Reasoning about the effects of actions in automated planning systems

This paper describes a temporal reasoning system that supports deductions for modeling the physics (i.e. cause and effect relationships) of a specified planning domain. We demonstrate how the process of planning can be profitably partitioned into two inferential components: one responsible for making choices relevant to the construction of a plan and a second responsible for maintaining an accurate picture of the future that takes into account the planner's intended actions. Causal knowledge about the effects of actions and the behavior of processes is stored apart from knowledge of plans for achieving specific tasks. Using this causal knowledge, the second component is able to predict the consequences of actions proposed by the first component and notice interactions that may affect the success of the plan under construction. By keeping track of the reasons why each prediction and choice is made, the resulting system is able to reason efficiently about the consequences of making new choices and retracting old ones. The system described in this paper makes it particularly simple and efficient to reason about actions whose effects vary depending upon the circumstances in which the actions are executed.     

Discounting axioms imply risk neutrality

Although most applications of discounting occur in risky settings, the best-known axiomatic justifications are deterministic. This paper provides an axiomatic rationale for discounting in a stochastic framework. Consider a representation of time and risk preferences with a binary relation on a real vector space of vector-valued discrete-time stochastic processes on a probability space. Four axioms imply that there are unique discount factors such that preferences among stochastic processes correspond to preferences among present value random vectors. The familiar axioms are weak ordering, continuity and nontriviality. The fourth axiom, decomposition, is non-standard and key. These axioms and the converse of decomposition are assumed in previous axiomatic justifications for discounting with nonlinear intraperiod utility functions in deterministic frameworks. Thus, the results here provide the weakest known sufficient conditions for discounting in deterministic or stochastic settings. In addition to the four axioms, if there exists a von Neumann-Morgenstern utility function corresponding to the binary relation, then that function is risk neutral (i.e., affine). In this sense, discounting axioms imply risk neutrality.     

Complete ignorance and independence axiom: Optimism,pessimism, indecisiveness

This paper studies the compatibility between a group of axioms characterizing rational behavior under complete ignorance and Savage's independence axiom. The axioms of complete ignorance include symmetry with respect to events, dominance and transitivity of strict preferences — possibly a very partial ordering of the choices, incomparabilities being admitted. Savage's independence axiom is a basic requirement in many theories of choice under uncertainty or risk. It is shown here that these requirements are indeed compatible, but conjointly imply that the decision-maker only exhibits zones of either pure optimism or pure pessimism or indecisive patterns of behavior.     

Interdependent binary choices under social influence: Phase diagram for homogeneous unbiased populations

Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are considered: the nonlocal or group interdependence model is used to study two interrelated groups making the same binary choice and the local or individual interdependence model represents a single group, where agents make two binary choices that depend on each other. For both models, phase diagrams and their implications in socioeconomic contexts are described and compared in the absence of private deterministic utilities (zero opinion fields). © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Ternary choices in repeated games and border collision bifurcations

Several recent contributions formalize and analyze binary choices games with externalities as those described by Schelling. Nevertheless, in the real world choices are not always binary, and players have often to decide among more than two alternatives. These kinds of interactions are examined in game theory where, starting from the well known rock-paper-scissor game, several other kinds of strategic interactions involving more than two choices are examined. In this paper we investigate how the dynamics evolve introducing one more option in binary choice games with externalities. The dynamics we obtain are always in a stable regime, that is, the structurally stable dynamics are only attracting cycles, but of any possible positive integer as period. We show that, depending on the structure of the game, the dynamics can be quite different from those existing when considering binary choices. The bifurcation structure, due to border collisions, is explained, showing the existence of so-called big-bang bifurcation points.     

Making choices with a binary relation: Relative choice axioms and transitive closures

This article presents an axiomatic analysis of the best choice decision problem from a reflexive crisp binary relation on a finite set (a digraph). With respect to a transitive digraph, optimality and maximality are usually accepted as the best fitted choice axioms to the intuitive notion of best choice. However, beyond transitivity (resp. acyclicity), optimality and maximality can characterise distinct choice sets (resp. empty sets). Accordingly, different and rather unsatisfying concepts have appeared, such as von Neumann–Morgenstern domination, weak transitive closure and kernels. Here, we investigate a new family of eight choice axioms for digraphs: relative choice axioms. Within choice theory, these axioms generalise top-cycle for tournaments, gocha, getcha and rational top-cycle for complete digraphs. We present their main properties such as existence, uniqueness, idempotence, internal structure, and cross comparison. We then show their strong relationship with optimality and maximality when the latter are not empty. Otherwise, these axioms identify a non-empty choice set and underline conflicts between chosen elements in strict preference circuits. Finally, we exploit the close link between this family and transitive closures to compute choice sets in linear time, followed by a relevant practical application.     

Axiomatic properties of inconsistency indices for pairwise comparisons

Pairwise comparisons are a well-known method for the representation of the subjective preferences of a decision maker. Evaluating their inconsistency has been a widely studied and discussed topic and several indices have been proposed in the literature to perform this task. As an acceptable level of consistency is closely related to the reliability of preferences, a suitable choice of an inconsistency index is a crucial phase in decision-making processes. The use of different methods for measuring consistency must be carefully evaluated, as it can affect the decision outcome in practical applications. In this paper, we present five axioms aimed at characterizing inconsistency indices. In addition, we prove that some of the indices proposed in the literature satisfy these axioms, whereas others do not, and therefore, in our view, they may fail to correctly evaluate inconsistency.     

Communication structure,trust and the free rider problem

Despite the recent wave of interest in the social and physical sciences regarding “complexity,” relatively title attention has been given to the logical foundation of complexity measurement. With this in mind, a number of fairly simple, “reasonable” axioms for the measurement of network complexity are here presented, and some of the implications of these axioms are considered. It is shown that the only family of graph complexity measures satisfying the “reasonable” axioms is of limited theoretical utility, and hence that those seeking more interesting measures of complexity must be willing to sacrifice at least one intuitively reasonable constraint. Several existing complexity measures are also described, and are differentiated from one another on an axiomatic basis. Finally, some suggestions are offered regarding future efforts at measuring graph complexity.     

模糊选择函数的Wφ-伪传递及Wφ-半序合理性刻画

在模糊偏好结构下,首先将Schwartz提出的收缩扩张公理模糊化,在选择集为正规模糊集的前提下,研究模糊选择函数Wφ-伪传递及Wφ半序合理的刻画问题。由于模糊化后的条件不再是选择函数伪传递合理的充分条件,因此,文章最后给出新的条件来刻画其合理性。     

模糊选择函数的合理性及拟传递合理性的刻画

首先给出模糊选择函数合理性的一个充分必要条件。然后将普通情况下Schw artz所提出的收缩扩张公理模糊化,在选择集为正规模糊集的前提下,研究了模糊选择函数拟传递合理性的刻画问题。我们指出,该模糊化后的条件仍是选择函数拟传递合理的必要条件,但已不再是拟传递合理的充分条件(我们用例子说明了这一点)。因此,在文章的最后,给出了比较强的一个充分条件。     

Characterization of certain orders using their associated choice functions

Binary relation and choice functions define two different languages for describing the decision maker's (DM's) preferences over a finite set of alternatives. The study of normal choice functions establishes a link between these two languages. The existence of this kind of function demonstrates the compatibility between the DM's local choices (paired comparisons or binary choices) and the DM's global choices. In this paper, we explore this kind of linkage in depth by studying characterizations of special binary relations (total order, weak order, partial order and quasi order) using certain properties of their associated choice functions.     

Rationing with baselines: the composition extension operator

We introduce a new operator for general rationing problems in which, besides conflicting claims, individual baselines play an important role in the rationing process. The operator builds onto ideas of composition, which are not only frequent in rationing, but also in related problems such as bargaining, choice, and queuing. We characterize the operator and show how it preserves some standard axioms in the literature on rationing. We also relate it to recent contributions in such literature.     

Variation of geometric invariant theory quotients

Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parameterizing isomorphism classes of geometric objects (vector bundles, polarized varieties, etc.). The quotient depends on a choice of an ample linearized line bundle. Two choices are equivalent if they give rise to identical quotients. A priori, there are infinitely many choices since there are infinitely many isomorphism classes of linearized ample line bundles. Hence several natural questions arise. Is the set of equivalence classes, and hence the set of non-isomorphic quotients, finite? How does the quotient vary under change of the equivalence class? In this paper we give partial answers to these questions in the case of actions of reductive algebraic groups on nonsingular projective algebraic varieties. We shall show that among ample line bundles which give projective geometric quotients there are only finitely many equivalence classes. These classes span certain convex subsets (chambers) in a certain convex cone in Euclidean space, and when we cross a wall separating one chamber from another, the corresponding quotient undergoes a birational transformation which is similar to a Mori flip.     

A Markov chains model of medical specialty choice†

Data from 118 members of three consecutive cohorts of students at a private Southern medical school are employed to develop a discrete parameter stationary Markov chains model of the medical specialty choice process. This model was then tested on independent subsamples from the same population, generating a series of predicted specialty choices which did not differ from observed choices by more than chance expectations. Suggestions for future research, beyond the present demonstration of the utility of a simple Markovian model of a choice process, are offered.     

关于有1模格的等价定义

进一步讨论有1模格的等价定义问题,得到并证明了一个(2,2,0)型代数成为有1模格的一个充分必要条件.这样大大简化了有1模格的等价定义.     

Compensatory transfers in two-player decision problems

This paper presents an axiomatic characterization of a family of solutions to two-player quasi-linear social choice problems. In these problems the players select a single action from a set available to them. They may also transfer money between themselves.The solutions form a one-parameter family, where the parameter is a non-negative number, t.The solutions can be interpreted as follows: Any efficient action can be selected. Based on this action, compute for each player a “best claim for compensation”. A claim for compensation is the difference between the value of an alternative action and the selected efficient action, minus a penalty proportional to the extent to which the alternative action is inefficient. The coefficient of proportionality of this penalty is t. The best claim for compensation for a player is the maximum of this computed claim over all possible alternative actions. The solution, at the parameter value t, is to implement the chosen efficient action and make a monetary transfer equal to the average of these two best claims. The characterization relies on three main axioms. The paper presents and justifies these axioms and compares them to related conditions used in other bargaining contexts. In Nash Bargaining Theory, the axioms analogous to these three are in conflict with each other. In contrast, in the quasi-linear social choice setting of this paper, all three conditions can be satisfied simultaneously.This work was supported by the Division of Research at the Harvard Business School. Thanks are due to the Cowles Foundation for Research in Economics at Yale University for its kind hospitality during the Spring of 2002. I have received helpful advice and comments from Youngsub Chun, Ehud Kalai, Herve Moulin, Al Roth, Ilya Segal, Adam Szeidl, Richard Zeckhauser, and other members of the Theory Seminars at Harvard, MIT, Princeton, Rice and Northwestern.     

Group preference aggregation in the multiplicative AHP The model of the group decision process and Pareto optimality

A recent paper has focused awareness on group aggregation procedures in the AHP, showing that geometric mean aggregation violates the desirable social choice axiom of Pareto optimality. We show that this violation can be attributed to the representation used to model the group decision process, thereby questioning the legitimacy of the Pareto optimality axiom. We furthermore propose a geometric mean group aggregation procedure which satisfies all the social choice axioms suggested.     

Strong representations of the polycyclic inverse monoids: Cycles and atoms

This paper was inspired by a monograph by Bratteli and Jorgensen, and the work of Kawamura. We introduce two new semigroups: a wide inverse submonoid of the polycyclic inverse monoid, called the gauge inverse monoid, and a Zappa-Szép product of an arbitrary free monoid with the free monoid on one generator. Both these monoids play an important role in studying arbitrary, not necessarily transitive, strong actions of polycyclic inverse monoids. As a special case of such actions, we obtain some new results concerning the strong actions of P ₂ on ℤ determined by the choice of one positive odd number. We explain the role played by Lyndon words in characterising these repesentations and show that the structure of the representation can be explained by studying the binary representations of the numbers $\frac{1} {p},\frac{2} {p}, \ldots \frac{{p - 1}} {p}$\frac{1} {p},\frac{2} {p}, \ldots \frac{{p - 1}} {p}. We also raise some questions about strong representations of the polycyclic monoids on free abelian groups.     

Information acquisition interactions in two-player quadratic games

This paper considers two-player quadratic games to examine the relation between strategic interactions in actions and in information decisions. We analyze the role of external effects and of the relative intensities with which the players’ actions interact with the uncertain payoff-relevant parameter. We show that, under some conditions on the quadratic preferences, information choices become substitutes when actions are sufficiently complementary. When attention is restricted to beauty contest games, our results contrast qualitatively with the case studied by Hellwig and Veldkamp (Review of Economic Studies, 76(1)223–251, 2009), where the set of players is a continuum.     

Fate, freedom and contingency

Argument for fatalism attempts to prove that free choice is a logical or conceptual impossibility. The paper argues that the first two premises of the argument are sound: propositions are either true or false and they have their truth-value eternally. But the claim that from the fatalistic premises with the introduction of some innocent further premise dire consequences follow as regards to the possibility of free choice is false. The introduced premise, which establishes the connection between the first two premises (which are about the nature of propositions) and the concept of free choice is not innocent. It creates the impression that the truth of certain propositions can somehow determine the occurrence of certain events. But no proposition can have such an effect since the counterfactuals “If proposition P were true, event E would happen” does not say anything about determination. The argument for fatalism is, however, not a boring sophism. It does reveal something about the nature of propositional representation. It shows that each proposition represents necessarily the fact what it represents, i.e. it shows that propositions have their truth conditions non-contingently. But from this nothing follows as regards to the contingent nature of the facts represented. On the bases of the first two premises of the argument for fatalism we cannot infer to the impossibility of free choice. The argument for fatalism should not be interpreted as an attempt to prove on purely logical or conceptual grounds that we do not have the ability to influence future events by our choices. But it could be used to show something about the nature of propositional representation.