Subjective expected utility theory revisited: A reductio ad absurdum paradox

A paradox is posed and analyzed in which people reverse their preferences for information on probabilities versus prizes once the range of the unknown probabilities is sufficiently narrowed. This reversal is shown to be incompatible with both objective expected utility (EU) as well as subjective versions in which the same probability transformation applies to all random variables. Experimental data are presented showing that the reversals occur with small, medium and large payoffs.The present paradox is compared with those of Allais and Ellsberg, and found to differ in substantive ways. It raises further questions about the normative status of expected utility theory, especially its treatment of probability and value. The paradox specifically calls into question EU's substitution and compound probability axioms.     

The chain store paradox

The chain store game is a simple game in extensive form which produces an inconsistency between game theoretical reasoning and plausible human behavior. Well-informed players must be expected to disobey game theoretical recommendations.The chain store paradox throws new light on the well-known difficulties arising in connection with finite repetitions of the prisoners dilemma game. Whereas these difficulties can be resolved by the assumption of secondary utilities arising in the course of playing the game, a similar approach to the chain store paradox is less satisfactory.It is argued that the explanation of the paradox requires a limited rationality view of human decision behavior. For this purpose a three-level theory of decision making is developed, where decisions can be made on different levels of rationality. This theory explains why insight into the rational solution of a decision problem does not necessarily mean that the corresponding course of action will be taken.     

Newcomb's paradox

This note proposes a new solution to the problem based on the information states available to the two opponents. The demon or predictor has two possible states on which to choose his course of action. These states are his predictions of the agents choice. The agent has only one state on which to make his choice. It is shown that unless the reward is small, the agent should make his choice probabilistically, using the same odds as the demon's chances of correct prediction.     

Notes on Ostrogorski's paradox

Conclusion This note has investigated the necessary conditions for the existence of Ostrogorski's Paradox, and it showed that the paradox depends on the sizes of the groups taking each possible set of stands on the salient issues. By revising its positions on relevant issues, the majority party can avert the paradox. With increased emphasis on single-issue voting observed in the United States and other Western democracies, the analysis of the paradox should guide the understanding of parties' responses to coalition formation processes among special interest groups. Indeed, the Apex conditions characterizing the paradox provide clues as to the strategy to be followed by the majority party in selecting its platform: the party should generally follow positions advocated by the largest group while presenting a coalition of all other groups.The helpful comments of Howard Tamashiro on an earliar draft of this paper are greatfully acknowledge.     

Avoiding the voter's paradox democratically

This paper is concerned with selecting an appropriate perspective from which to understand and evaluate social-decision procedures. Distinguishing between agentrationality and option-rationality, the author argues that a rational agent may choose a social-decision procedure that is not itself agent-rational (but merely option-rational). The argument puts the voter's paradox in a context allowing evaluation of (a) its general import and (b) practical proposals for avoiding it in particular cases. Arrow's four conditions for a social-decision procedure are shown to have little relevance to the understanding or evaluation of constitutions. The author concludes that the more fruitful perspective for discussing social-decision procedures is that of option-rationality rather than (as Arrow, Wolff, and others have supposed) that of agent-rationality.     

Learning in the Allais paradox

Whereas both the Allais paradox, the first empirical challenge of the classical rationality assumptions, and learning have been the focus of many experimental investigations, no experimental study exists today into learning in the pure context of the Allais paradox. This paper presents such a study. We find that choices converge to expected utility maximization if subjects are given the opportunity to learn by both thought and experience, but less so when they learn by thought only. To the extent that genuine preferences should be measured with proper learning and incentives, our study gives the first pure demonstration that irrationalities such as in the Allais paradox are less pronounced than often thought. Paul Anand and Stefan Trautmann made helpful comments.     

Survival through the Allais paradox

This paper investigates the allegation that behavior such as the Allais Paradox reduces the probability of survival. Examples are demonstrated where maximizing probability of survival in two choice situations imply a set of choices that add up to the Allais Paradox.     

The doctrinal paradox, the discursive dilemma, and logical aggregation theory

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager??s doctrinal paradox and List and Pettit??s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ??general logic?? built in this framework.     

Alternative libertarian claims and Sen's paradox

One of the ways of escaping from Sen's impossibility of a Paretian liberal is to weaken Sen's libertarian condition imposed on the collective choice rule. This paper compares three different versions of a revised libertarian claim: (1) Gibbard's theory of alienable rights (1974), (2) Gaertner's and Krüger's approach of self-supporting preferences (1981), and (3) a modification of Gibbard's theory which combines a weakened condition for alienating rights with the requirement of unconditional preferences. A new possibility theorem is obtained for version (3). It is shown that all three approaches are logically independent. Furthermore, it turns out that, under the original as well as the modified version of Gibbard's theory, the alienation of rights can be achieved through strategic misrepresentation of preferences by other members of society, whereas the concept of self-supporting preferences does not admit this kind of manipulation of rights. Approach (2) appears, therefore, to agree more closely with our intuitions concerning the nature of individual rights.     

The paradox of inter-country adoption: analysing Romania's experience as a sending country

This article explores the effects of inter-country adoption on the development of in-country services to protect children and support families in Romania. The country's child care legislation gives formal priority to domestic alternatives to institutional care – preventive services, family reunification, foster care and in-country adoption. Despite this, inter-country adoption continues to play a central role in Romania's child welfare system. The article analyses the multiple and complex factors at policy and practice levels that lie behind this situation. It is concluded that whilst inter-country adoption may be used to secure some resources for the development of in-country services, it paradoxically undermines the effectiveness of those services for the children who are left behind.     

Promise and paradox in socioeconomic status conceptions

The author examines holistic competence and its assessment as defined in the Council for Social Work Education (CSWE’s)-EPAS 2015. Draft 3 of CSWE’s EPAS 2015 requires the use of a holistic competency model by accredited BSW and MSW social work programs. The model is an efficient way to assess student competence and overall program outcomes. Yet, this model, based on human resource concepts, is largely unfamiliar in the United States and is discussed minimally in the U.S. social work literature. This article details the goals and purposes of the model with linkage to EPAS 2015 language. Examples of methods of holistic assessment are offered to begin further professional discussion in American social work education. The strengths and limitations of this model are also identified.     

Power and size: A new paradox

An analysis of several different indices of voting power reveals that the voting power of a member of a weighted voting body may increase, rather than decrease, when new members are added to the original body. Real instances of this phenomenon, called the paradox of new members, are shown to have occurred when new states were added to the U.S. Electoral College and new countries to the European Community Council of Ministers. Conditions for the existence of the paradox, and probabilities of its occurrence in small and moderate-size voting bodies, are given. Efficient algorithms for the calculation of the voting power indices, based on generating functions, are also outlined.