Penalizing strategic preference manipulation in multi-agent decision making

We consider a problem that can arise in group decision-making when the selection process is based upon a group preference function obtained by an aggregation of the individual preference functions of the group members. We observe the possibility of the individual agents strategically manipulating the information they provide so as to further their own goal of getting their most preferred alternative selected by the group. With this in mind we suggest ways of modifying the formulation of the group decision functions to discourage strategic manipulation by the participating agents.

This paper seeks to prove that under a large class of group decision rules some sincere voting situations will be unstable because of strategic manipulation by single individuals. The concept of stability used is weaker than the stability concepts figuring in many earlier contributions in this area, insofar as under the concept used here any individual, while disrupting a given voting situation, considers the possibility of retaliation by other individuals. DUMMETT AND FARQUHARSON [2], Murakami [7], Farquharson [3], Sen [14], Gibbard [4], Satterthwaite [13], and Pattanaik [10, 11, and 12] have discussed various aspects of the problem of stability in voting. The general conclusion which emerges from these writings seems to be that stability of all possible sincere voting situations (which implies the absence of strategic distortion of preferences by voters) is an extremely rare feature of democratic group decision procedures. However, the notion of stability or equilibrium underlying many of these contributions is a simple one and does not take into account several phenomena usually associated with strategic voting such as the possibility of counter-coalitions when a coalition (of one or more individuals) threatens to disrupt a voting situation. The purpose of this paper is twofold. First, it introduces a less demanding notion of stability which takes into account the possibility of formation of countercoalitions when an individual seeks to influence the outcome in his own favor by strategic manipulations in voting. Secondly, using this very weak notion of stability, it is shown that, while under the changed definition the possibility of having unstable sincere voting situations because of strategic voting by single individuals is somewhat reduced, invulnerability of all possible sincere voting situations to voting maneuvres of single individuals still remains a very rare property among democratic group decision rules based on pairwise comparisons. We lay down the basic notation and some preliminary definitions in Section 1. In Section 2 we introduce a notion of stability taking into account the possibility of counter-coalitions. Using this very weak definition of stability, in Section 3 we show that under most democratic group decision rules based on pairwise comparisons, there is the danger of having unstable sincere voting situations owing to strategic manipulations by single individuals. We conclude in Section 4.

We consider the problem of preference aggregation in group decision making. The role of the collaborative imperative used by the group in determining the form of the aggregation function is noted. We focus on one collaborative imperative, called the primal, deriving from participant autonomy, an agent doesn't have to accept a decision by the group it doesn't like. We showed that t-norms and more generally the class of uninorms having zero fixation provide appropriate aggregation operators to implement this primal collaborative imperative. We then discuss the possibility of an agent using a strategic manipulation of its preference information to get its preferred alternative. A mechanism based upon the use of an importance weighting is then suggested for modifying the construction of the group decision function to defend against strategic manipulation.

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences.

With regard to uncertain multi-criteria decision-making problems, in which the criteria values of alternatives are in the form of trapezoidal fuzzy numbers and the criteria weights are completely known, a prospect value function of trapezoidal fuzzy numbers based on risk attitudes of decision makers is defined, and the preference function in PROMETHEE method is replaced by the possibility degree of prospect value function of trapezoidal fuzzy numbers. Then a new preference function with risk attitudes of decision maker and an improved PROMETHEE II method based on prospect theory are proposed. The new preference function takes into consideration that the decision maker has preference on alternatives which not always varies with criteria values linearly or stepwise but varies with his or her subjective feelings in the real decision-making problems, and the method extends the form of preference function and better reflects the decision makerpsilas preference. Finally, an example is given to show the feasibility and availability of the method proposed above.

Social trust evolution analysis: Group decision making by utilizing stochastic Petri nets and strategic manipulation

This paper suggests an evaluation of the plurality rule according to how much it can be manipulated by individuals. We analyze strategic voting with reference not only to the usual notion of Nash equilibrium but also to some weaknesses of this notion, depending on the assumptions about how the individual agents choose their strategies. We provide two types of results for each concept of equilibrium: First, we give necessary and sufficient conditions for a profile to be an equilibrium when the plurality rule is used; and second, we present formulas giving the exact frequencies of unstable situations in the three-alternative case.

The practice of limiting program benefits to specific groups in the population through the specification of eligibility and targeting rules is relatively common among government sponsored programs. In some cases, such as Social Security, Supplemental Security Income, and Medicaid, the eligibility criteria are established by Federal and state regulations. The local community and the local administrators of the program can exercise some discretion in the enforcement of these regulations, but they are seldom able to change the specific eligibility rules. This situation contrasts with decentralized programs in which both the specification and enforcement of eligibility and targeting rules are determined at the local level. The result of this decentralization in rule making has been the generally predictable variation in the development and use of eligibility and targeting rules by local organizations. While this observed variation has been both praised and criticized, relatively little research has been done to determine the sources of this observed variation in rule use. Efforts to associate rule use with measures of decentralization are an exception to this generalization. Previous studies of bureaucratic behavior, especially studies which have employed a rational actor approach, have argued that decisions by administrators will depend on their individual preference functions and on various constraints limiting their choices (Tullock, 1965; Niskanen, 1975; Allison, 1971). Although not the central focus of these studies, explanations for the observed variation in rule use by local agencies have been suggested. However, only limited attempts have been made to explore the reasonableness of these suggestions. The objective of this paper is to formalize a rational actor model of bureaucratic behavior designed to explore variations in the use of eligibility rules, and to test this model using data collected on the use of eligibility rules by local organizations. Part 1 presents the theoretical model designed

Measuring female mating preferences

The cost of obtaining good information regarding the various probability distributions needed for the solution of most stochastic decision problems is considerable. It is important to consider questions such as: (1) what minimal amounts of information are sufficient to determine optimal decision rules; (2) what is the value of obtaining knowledge of the actual realization of the random vectors; and (3) what is the value of obtaining some partial information regarding the actual realization of the random vectors. This paper is primarily concerned with questions two and three when the decision maker has an a priori knowledge of the joint distribution function of the random variables. Some remarks are made regarding results along the lines of question one. Mention is made of assumptions sufficient so that knowledge of means, or of means, variances, co-variances and n-moments are sufficient for the calculation of optimal decision rules. The analysis of the second question leads to the development of bounds on the value of perfect information. For multiperiod problems it is important to consider when the perfect information is available. Jensen's inequality is the key tool of the analysis. The calculation of the bounds requires the solution of nonlinear programs and the numerical evaluation of certain functions. Generally speaking, tighter bounds may be obtained only at the expense of additional information and computational complexity. Hence, one may wish to compute some simple bounds to decide upon the advisability of obtaining more information. For the analysis of the value of partial information it is convenient to introduce the notion of a signal. Each signal represents the receipt of certain information, and these signals are drawn from a given probability distribution. When a signal is received, it alters the decision maker's perception of the probability distributions inherent in his decision problem. The choice between different information structures must then take into account these probability distributions as well as the decision maker's preference function. A hierarchy of bounds may be determined for partial information evaluation utilizing the tools of the multiperiod perfect information case. However, the calculation of these bounds is generally considerably more dicult than the calculation of similar boulids in the perfect information case. Most of the analysis is directed towards problems in which the decision maker has a linear utility function over profits, costs or some other numerical variable. However, some of the bounds generalize to the case when the utility function is strictly increasing and concave.

Chapter 10 - Preference functions and risk-adjusted performance measures

ONE OF TIlE MOST interesting characteristics of recent aggregative ino(dels of economic growth is perhaps the specification of optimal growth paths under varying assumptions and conditions defining optiinality. Assuming that an optimal growth path for a fixed horizon can be specified for a developed or an underdeveloped economy, difficult decision problems of macro-dyniamic policy-making arise, when appropriate governmental actions are needed to secure the convergence of the observed growth path to the optimal one. The solutions of these decision problems by simple mathematical models are considered here with special emphasis on their uncertainty and dynamic aspects. The implications of alternative preference functions are analyzed here to show how optimal decision rules can be derived under various orders of truncation2, where truncation refers to the (degree of incomplete sp)ecification of the probability distribution of the random elements of the problem, i.e., the risk preference function (or disutility function) of the problem. Our approach would be to analyze the concept of 'a linear decision rule' developed by Theil [71 and emphasized recently by Holt [6] who used a quadratic risk function in a simple aggregative Keynesian model based on the multiplicr, the income identity and private investment as the only random variable. For illustrative purposes, we would use the principle of optimality of Pontryagin [9] as a generalization of the extremum conditions of variational calculus to derive the optimal time

How are congressional party leaders chosen? In the first comprehensive study since Robert Peabody's classic Leadership in Congress, this book draws on newly collected data about U.S. House members who have sought leadership positions from the 1960s to the present—data including whip tallies, public and private vote commitments, interviews, and media accounts—to provide new insights into how the selection process truly works. Elections for congressional party leaders are conventionally seen as a function of either legislators' ideological preferences or factors too idiosyncratic to permit systematic analysis. Analyzing six decades' worth of information, the book finds evidence for a new comprehensive model of vote choice in House leadership elections that incorporates both legislators' goals and their connections with leadership candidates.

Effective COVID-19 vaccines are the best weapons against the COVID-19 pandemic and have become a strategic property of local governments. Experienced experts need to be invited to improve the accuracy of COVID-19 vaccine selection; such a selection process can be regarded as a large-scale group decision-making (LSGDM) problem. Many LSGDM models have been proposed in order to overcome the non-independence of experts. However, the objective empathetic relationships among experts which can affect decision results have been ignored. To fill these gaps, this article proposes a LSGDM method based on empathetic network analysis (ENA). First, we identify the dissociative empathetic network, central empathetic network, and general empathetic network. Then, we determine the results of internal preference evolution from the perspective of preference interactions. We adopt the fuzzy c-means (FCM) clustering algorithm to divide a large group of experts into several subgroups according to the empathetic centrality of experts, and then propose three kinds of feedback mechanisms with respect to the empathetic relationships for central, dissociative, and general empathetic networks to improve the quality of the consensus-reaching process. Finally, an illustrative example related to the selection of COVID-19 vaccines is presented to validate the proposed model.

Different consensus models for group decision-making (GDM) problems have been proposed in the literature. However, all of them consider the consensus reaching process a rigid or inflexible one because its behavior remains fixed in all rounds of the consensus process. The aim of this paper is to improve the consensus reaching process in GDM problems defined in multigranular linguistic contexts, i.e., by using linguistic term sets with different cardinality to represent experts' preferences. To do that, we propose an adaptive consensus support system model for this type of decision-making problem, i.e., a process that adapts its behavior to the agreement achieved in each round. This adaptive model increases the convergence toward the consensus and, therefore, reduces the number of rounds to reach it.