Does Learning Diminish Violations of Independence, Coalescing and Monotonicity?

Violations of expected utility theory are sometimes attributed to imprecise preferences interacting with a lack of learning opportunity in the experimental laboratory. This paper reports an experimental test of whether a learning opportunity which engenders accurate probability assessments, by enhancing understanding of the meaning of stated probability information, causes anomalous behaviour to diminish. The data show that whilst in some cases expected utility maximising behaviour increases with the learning opportunity, so too do systematic violations. Therefore, there should be no presumption that anomalous behaviour under risk is transient and that discovered preferences will be appropriately described by expected utility theory.     

Sincerity and manipulation under approval voting

Under approval voting, each voter can nominate as many candidates as she wishes and the election winners are those candidates that are nominated most often. A voter is said to have voted sincerely if she prefers all those candidates she nominated to all other candidates. As there can be a set of winning candidates rather than just a single winner, a voter’s incentives to vote sincerely will depend on what assumptions we are willing to make regarding the principles by which voters extend their preferences over individual candidates to preferences over sets of candidates. We formulate two such principles, replacement and deletion, and we show that, under approval voting, a voter who accepts those two principles and who knows how the other voters will vote will never have an incentive to vote insincerely. We then discuss the consequences of this result for a number of standard principles of preference extension in view of sincere voting under approval voting.     

Pareto improvements by Pareto strategic voting under majority voting with risk loving and risk avoiding voters — A note

Voters satisfy maximin or maximax in their choices between sets of alternatives and secure a Pareto improvement by all voting strategically under simple majority voting for particular sincere preferences. Thus the assumption that strategic voting is a bad thing is challenged and the idea that we should reject voting because of the possibility of misrepresentation dismissed.     

Beneficial safety decreases

We construct a model of rational choice under risk with biased risk judgement. On its basis, we argue that sometimes, a regulator aiming at maximising social welfare should affect the environment in such a way that it becomes ‘less safe’ in common perception. More specifically, we introduce a bias into each agent’s choice of optimal risk levels: consequently, in certain environments, agents choose a behaviour that realises higher risks than intended. Individuals incur a welfare loss through this bias. We show that by deteriorating the environment, the regulator can motivate individuals to choose behaviour that is less biased, and hence realises risk levels closer to what individuals intended. We formally investigate the conditions under which such a Beneficial Safety Decrease—i.e. a deteriorating intervention that has a positive welfare effect—exists. Finally, we discuss three applications of our model.     

Individual fairness in Harsanyi’s utilitarianism: operationalizing all-inclusive utility

Fairness can be incorporated into Harsanyi’s utilitarianism through all-inclusive utility. This retains the normative assumptions of expected utility and Pareto-efficiency, and relates fairness to individual preferences. It makes utilitarianism unfalsifiable, however, if agents’ all-inclusive utilities are not explicitly specified. This note proposes a two-stage model to make utilitarian welfare analysis falsifiable by specifying all-inclusive utilities explicitly through models of individual fairness preferences. The approach is applied to include fairness in widely discussed allocation examples.     

A theorem for Bayesian group decisions

This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but we do not assume, a priori, that the group as a whole accepts those assumptions. Instead, we impose a multiattribute utility independence condition on the preferences of the group with respect to the expected utilities of its actions as appraised by its members. The result is that the expected utility of an alternative for the group is a weighted average of the expected utilities of that alternative for its members. The weights must be determined collectively by the group. Pareto optimality is not assumed, though the result is consistent with Pareto optimality.     

The uncovered set in spatial voting games

In a majority rule voting game, the uncovered set is the set of alternatives each of which can defeat every other alternative in the space either directly or indirectly at one remove. Research has suggested that outcomes under most reasonable agenda processes (both sincere and sophisticated) will be confined to the uncovered set. Most research on the uncovered set has been done in the context of voting games with a finite number of alternatives and relatively little is known about the properties of the uncovered set in spatial voting games.We examine the geometry of the uncovered set in spatial voting games and the geometry of two important subsets of the uncovered set, the Banks set and the Schattschneider set. In particular, we find both general upper and lower limits on the size of the uncovered set, and we give the exact bounds of the uncovered set for situations with three voters. For situations with three voters, we show that the Banks set is identical to the uncovered set.     

A Method for Eliciting Utilities and its Application to Collective Choice

Designing a mechanism that provides a direct incentive for an individual to report her utility function over several alternatives is a difficult task. A framework for such mechanism design is the following: an individual (a decision maker) is faced with an optimization problem (e.g., maximization of expected utility), and a mechanism designer observes the decision maker’s action. The mechanism does reveal the individual’s utility truthfully if the mechanism designer, having observed the decision maker’s action, infers the decision maker’s utilities over several alternatives. This paper studies an example of such a mechanism and discusses its application to the problem of optimal social choice. Under certain simplifying assumptions about individuals’ utility functions and about how voters choose their voting strategies, this mechanism selects the alternative that maximizes Harsanyi’s social utility function and is Pareto-efficient.     

Sophisticated voting under the plurality procedure: A test of a new definition

The Niemi-Frank definition of sophisticated voting can now be evaluated on two grounds. First, we can compare our definition to Farquharson's. For the most part, the two definitions yield identical outcomes. Both pickCondorcet winners a very high proportion of the time and prevent the selection of Condorcet losers. The major differences are in the logic underlying the two definitions and in the rate of determinacy of outcomes. Here there is a tradeoff. The logic underlying the Farquharson model is especially persuasive, although it is our feeling that the Niemi-Frank definition comes closer to mirroring the way in which voters might actually analyze a plurality situation. In any case, the price paid by the Farquharson definition for its ironclad logic is a much higher rate of indeterminacy. In over half of the cases, the Farquharson logic fails to lead to any conclusion whatsoever. The Niemi-Frank definition yields many more determinate situations, with mostly Condorcet winners and with strategies that make good, if not completely unassailable sense. A second way of evaluating the Niemi-Frank definition is in comparison with sincere voting. A commonly-cited shortcoming of plurality voting is that often fails to choose a Condorcet winner. As we notedearlier, sophisticated plurality voting, unlike binary voting, is imperfect in this respect. Nonetheless, even taking account of the indeterminacy thatremains in the Niemi-Frank definition, sophisticated voting picked a Condorcet winner about 10 percent more frequently than did sincere voting as well as eliminating the possibility of a Condorcet loser being chosen. By this measure, the Niemi-Frank definition is not only acceptable but suggests that this form of strategic behavior actually leads tobetter outcomes. By proposing and now by testing a new definition of sophisticated voting under plurality rule, we have begun to make some headway on understanding strategic behavior and its effects in an outwardly simple yet deceptively complex voting system. We are, of course, far from finished. Most significantly, our definition applies to only three alternatives, and Farquharson's (even if one is willing to live with its high indeterminacy) becomes extraordinarily cumbersome with more than three alternatives? In any event, the results of this foray into sophisticated nonbinary voting suggests once again that strategic behavior, rather than making things worse, improves the chances that the outcome will be the one most favored by the majority criterion.     

The preservation of multivariate comparative statics in nonexpected utility theory

This article investigates the preservation of multivariate expected utility comparative statics for “smooth” nonexpected utility representations. Specifically, we answer the following question: if an expected utility comparative statics property depends only on preferences over sure prospects, then when will a nonexpected utility maximizer with identical sure preferences also satisfy that property? We demonstrate that the effects of increased risk aversion are preserved under the “Almost Degenerate Independence” axiom, but that those of distribution changes of exogenous risks are not preserved under stringent assumptions. Hence, nonexpected utility comparative statics may diverge from expected utility, even for “first-order” properties—those whose effect is determinable from restrictions on “local” utility functions.     

Consequentialist foundations for expected utility

Behaviour norms are considered for decision trees which allow both objective probabilities and uncertain states of the world with unknown probabilities. Terminal nodes have consequences in a given domain. Behaviour is required to be consistent in subtrees. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree. It implies that behaviour reveals a revealed preference ordering satisfying both the independence axiom and a novel form of sure-thing principle. Continuous consequentialist behaviour must be expected utility maximizing. Other plausible assumptions then imply additive utilities, subjective probabilities, and Bayes' rule.     

A note on decisions under uncertainty: the impact of the choice of the welfare measure

The paper addresses the question, how policy decisions under uncertainty depend on the underlying welfare concept. We study three different welfare measures: The first is directly based on the ex ante (expected) utility of a representative consumer whereas the second relies on an ex ante and the third on an ex post valuation of policy changes compared to the status quo. We show that decisions based on these measures coincide if and only if risk-neutral expected utility maximization is applied. Differences between the decisions are analyzed for both, risk-averse expected utility maximization and the MaxiMin criterion. For risk-averse decision makers, differences between the first and the second concept arise if the absolute risk-aversion of the decision maker is not constant in income. For risk-aversion and the MaxiMin criterion, the effort levels to provide a public good based on an optimization of ex post utility changes exceed those based on the first or second concept. Implications for environmental policy decisions based on the concepts of abatement costs and benefits from abatement are discussed.     

Morality and welfare

The economic theory of utility does not take into account moral behaviour, that is behaviour in which an individual faced with two courses of action may choose the one which is less profitable to him. It is shown in this paper that the economic approach can be broadened to take such behaviour into account. The individual is considered to maximize a higher welfare function whose arguments are (a) his utility and (b) higher goods or moral value. The latter are goals which he ought to achieve. The amount of higher goods achieved depends upon his moral preference. The ranking of different acts is complete - an assumption commonly made in economics with regard to bundles of goods. In an extension of the economic model of optimization over time, the individual is considered to maximize his higher welfare over his lifetime. This may require raising his moral preference.     

Approval voting and strategy analysis: A Venetian example

The author presents a historic reconstruction of the single-member constituency election system known as approval voting which was used to elect Venetian dogi for over 500 years. An interesting procedure theoretically, concurrent approval voting is the only sincere single-winner election system. Central issues concerning strategy choice under uncertainty are investigated using a contingency-dependent framework of individual behavior given prior probability distributions over decision relevant propositions. Extensions are then proposed for the use of approval procedures in modern elections and other collective decision-making situations. Finally the advantages of trichotomous preferences in decision and strategy analysis are argued.Masculine personal pronouns are used when discussing doge elections, otherwise feminine pronouns are used.     

Cost Perceptions and Voter Demand for Environmental Risk Regulation: The Double Effect of Hidden Costs

This paper reports the first detailed empirical examination of the effects of voter cost perceptions on demand for environmental risk regulations. Using a statewide random sample of Washington's electorate, I examine voting behavior for a proposed regulation of gasoline stations under varying cost and distributional assumptions. Results suggest normative concerns are as important in explaining support as are expected risk reduction benefits. These norms include making polluters pay, imposing larger burdens on polluters with higher ability to pay, and enforcing public property rights. In contrast, potential price increases as a result of regulation have negligible effects on voter support.     

Reconceptualising Social Exclusion: A Critical Response to the Neoliberal Welfare Reform Agenda and the Underclass Thesis

The application of free‐market principles to welfare reform in western industrialised nations is underpinned by contentious assumptions about human behaviour. In the postwar era, welfare policies largely considered disadvantage and exclusion as structural problems of the economy and society generally; disadvantaged individuals were considered ‘victims’ of their environment. More recently, conservative contributors have re‐emphasised disadvantage and exclusion as largely due to behavioural problems of the ‘undeserving poor’, manifest in what is believed to be an ‘underclass’. Critics of the current welfare reform agenda have voiced their concerns about the individualist assumptions that underpin it but their response to date is insufficient because they have generally neglected human agency and have failed to acknowledge individuals as capable actors. While there has been a revival of interest in human agency, greater recognition of agency in debates about welfare is required to mount a credible critique of the conservative assumptions about human behaviour in order to develop a more sensitive theory of the activities of the poor. One of the ways in which this may be achieved is by reconceptualising the concept of social exclusion and highlighting a ‘strong’ rather than a ‘weak’ version.     

Feddersen and Pesendorfer meet Ellsberg

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis (Theor Econo 11(3): 865–895, 2016) shows that when voters have ambiguous prior beliefs—a (closed, convex) set of priors—and follow maxmin expected utility (MEU), such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error (such as conviction in jury trials). In a classical model, Feddersen and Pesendorfer (Am Politi Sci Rev 92(1):23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis (Theor Econo 11(3): 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals.

     

Expected utility: An anniversary and a new era

During the past generation, expected utility theory has been widely accepted as the normative standard for decision making under risk and under uncertainty. However, it is now known that reasonable people often violate its assumptions, and a number of generalizations of the theory have been developed to accommodate some of the more common violations. This essay recalls the origins of expected utility in the early 1700s, notes its axiomatizations on the basis of preference comparisons in the mid-1900s, describes violations of those axioms uncovered since then, outlines new theories stimulated by the violations, and suggests where the field might be headed in the next few decades.     

Valuing Others’ Information under Imperfect Expectations

Sometimes we believe that others receive harmful information. However, Marschak’s value of information framework always assigns non-negative value under expected utility: it starts from the decision maker’s beliefs – and one can never anticipate information’s harmfulness for oneself. The impact of decision makers’ capabilities to process information and of their expectations remains hidden behind the individual and subjective perspective Marschak’s framework assumes. By introducing a second decision maker as a point of reference, this paper introduces a way for evaluating others’ information from a cross-individual, imperfect expectations perspective for agents maximising expected utility. We define the cross-value of information that can become negative – then the information is “harmful” from a cross-individual perspective – and we define (mutual) cost of limited information processing capabilities and imperfect expectations as an opportunity cost from this same point of reference. The simple relationship between these two expected utility-based concepts and Marschak’s framework is shown, and we discuss evaluating short-term reactions of stock market prices to new information as an important domain of valuing others’ information.