtained. The relationship holds for any set of probabilities, or culture, governing the selection of the preference orderings by the voters.     

Large deviations and multinomial probit choice

We consider a discrete choice model in which the payoffs to each of an agent?s n actions are subjected to the average of m i.i.d. shocks, and use tools from large deviations theory to characterize the rate of decay of the probability of choosing a given suboptimal action as m approaches infinity. Our model includes the multinomial probit model of Myatt and Wallace (2003) [5] as a special case. We show that their formula describing the rates of decay of choice probabilities is incorrect, provide the correct formula, and use our large deviations analysis to provide intuition for the difference between the two.     

A decomposition of training probabilities

The determinants of workers' training probabilities are analysed. A distinction is made between the unconditional probability that a worker is employed by a firm that provides any training opportunities at all, and the conditional probability that the worker receives training given that s/he works for a firm that provides training. For this analysis a censored version of the bivariate probit model is applied. The results indicate that establishment size, industry dummies, type of schooling, age and experience affect only the unconditional probability, whereas the type of labour contract, working hours and job level affect only the conditional probability. Years of formal schooling affect both probabilities; more highly educated workers are both more likely to work for training-providing firms and, given that they work for such a firm, to be selected for training programmes.     

Conditional belief types

We study type spaces where a player's type at a state is a conditional probability on the space. We axiomatize these spaces using conditional belief operators, examining three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certain of her beliefs. Second, echo, according to which the unconditional beliefs implied by the condition must be held given the condition. Third, determination, which says that the conditional beliefs are the unconditional beliefs that are conditionally certain. Echo implies that conditioning on an event is the same as conditioning on the event being certain, which formalizes the standard informal interpretation of conditional probability. The game-theoretic application of our model, discussed within an example, sheds light on a number of issues in the analysis of extensive form games. Type spaces are closely related to the sphere models of counterfactual conditionals and to models of hypothetical knowledge.     

An ordinal characterization of the linear opinion pool

Given a collection of individual ordinal probabilities on a finite state space, we discuss an ordinal condition that is necessary and sufficient for an ordinal probability to be represented as a weighted average of probability representations of the individual probabilities. We also give necessary and sufficient conditions for when such an ordinal probability can be represented as an unweighted average of probability representations. Many thanks are due to an anonymous referee, who provided detailed comments and corrections which greatly improved this paper.     

Induced Preferences, Nonadditive Beliefs, and Multiple Priors

We study a decision maker who follows the Savage axioms. We show that if he or she is able to take unobservable actions that influence the probabilities of outcomes, then it can appear to an outsider as if his or her subjective probabilities are nonadditive. Implications for multiperiod decision are explored. We extend the model to include a second individual who is also able to take a hidden action. We show that this may induce uncertainty-averse preferences over some class of acts, even if the second individual acts to help the decision maker with high probability.     

Intergovernmental transfers and political competition measured by pivotal probability - Evidence from Hungary

I estimate the effects of political competition on the allocation of intergovernmental transfers to Hungarian municipalities between 1998 and 2006. The intergovernmental transfers were intended to finance schooling, elder care, and administrative needs in municipalities. Rather than use closeness of the dominant blocks' vote share, which is the standard measure of political competition, I instead employ (Myerson, 2000)'s pivotal probabilities, calculated at the municipality level. As a result, the number of voters, in addition to the vote difference, is taken into account when describing political competition at the municipal level. I argue that under mixed-member proportional systems, as well as under proportional systems in general, pivotal probability reflects the political reality better than closeness can. I find evidence that swing municipalities in villages are targeted and, ceteris paribus, that poorer regions receive larger transfer amounts than other areas.     

Futures research scenarios and time succession

The possibility of introducing time-succession into a type of scenario approach used in futures research is examined, starting from Duperrin and Godet's SMIC-74 method, which deals with sets of nondated binary events and requires as input data the individual probabilities of these events and their time-independent conditional probabilities, taken by pairs. Time succession is then considered successively at two levels: 1)as a means used just to make conditional probabilities more accessible to intuition, following a proposal of Mitchell and Tydeman, to which a simplification is suggested; and 2) as a characteristic to be kept in the time-succession dependent scenarios that are finally dealt with. In the second the investigated period is split into q time “scenes,” as suggested by Olaf Helmer, and a method is proposed using the same algorithm as is used in SMIC-74, but in which binary events, as basic elements, are replaced by “boxed-events.” A boxed-event consists in the couple formed by an event and a “box” that represents either one of the q time scenes or the nonoccurrence of the event. The procedure by which experts can be consulted about the individual and conditional probability data required is described in some detail.     

A theory of subjective compound lotteries

We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.     

Family labour force participation: Multinomial logit estimates

Studies of labour force participation choices are mostly aimed at explaining determinants of participation for individuals. The objective of this study is the empirical estimation of the parameters of family participation decisions.

Family participation decisions can be analysed as a choice problem of a family between a finite number of distinct alternatives. The appropriate estimation procedure for a model involving choice among multiple discrete alternatives requires a statistical technique different from ordinary least squares. In this study I use the multinomial logit model. A logit model allows me to explain the probability that a particular participation alternative will be chosen by a family as a function of a set of independent variables.

It is found that economic variables such as wage rates and wealth, play a significant role in affecting the probabilities of choosing a particular labour force participation alternative. This study shows that an increase in the market wage for a family member not only increases the probability of labour force participation for that family member, but at the same time also reduces the probability of participation for his or her partner. Hence there is both a pure and a cross-substitution effect in participation. There is also an income effect. As wealth increases families will, in some sense, buy more leisure. Furthermore, they will allocate the extra leisure in a certain order: it is found in this study that the wife's probability of participation reduces sooner and faster than the husband's probability, as wealth increases.     

Costs or gross benefits? – What mainly drives cross-sectional variance in Internet adoption

In this paper, we propose an empirical model of Internet adoption which takes into account the household’s desire to adopt the Internet. Our research supports three central findings. First, we determine the main factors that explain the cross-sectional variance in gross benefits. Second, we estimate the predicted probabilities that a household does not desire to adopt the Internet and that a household desires to adopt the Internet but does not because its adoption costs are higher than its gross benefits. We show that while the cross-sectional variance in the first predicted probability is high, the cross-sectional variance in the second one is low (except for the age factor). Third, we compute the predicted adoption probability assuming that the adoption costs are homogeneous across households. We show that, for a given dimension (except for the age factor), the adoption rate will be only slightly modified if the adoption costs are homogeneous across households. Our results support the argument that the digital divide is mainly due to differences in gross benefits of adoption.     

A Comparative Static Model of the Relationship between Immigration and the Short-Run Job Prospects of Unemployed Residents

A novel theoretical approach is developed to illustrate the consequences of immigration for the probability that unemployed residents gain a job. Through the use of the vacancies to unemployment ratio it is shown that immigration in theory can either increase or decrease unemployed residents' employment probabilities, but that, contrary to populist rhetoric, an increase is more likely the more recessed is the labour market. With reference to feasible Australian values of the parameters of interest, it is demonstrated that in practically all circumstances immigration increases the overall employment prospects of unemployed residents. Even so, the analysis is very short run, and strong conclusions as to what might be happening over the longer term are not appropriate.     

The enduring allure of objective probability

Probability measures are properly considered subjective, if only as a result of the knowledge limitations of human experience. Even if objective probability can be demonstrated as an unambiguously verifiable property of the physical world, our necessarily imperfect access to such aspects of reality would necessitate the construction of subjective probability measures for examinations of human behavior. This paper will explore the distinction between subjective and purportedly objective probability in principle, and demonstrate that actual probabilities can only be subjective, at least ex ante. The paper will next examine the persistent efforts of philosophers, mathematicians, and particularly quantitatively-inclined social scientists, to construct and employ mistaken conceptions of purportedly objective probability. The neo-indeterminist interpretation of sub-atomic particle physics is addressed next, with its attempt to construct an objective-probabilistic account of reality based on the Heisenberg uncertainty principle. An explanation is suggested for the persistent allure of objective probability in the social sciences, which purports to offer a more economical and parsimonious basis for human behavior and the formation of expectations. The view that there are ontologically privileged, objectively-verifiable probabilities and expectations, will be examined and criticized. It appears to be one source of the discredited, though nonetheless widespread and persistent, belief in the efficacy and feasibility of central economic planning.     

Too good to be true? The (In)credibility of the UK inflation fan charts

This paper presents some simple methods to estimate the probability that realized inflation will breach a given inflation target range over a specified period, based on the Bank of England’s RPIX inflation forecasting model and the Monetary Policy Committee’s forecasts of the parameters on which this model is built. Illustrative results for plausible target ranges over the period up to 04Q1 indicate that these probabilities are low, if not very low, and strongly suggest that the Bank’s model over-estimates inflation risk.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

Market Size and the Survival of Foreign‐owned Firms*

We develop a general equilibrium model with heterogeneous firms and foreign direct investment cost uncertainty and investigate the survival of foreign‐owned firms. The survival probabilities of foreign‐owned firms depend on firm‐level characteristics, such as productivity, and host country characteristics, such as market size. We show that a foreign‐owned firm will be less likely to be shut down when its parent firm's productivity is higher and its indigenous competitors are less productive. Although a larger market size will always reduce the survival probability of indigenous firms, it can lead to a higher survival probability for foreign‐owned firms if their parent firms are sufficiently productive.     

The network of weighted majority rules and its geometric realizations

In a previous work the first author considered the network G(n,p) of weighted majority rules (WMR) for n decision makers whose competencies are given by their probabilities p=(p₁,…,p_n) of making a correct decision. On this paper we consider chains of decision profiles, which must occur in G(n,p) in a fixed order, and show that they can be mapped onto straight lines in a low-dimensional geometric realization. The minimal number of directions which must used to separate all edges is given as the chromatic number of a certain incidence graph. We also define degenerate networks in which several nodes coalesce.